Merge pull request #60 from kris7t/rules

Refinement rule support

56 files changed, 2531 insertions, 1262 deletions

diff --git a/subprojects/docs/package.json b/subprojects/docs/package.json
index 9ecd6820..0771c08d 100644
--- a/subprojects/docs/package.json
+++ b/subprojects/docs/package.json
@@ -30,19 +30,19 @@
   },
   "homepage": "https://refinery.tools",
   "dependencies": {
-    "@docusaurus/core": "^3.3.2",
-    "@docusaurus/plugin-content-docs": "^3.3.2",
-    "@docusaurus/plugin-content-pages": "^3.3.2",
-    "@docusaurus/plugin-sitemap": "^3.3.2",
-    "@docusaurus/theme-classic": "^3.3.2",
-    "@docusaurus/theme-common": "^3.3.2",
-    "@docusaurus/theme-search-algolia": "^3.3.2",
+    "@docusaurus/core": "^3.4.0",
+    "@docusaurus/plugin-content-docs": "^3.4.0",
+    "@docusaurus/plugin-content-pages": "^3.4.0",
+    "@docusaurus/plugin-sitemap": "^3.4.0",
+    "@docusaurus/theme-classic": "^3.4.0",
+    "@docusaurus/theme-common": "^3.4.0",
+    "@docusaurus/theme-search-algolia": "^3.4.0",
     "@fontsource-variable/jetbrains-mono": "^5.0.21",
     "@fontsource-variable/open-sans": "^5.0.29",
     "@fontsource/open-sans": "^5.0.28",
     "@material-icons/svg": "^1.0.33",
     "@mdx-js/react": "^3.0.1",
-    "@swc/core": "^1.5.7",
+    "@swc/core": "^1.6.1",
     "clsx": "^2.1.1",
     "mdast-util-mdx": "^3.0.0",
     "prism-react-renderer": "^2.3.1",
@@ -55,15 +55,15 @@
     "terser-webpack-plugin": "^5.3.10",
     "unified": "^11.0.4",
     "unist-util-visit": "^5.0.0",
-    "webpack": "^5.91.0"
+    "webpack": "^5.92.0"
   },
   "devDependencies": {
-    "@docusaurus/mdx-loader": "^3.3.2",
-    "@docusaurus/module-type-aliases": "^3.3.2",
-    "@docusaurus/types": "^3.3.2",
+    "@docusaurus/mdx-loader": "^3.4.0",
+    "@docusaurus/module-type-aliases": "^3.4.0",
+    "@docusaurus/types": "^3.4.0",
     "@types/babel__core": "^7.20.5",
     "@types/mdast": "^4.0.4",
-    "@types/node": "^20.12.12",
+    "@types/node": "^20.14.2",
     "@types/react": "^18.3.3",
     "@types/react-dom": "^18.3.0",
     "@types/unist": "^3.0.2"
diff --git a/subprojects/frontend/package.json b/subprojects/frontend/package.json
index 859a4b5c..ae1103d6 100644
--- a/subprojects/frontend/package.json
+++ b/subprojects/frontend/package.json
@@ -28,13 +28,13 @@
   },
   "homepage": "https://refinery.tools",
   "dependencies": {
-    "@codemirror/autocomplete": "^6.16.0",
-    "@codemirror/commands": "^6.5.0",
-    "@codemirror/language": "^6.10.1",
+    "@codemirror/autocomplete": "^6.16.2",
+    "@codemirror/commands": "^6.6.0",
+    "@codemirror/language": "^6.10.2",
     "@codemirror/lint": "^6.8.0",
     "@codemirror/search": "^6.5.6",
     "@codemirror/state": "^6.4.1",
-    "@codemirror/view": "^6.26.3",
+    "@codemirror/view": "^6.28.1",
     "@emotion/cache": "^11.11.0",
     "@emotion/react": "^11.11.4",
     "@emotion/serialize": "^1.1.4",
@@ -46,12 +46,12 @@
     "@hpcc-js/wasm": "^2.16.2",
     "@lezer/common": "^1.2.1",
     "@lezer/highlight": "^1.2.0",
-    "@lezer/lr": "^1.4.0",
+    "@lezer/lr": "^1.4.1",
     "@material-icons/svg": "^1.0.33",
-    "@mui/icons-material": "^5.15.18",
-    "@mui/material": "^5.15.18",
-    "@mui/system": "^5.15.15",
-    "@mui/x-data-grid": "^7.5.1",
+    "@mui/icons-material": "^5.15.20",
+    "@mui/material": "^5.15.20",
+    "@mui/system": "^5.15.20",
+    "@mui/x-data-grid": "^7.7.0",
     "ansi-styles": "^6.2.1",
     "csstype": "^3.1.3",
     "d3": "^7.9.0",
@@ -64,15 +64,15 @@
     "lodash-es": "^4.17.21",
     "loglevel": "^1.9.1",
     "loglevel-plugin-prefix": "^0.8.4",
-    "mobx": "^6.12.3",
+    "mobx": "^6.12.4",
     "mobx-react-lite": "^4.0.7",
     "ms": "^2.1.3",
     "nanoid": "^5.0.7",
     "notistack": "^3.0.1",
     "react": "^18.3.1",
     "react-dom": "^18.3.1",
-    "react-resize-detector": "^10.0.1",
-    "svg2pdf.js": "^2.2.3",
+    "react-resize-detector": "^11.0.1",
+    "svg2pdf.js": "^2.2.4",
     "xstate": "^4.38.3",
     "zod": "^3.23.8"
   },
@@ -88,7 +88,7 @@
     "@types/lodash-es": "^4.17.12",
     "@types/micromatch": "^4.0.7",
     "@types/ms": "^0.7.34",
-    "@types/node": "^20.12.12",
+    "@types/node": "^20.14.2",
     "@types/pnpapi": "^0.0.5",
     "@types/react": "^18.3.3",
     "@types/react-dom": "^18.3.0",
@@ -98,7 +98,7 @@
     "micromatch": "^4.0.7",
     "pnpapi": "^0.0.0",
     "typescript": "5.4.5",
-    "vite": "^5.2.11",
+    "vite": "^5.3.1",
     "vite-plugin-pwa": "^0.20.0",
     "workbox-window": "^7.1.0"
   }
diff --git a/subprojects/frontend/src/language/folding.ts b/subprojects/frontend/src/language/folding.ts
index b4d4ca22..0afabfa0 100644
--- a/subprojects/frontend/src/language/folding.ts
+++ b/subprojects/frontend/src/language/folding.ts
@@ -109,7 +109,7 @@ function foldWithSibling(node: SyntaxNode): FoldRange | null {
   return null;
 }
 
-function foldWholeNode(node: SyntaxNode): FoldRange {
+export function foldWholeNode(node: SyntaxNode): FoldRange {
   return {
     from: node.from,
     to: node.to,
diff --git a/subprojects/frontend/src/language/problem.grammar b/subprojects/frontend/src/language/problem.grammar
index 7949f90c..a172835d 100644
--- a/subprojects/frontend/src/language/problem.grammar
+++ b/subprojects/frontend/src/language/problem.grammar
@@ -63,11 +63,11 @@ statement {
   //   kw<"fn"> RelationName RelationName ParameterList<Parameter>?
   //   FunctionBody { ("=" sep<OrOp, Case>)? "." }
   // } |
-  //RuleDefinition {
-  //  kw<"rule">
-  //  RuleName ParameterList<Parameter>?
-  //  RuleBody { ":" sep<OrOp, Conjunction> "==>" sep<OrOp, Consequent> "." }
-  //} |
+  RuleDefinition {
+    (ckw<"decision"> | ckw<"propagation">)? kw<"rule">
+    RuleName ParameterList<Parameter>?
+    RuleBody { ("<->" sep<OrOp, Conjunction>)? ("==>" sep<OrOp, Consequent>)? "." }
+  } |
   AtomDeclaration {
     kw<"declare">? ckw<"atom"> sep<",", AtomNodeName> "."
   } |
@@ -96,7 +96,12 @@ FeatureDeclaration {
   ";"?
 }
 
-Parameter { RelationName? VariableName }
+Parameter {
+  kw<"candidate">? (kw<"may"> | kw<"must">)?
+  RelationName?
+  (AndBinding | StarBinding)?
+  VariableName
+}
 
 // Use @dynamicPrecedence to prevent a(b) from being parsed as Expr { a } Expr { b }
 // instead of Atom { a(b) }
@@ -125,7 +130,12 @@ BinaryExpr {
 }
 
 UnaryExpr {
-  !prefix ("+" | "-" | "!" | kw<"count">) Expr
+  !prefix
+  (
+    "+" | "-" | "!" | kw<"count"> |
+    kw<"candidate"> | kw<"may"> | kw<"must">
+  )
+  Expr
 }
 
 CastExpr { !cast Expr kw<"as"> DatatypeName }
@@ -136,20 +146,22 @@ Aggregation {
 
 Atom { RelationName "+"? ParameterList<Expr> }
 
-//Consequent { ("," | Action)+ }
+Consequent { ("," | Action)+ }
 
-//Action {
-//   ckw<"new"> VariableName ("<:" VariableName)? |
-//   kw<"delete"> VariableName |
-//   Literal
-//}
+Action {
+  (NotOp | UnknownOp)? RelationName
+  ParameterList<AssertionActionArgument>
+  (":" Expr)?
+}
 
 AssertionArgument { NodeName | StarArgument }
 
+AssertionActionArgument { VariableName | StarArgument }
+
 Constant { Real | String | StarMult | LogicValue }
 
 ReferenceKind {
-  kw<"refers"> | ckw<"contains"> | kw<"container">
+  kw<"refers"> | ckw<"contains"> | kw<"container"> | kw<"partial">
 }
 
 LogicValue {
@@ -170,7 +182,7 @@ RelationName { QualifiedName ~name }
 
 DatatypeName { QualifiedName }
 
-//RuleName { QualifiedName }
+RuleName { QualifiedName }
 
 AtomNodeName { QualifiedName }
 
@@ -247,5 +259,9 @@ sep1<separator, content> { content (separator content)* }
 
   StarArgument { "*" }
 
+  StarBinding { "*" }
+
+  AndBinding { "&" }
+
   "{" "}" "(" ")" "[" "]" "." ".." "," ":" "->" "<->" "+" "-" "**" "=" "+="
 }
diff --git a/subprojects/frontend/src/language/problemLanguageSupport.ts b/subprojects/frontend/src/language/problemLanguageSupport.ts
index dd5d6347..5ca162d9 100644
--- a/subprojects/frontend/src/language/problemLanguageSupport.ts
+++ b/subprojects/frontend/src/language/problemLanguageSupport.ts
@@ -14,7 +14,12 @@ import {
 } from '@codemirror/language';
 import { styleTags, tags as t } from '@lezer/highlight';
 
-import { foldBlockComment, foldConjunction, foldDeclaration } from './folding';
+import {
+  foldBlockComment,
+  foldConjunction,
+  foldDeclaration,
+  foldWholeNode,
+} from './folding';
 import {
   indentBlockComment,
   indentDeclaration,
@@ -30,11 +35,13 @@ const parserWithMetadata = parser.configure({
       'module problem class enum pred fn scope': t.definitionKeyword,
       'import as declare atom multi': t.definitionKeyword,
       'extern datatype aggregator': t.definitionKeyword,
-      'abstract extends refers contains container opposite': t.modifier,
+      rule: t.definitionKeyword,
+      'abstract extends refers contains container partial opposite': t.modifier,
       default: t.modifier,
+      'propagation decision': t.modifier,
       'true false unknown error': t.keyword,
+      'candidate may must': t.operatorKeyword,
       'count in is': t.operatorKeyword,
-      // 'new delete': t.keyword,
       NotOp: t.operator,
       UnknownOp: t.operator,
       OrOp: t.separator,
@@ -45,7 +52,7 @@ const parserWithMetadata = parser.configure({
       'RelationName/QualifiedName': t.typeName,
       'DatatypeName/QualifiedName': t.keyword,
       'AggregatorName/QualifiedName': t.operatorKeyword,
-      // 'RuleName/QualifiedName': t.typeName,
+      'RuleName/QualifiedName': t.typeName,
       'AtomNodeName/QualifiedName': t.atom,
       'VariableName/QualifiedName': t.variableName,
       'ModuleName/QualifiedName': t.typeName,
@@ -62,7 +69,7 @@ const parserWithMetadata = parser.configure({
       ScopeDeclaration: indentDeclaration,
       PredicateBody: indentPredicateOrRule,
       // FunctionBody: indentPredicateOrRule,
-      // RuleBody: indentPredicateOrRule,
+      RuleBody: indentPredicateOrRule,
       BlockComment: indentBlockComment,
     }),
     foldNodeProp.add({
@@ -71,9 +78,9 @@ const parserWithMetadata = parser.configure({
       ParameterList: foldInside,
       PredicateBody: foldInside,
       // FunctionBody: foldInside,
-      // RuleBody: foldInside,
+      RuleBody: foldInside,
       Conjunction: foldConjunction,
-      // Consequent: foldWholeNode,
+      Consequent: foldWholeNode,
       AtomDeclaration: foldDeclaration,
       NodeDeclaration: foldDeclaration,
       ScopeDeclaration: foldDeclaration,
@@ -92,7 +99,7 @@ const problemLanguage = LRLanguage.define({
       },
       line: '%',
     },
-    indentOnInput: /^\s*(?:\{|\}|\(|\)|->|;|\.)$/,
+    indentOnInput: /^\s*(?:\{|\}|\(|\)|->|==>|;|\.)$/,
   },
 });
 
diff --git a/subprojects/generator-cli/src/main/java/tools/refinery/generator/cli/commands/GenerateCommand.java b/subprojects/generator-cli/src/main/java/tools/refinery/generator/cli/commands/GenerateCommand.java
index b1c28df0..0fb97316 100644
--- a/subprojects/generator-cli/src/main/java/tools/refinery/generator/cli/commands/GenerateCommand.java
+++ b/subprojects/generator-cli/src/main/java/tools/refinery/generator/cli/commands/GenerateCommand.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -17,9 +17,12 @@ import java.io.IOException;
 import java.util.ArrayList;
 import java.util.List;
 import java.util.Map;
+import java.util.regex.Pattern;
 
 @Parameters(commandDescription = "Generate a model from a partial model")
 public class GenerateCommand {
+        private static final Pattern EXTENSION_REGEX = Pattern.compile("(.+)\\.([^./\\\\]+)");
+
         @Inject
         private ProblemLoader loader;
 
@@ -31,6 +34,7 @@ public class GenerateCommand {
         private List<String> scopes = new ArrayList<>();
         private List<String> overrideScopes = new ArrayList<>();
         private long randomSeed = 1;
+        private int count = 1;
 
         @Parameter(description = "input path", required = true)
         public void setInputPath(String inputPath) {
@@ -57,21 +61,47 @@ public class GenerateCommand {
                 this.randomSeed = randomSeed;
         }
 
+        @Parameter(names = {"-solution-number", "-n"}, description = "Maximum number of solutions")
+        public void setCount(int count) {
+                if (count <= 0) {
+                        throw new IllegalArgumentException("Count must be positive");
+                }
+                this.count = count;
+        }
+
         public void run() throws IOException {
+                if (count > 1 && isStandardStream(outputPath)) {
+                        throw new IllegalArgumentException("Must provide output path if count is larger than 1");
+                }
                 loader.extraPath(System.getProperty("user.dir"));
                 var problem = isStandardStream(inputPath) ? loader.loadStream(System.in) : loader.loadFile(inputPath);
                 problem = loader.loadScopeConstraints(problem, scopes, overrideScopes);
+                generatorFactory.partialInterpretationBasedNeighbourhoods(count >= 2);
                 var generator = generatorFactory.createGenerator(problem);
                 generator.setRandomSeed(randomSeed);
+                generator.setMaxNumberOfSolutions(count);
                 generator.generate();
-                var solution = generator.serializeSolution();
-                var solutionResource = solution.eResource();
                 var saveOptions = Map.of();
-                if (isStandardStream(outputPath)) {
-                        printSolution(solutionResource, saveOptions);
+                if (count == 1) {
+                        var solution = generator.serializeSolution();
+                        var solutionResource = solution.eResource();
+                        if (isStandardStream(outputPath)) {
+                                printSolution(solutionResource, saveOptions);
+                        } else {
+                                try (var outputStream = new FileOutputStream(outputPath)) {
+                                        solutionResource.save(outputStream, saveOptions);
+                                }
+                        }
                 } else {
-                        try (var outputStream = new FileOutputStream(outputPath)) {
-                                solutionResource.save(outputStream, saveOptions);
+                        int solutionCount = generator.getSolutionCount();
+                        for (int i = 0; i < solutionCount; i++) {
+                                generator.loadSolution(i);
+                                var solution = generator.serializeSolution();
+                                var solutionResource = solution.eResource();
+                                var pathWithIndex = getFileNameWithIndex(outputPath, i + 1);
+                                try (var outputStream = new FileOutputStream(pathWithIndex)) {
+                                        solutionResource.save(outputStream, saveOptions);
+                                }
                         }
                 }
         }
@@ -85,4 +115,12 @@ public class GenerateCommand {
         private void printSolution(Resource solutionResource, Map<?, ?> saveOptions) throws IOException {
                 solutionResource.save(System.out, saveOptions);
         }
+
+        private String getFileNameWithIndex(String simpleName, int index) {
+                var match = EXTENSION_REGEX.matcher(simpleName);
+                if (match.matches()) {
+                        return "%s_%03d.%s".formatted(match.group(1), index, match.group(2));
+                }
+                return "%s_%03d".formatted(simpleName, index);
+        }
 }
diff --git a/subprojects/generator/src/main/java/tools/refinery/generator/ModelGenerator.java b/subprojects/generator/src/main/java/tools/refinery/generator/ModelGenerator.java
index 36190b76..8dff5622 100644
--- a/subprojects/generator/src/main/java/tools/refinery/generator/ModelGenerator.java
+++ b/subprojects/generator/src/main/java/tools/refinery/generator/ModelGenerator.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -11,6 +11,7 @@ import tools.refinery.language.semantics.ProblemTrace;
 import tools.refinery.language.semantics.SolutionSerializer;
 import tools.refinery.logic.AbstractValue;
 import tools.refinery.store.dse.strategy.BestFirstStoreManager;
+import tools.refinery.store.dse.transition.statespace.SolutionStore;
 import tools.refinery.store.map.Version;
 import tools.refinery.store.model.ModelStore;
 import tools.refinery.store.reasoning.interpretation.PartialInterpretation;
@@ -22,7 +23,8 @@ public class ModelGenerator extends ModelFacade {
         private final Version initialVersion;
         private final Provider<SolutionSerializer> solutionSerializerProvider;
         private long randomSeed = 1;
-        private boolean lastGenerationSuccessful;
+        private int maxNumberOfSolutions = 1;
+        private SolutionStore solutionStore;
 
         ModelGenerator(ProblemTrace problemTrace, ModelStore store, ModelSeed modelSeed,
                                    Provider<SolutionSerializer> solutionSerializerProvider) {
@@ -37,26 +39,51 @@ public class ModelGenerator extends ModelFacade {
 
         public void setRandomSeed(long randomSeed) {
                 this.randomSeed = randomSeed;
-                this.lastGenerationSuccessful = false;
+                this.solutionStore = null;
         }
 
+        public int getMaxNumberOfSolutions() {
+                return maxNumberOfSolutions;
+        }
+
+        public void setMaxNumberOfSolutions(int maxNumberOfSolutions) {
+                this.maxNumberOfSolutions = maxNumberOfSolutions;
+                this.solutionStore = null;
+        }
+
+        public int getSolutionCount() {
+                if (!isLastGenerationSuccessful()) {
+                        return 0;
+                }
+                return this.solutionStore.getSolutions().size();
+        }
+
+        public void loadSolution(int index) {
+                if (index >= getSolutionCount()) {
+                        throw new IndexOutOfBoundsException("No such solution");
+                }
+                getModel().restore(solutionStore.getSolutions().get(index).version());
+        }
+
+        // It makes more sense to check for success than for failure.
+        @SuppressWarnings("BooleanMethodIsAlwaysInverted")
         public boolean isLastGenerationSuccessful() {
-                return lastGenerationSuccessful;
+                return solutionStore != null;
         }
 
         // This method only makes sense if it returns {@code true} on success.
         @SuppressWarnings("BooleanMethodIsAlwaysInverted")
         public boolean tryGenerate() {
-                lastGenerationSuccessful = false;
+                solutionStore = null;
                 randomSeed++;
-                var bestFirst = new BestFirstStoreManager(getModelStore(), 1);
+                var bestFirst = new BestFirstStoreManager(getModelStore(), maxNumberOfSolutions);
                 bestFirst.startExploration(initialVersion, randomSeed);
                 var solutions = bestFirst.getSolutionStore().getSolutions();
                 if (solutions.isEmpty()) {
                         return false;
                 }
                 getModel().restore(solutions.getFirst().version());
-                lastGenerationSuccessful = true;
+                solutionStore = bestFirst.getSolutionStore();
                 return true;
         }
 
@@ -80,7 +107,7 @@ public class ModelGenerator extends ModelFacade {
         }
 
         private void checkSuccessfulGeneration() {
-                if (!lastGenerationSuccessful) {
+                if (!isLastGenerationSuccessful()) {
                         throw new IllegalStateException("No generated model is available");
                 }
         }
diff --git a/subprojects/generator/src/main/java/tools/refinery/generator/ModelGeneratorFactory.java b/subprojects/generator/src/main/java/tools/refinery/generator/ModelGeneratorFactory.java
index 587601f2..ec273cf4 100644
--- a/subprojects/generator/src/main/java/tools/refinery/generator/ModelGeneratorFactory.java
+++ b/subprojects/generator/src/main/java/tools/refinery/generator/ModelGeneratorFactory.java
@@ -15,8 +15,11 @@ import tools.refinery.store.dse.transition.DesignSpaceExplorationAdapter;
 import tools.refinery.store.model.ModelStore;
 import tools.refinery.store.query.interpreter.QueryInterpreterAdapter;
 import tools.refinery.store.reasoning.ReasoningAdapter;
+import tools.refinery.store.reasoning.interpretation.PartialNeighbourhoodCalculator;
 import tools.refinery.store.reasoning.literal.Concreteness;
+import tools.refinery.store.statecoding.StateCodeCalculatorFactory;
 import tools.refinery.store.statecoding.StateCoderAdapter;
+import tools.refinery.store.statecoding.neighbourhood.NeighbourhoodCalculator;
 import tools.refinery.store.util.CancellationToken;
 
 import java.util.Collection;
@@ -33,6 +36,8 @@ public final class ModelGeneratorFactory {
 
         private boolean debugPartialInterpretations;
 
+        private boolean partialInterpretationBasedNeighbourhoods;
+
         public ModelGeneratorFactory cancellationToken(CancellationToken cancellationToken) {
                 this.cancellationToken = cancellationToken;
                 return this;
@@ -43,6 +48,10 @@ public final class ModelGeneratorFactory {
                 return this;
         }
 
+        public void partialInterpretationBasedNeighbourhoods(boolean partialInterpretationBasedNeighbourhoods) {
+                this.partialInterpretationBasedNeighbourhoods = partialInterpretationBasedNeighbourhoods;
+        }
+
         public ModelGenerator createGenerator(Problem problem) {
                 var initializer = initializerProvider.get();
                 initializer.readProblem(problem);
@@ -51,7 +60,8 @@ public final class ModelGeneratorFactory {
                                 .cancellationToken(cancellationToken)
                                 .with(QueryInterpreterAdapter.builder())
                                 .with(PropagationAdapter.builder())
-                                .with(StateCoderAdapter.builder())
+                                .with(StateCoderAdapter.builder()
+                                                .stateCodeCalculatorFactory(getStateCoderCalculatorFactory()))
                                 .with(DesignSpaceExplorationAdapter.builder())
                                 .with(ReasoningAdapter.builder()
                                                 .requiredInterpretations(getRequiredInterpretations()));
@@ -62,7 +72,13 @@ public final class ModelGeneratorFactory {
         }
 
         private Collection<Concreteness> getRequiredInterpretations() {
-                return debugPartialInterpretations ? Set.of(Concreteness.PARTIAL, Concreteness.CANDIDATE) :
+                return debugPartialInterpretations || partialInterpretationBasedNeighbourhoods ?
+                                Set.of(Concreteness.PARTIAL, Concreteness.CANDIDATE) :
                                 Set.of(Concreteness.CANDIDATE);
         }
+
+        private StateCodeCalculatorFactory getStateCoderCalculatorFactory() {
+                return partialInterpretationBasedNeighbourhoods ? PartialNeighbourhoodCalculator.FACTORY :
+                                NeighbourhoodCalculator::new;
+        }
 }
diff --git a/subprojects/language-ide/src/main/java/tools/refinery/language/ide/syntaxcoloring/ProblemSemanticHighlightingCalculator.java b/subprojects/language-ide/src/main/java/tools/refinery/language/ide/syntaxcoloring/ProblemSemanticHighlightingCalculator.java
index 06f0e758..58d6748a 100644
--- a/subprojects/language-ide/src/main/java/tools/refinery/language/ide/syntaxcoloring/ProblemSemanticHighlightingCalculator.java
+++ b/subprojects/language-ide/src/main/java/tools/refinery/language/ide/syntaxcoloring/ProblemSemanticHighlightingCalculator.java
@@ -125,7 +125,7 @@ public class ProblemSemanticHighlightingCalculator extends DefaultSemanticHighli
                         classesBuilder.add(ERROR_CLASS);
                 }
                 if (eObject instanceof Node node) {
-                        highlightNode(node, reference, classesBuilder);
+                        highlightNode(node, classesBuilder);
                 }
                 if (eObject instanceof Relation relation) {
                         var typeHash = typeHashProvider.getTypeHash(relation);
@@ -137,10 +137,8 @@ public class ProblemSemanticHighlightingCalculator extends DefaultSemanticHighli
                 return classes.toArray(new String[0]);
         }
 
-        private static void highlightNode(Node node, EReference reference, ImmutableList.Builder<String> classesBuilder) {
-                if (reference == ProblemPackage.Literals.VARIABLE_OR_NODE_EXPR__VARIABLE_OR_NODE) {
-                        classesBuilder.add(NODE_CLASS);
-                }
+        private static void highlightNode(Node node, ImmutableList.Builder<String> classesBuilder) {
+                classesBuilder.add(NODE_CLASS);
                 if (ProblemUtil.isAtomNode(node)) {
                         classesBuilder.add(ATOM_NODE_CLASS);
                 }
diff --git a/subprojects/language-model/problem.aird b/subprojects/language-model/problem.aird
index f8a50a76..74c658d4 100644
--- a/subprojects/language-model/problem.aird
+++ b/subprojects/language-model/problem.aird
@@ -7,19 +7,19 @@
     <semanticResources>build/resources/main/model/problem.genmodel</semanticResources>
     <ownedViews xmi:type="viewpoint:DView" uid="_CsAAYKA4EeuqkpDnuik1sg">
       <viewpoint xmi:type="description:Viewpoint" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']"/>
-      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_CsYa4KA4EeuqkpDnuik1sg" name="declarations" repPath="#_CsUwgKA4EeuqkpDnuik1sg" changeId="1709659837733">
+      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_CsYa4KA4EeuqkpDnuik1sg" name="declarations" repPath="#_CsUwgKA4EeuqkpDnuik1sg" changeId="1717085395802">
         <description xmi:type="description_1:DiagramDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']"/>
         <target xmi:type="ecore:EPackage" href="src/main/resources/model/problem.ecore#/"/>
       </ownedRepresentationDescriptors>
-      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_z1bOYF3lEe2LuOZzJ_LhLg" name="expressions" repPath="#_z1YyIF3lEe2LuOZzJ_LhLg" changeId="1709659698980">
+      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_z1bOYF3lEe2LuOZzJ_LhLg" name="expressions" repPath="#_z1YyIF3lEe2LuOZzJ_LhLg" changeId="1715884068732">
         <description xmi:type="description_1:DiagramDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']"/>
         <target xmi:type="ecore:EPackage" href="src/main/resources/model/problem.ecore#/"/>
       </ownedRepresentationDescriptors>
-      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_xj9yMF4eEe2rXNsIDUvqhw" name="assertions" repPath="#_xj6H0F4eEe2rXNsIDUvqhw" changeId="1706657349781">
+      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_xj9yMF4eEe2rXNsIDUvqhw" name="assertions" repPath="#_xj6H0F4eEe2rXNsIDUvqhw" changeId="1715963376752">
         <description xmi:type="description_1:DiagramDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']"/>
         <target xmi:type="ecore:EPackage" href="src/main/resources/model/problem.ecore#/"/>
       </ownedRepresentationDescriptors>
-      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_sCFokF4fEe2rXNsIDUvqhw" name="actions" repPath="#_sCFBgF4fEe2rXNsIDUvqhw" changeId="1706657349781">
+      <ownedRepresentationDescriptors xmi:type="viewpoint:DRepresentationDescriptor" uid="_sCFokF4fEe2rXNsIDUvqhw" name="actions" repPath="#_sCFBgF4fEe2rXNsIDUvqhw" changeId="1715963438471">
         <description xmi:type="description_1:DiagramDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']"/>
         <target xmi:type="ecore:EPackage" href="src/main/resources/model/problem.ecore#/"/>
       </ownedRepresentationDescriptors>
@@ -100,11 +100,23 @@
         <children xmi:type="notation:Node" xmi:id="_QKLK0KA6EeuqkpDnuik1sg" type="2003" element="_QKD2EKA6EeuqkpDnuik1sg">
           <children xmi:type="notation:Node" xmi:id="_QKLK06A6EeuqkpDnuik1sg" type="5007"/>
           <children xmi:type="notation:Node" xmi:id="_QKLK1KA6EeuqkpDnuik1sg" type="7004">
+            <children xmi:type="notation:Node" xmi:id="_JR-dPBOyEe-4k7CzzL6IsA" type="3010" element="_JRfVABOyEe-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_JR-dPROyEe-4k7CzzL6IsA" fontColor="2697711" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_JR-dPhOyEe-4k7CzzL6IsA"/>
+            </children>
+            <children xmi:type="notation:Node" xmi:id="_LJy6eROyEe-4k7CzzL6IsA" type="3010" element="_LJG98BOyEe-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_LJy6ehOyEe-4k7CzzL6IsA" fontColor="2697711" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_LJy6exOyEe-4k7CzzL6IsA"/>
+            </children>
+            <children xmi:type="notation:Node" xmi:id="_he4bMBO0Ee-4k7CzzL6IsA" type="3010" element="_heTzcBO0Ee-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_he4bMRO0Ee-4k7CzzL6IsA" fontColor="2697711" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_he4bMhO0Ee-4k7CzzL6IsA"/>
+            </children>
             <styles xmi:type="notation:SortingStyle" xmi:id="_QKLK1aA6EeuqkpDnuik1sg"/>
             <styles xmi:type="notation:FilteringStyle" xmi:id="_QKLK1qA6EeuqkpDnuik1sg"/>
           </children>
           <styles xmi:type="notation:ShapeStyle" xmi:id="_QKLK0aA6EeuqkpDnuik1sg" fontName="Noto Sans" fontHeight="8"/>
-          <layoutConstraint xmi:type="notation:Bounds" xmi:id="_QKLK0qA6EeuqkpDnuik1sg" x="1687" y="530" width="120" height="100"/>
+          <layoutConstraint xmi:type="notation:Bounds" xmi:id="_QKLK0qA6EeuqkpDnuik1sg" x="1656" y="516" width="174" height="114"/>
         </children>
         <children xmi:type="notation:Node" xmi:id="_jP6FkKA6EeuqkpDnuik1sg" type="2003" element="_jPpm4KA6EeuqkpDnuik1sg">
           <children xmi:type="notation:Node" xmi:id="_jP6soKA6EeuqkpDnuik1sg" type="5007"/>
@@ -246,6 +258,10 @@
         <children xmi:type="notation:Node" xmi:id="_N0FQ4CrZEeyyC-O0_LlY9w" type="2003" element="_NzpMACrZEeyyC-O0_LlY9w">
           <children xmi:type="notation:Node" xmi:id="_N0F38CrZEeyyC-O0_LlY9w" type="5007"/>
           <children xmi:type="notation:Node" xmi:id="_N0F38SrZEeyyC-O0_LlY9w" type="7004">
+            <children xmi:type="notation:Node" xmi:id="_-wphkBOzEe-4k7CzzL6IsA" type="3010" element="_-wOq0BOzEe-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_-wphkROzEe-4k7CzzL6IsA" fontColor="2697711" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_-wphkhOzEe-4k7CzzL6IsA"/>
+            </children>
             <styles xmi:type="notation:SortingStyle" xmi:id="_N0F38irZEeyyC-O0_LlY9w"/>
             <styles xmi:type="notation:FilteringStyle" xmi:id="_N0F38yrZEeyyC-O0_LlY9w"/>
           </children>
@@ -289,11 +305,15 @@
               <styles xmi:type="notation:FontStyle" xmi:id="_9ZwJoc9jEe6T2u19X9cqmQ" fontName="Noto Sans" fontHeight="8"/>
               <layoutConstraint xmi:type="notation:Location" xmi:id="_9ZwJos9jEe6T2u19X9cqmQ"/>
             </children>
+            <children xmi:type="notation:Node" xmi:id="_Cl4ksB6fEe-D29eT4GV5Hg" type="3010" element="_Ck5GMB6fEe-D29eT4GV5Hg">
+              <styles xmi:type="notation:FontStyle" xmi:id="_Cl4ksR6fEe-D29eT4GV5Hg" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_Cl4ksh6fEe-D29eT4GV5Hg"/>
+            </children>
             <styles xmi:type="notation:SortingStyle" xmi:id="_xp2JgjNlEe2fD4dIhR_vzA"/>
             <styles xmi:type="notation:FilteringStyle" xmi:id="_xp2JgzNlEe2fD4dIhR_vzA"/>
           </children>
           <styles xmi:type="notation:ShapeStyle" xmi:id="_xp1icTNlEe2fD4dIhR_vzA" fontName="Noto Sans" fontHeight="8"/>
-          <layoutConstraint xmi:type="notation:Bounds" xmi:id="_xp1icjNlEe2fD4dIhR_vzA" x="574" y="1280" width="120" height="100"/>
+          <layoutConstraint xmi:type="notation:Bounds" xmi:id="_xp1icjNlEe2fD4dIhR_vzA" x="574" y="1280" width="120" height="115"/>
         </children>
         <children xmi:type="notation:Node" xmi:id="_782skF9mEe2rXNsIDUvqhw" type="2003" element="_78pRMF9mEe2rXNsIDUvqhw">
           <children xmi:type="notation:Node" xmi:id="_783ToF9mEe2rXNsIDUvqhw" type="5007"/>
@@ -436,6 +456,48 @@
           <styles xmi:type="notation:ShapeStyle" xmi:id="_jlSckdsVEe6c9ehqpe3s7A" fontName="Noto Sans" fontHeight="8"/>
           <layoutConstraint xmi:type="notation:Bounds" xmi:id="_jlScktsVEe6c9ehqpe3s7A" x="1128" y="716" width="147" height="100"/>
         </children>
+        <children xmi:type="notation:Node" xmi:id="_3c-frBOzEe-4k7CzzL6IsA" type="2003" element="_3cdiQBOzEe-4k7CzzL6IsA">
+          <children xmi:type="notation:Node" xmi:id="_3c-frxOzEe-4k7CzzL6IsA" type="5007"/>
+          <children xmi:type="notation:Node" xmi:id="_3c-fsBOzEe-4k7CzzL6IsA" type="7004">
+            <children xmi:type="notation:Node" xmi:id="_5DOEsBOzEe-4k7CzzL6IsA" type="3010" element="_5Cz1ABOzEe-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_5DOEsROzEe-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_5DOEshOzEe-4k7CzzL6IsA"/>
+            </children>
+            <children xmi:type="notation:Node" xmi:id="_7IGGgBOzEe-4k7CzzL6IsA" type="3010" element="_7Hb_MBOzEe-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_7IGGgROzEe-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_7IGGghOzEe-4k7CzzL6IsA"/>
+            </children>
+            <children xmi:type="notation:Node" xmi:id="_8KIyUBOzEe-4k7CzzL6IsA" type="3010" element="_8JiVYBOzEe-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_8KIyUROzEe-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_8KIyUhOzEe-4k7CzzL6IsA"/>
+            </children>
+            <styles xmi:type="notation:SortingStyle" xmi:id="_3c-fsROzEe-4k7CzzL6IsA"/>
+            <styles xmi:type="notation:FilteringStyle" xmi:id="_3c-fshOzEe-4k7CzzL6IsA"/>
+          </children>
+          <styles xmi:type="notation:ShapeStyle" xmi:id="_3c-frROzEe-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+          <layoutConstraint xmi:type="notation:Bounds" xmi:id="_3c-frhOzEe-4k7CzzL6IsA" x="2298" y="1280" width="120" height="100"/>
+        </children>
+        <children xmi:type="notation:Node" xmi:id="_Z2K9bBO0Ee-4k7CzzL6IsA" type="2003" element="_Z12NQBO0Ee-4k7CzzL6IsA">
+          <children xmi:type="notation:Node" xmi:id="_Z2K9bxO0Ee-4k7CzzL6IsA" type="5007"/>
+          <children xmi:type="notation:Node" xmi:id="_Z2K9cBO0Ee-4k7CzzL6IsA" type="7004">
+            <children xmi:type="notation:Node" xmi:id="_eBUvNhO0Ee-4k7CzzL6IsA" type="3010" element="_eBCbUBO0Ee-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_eBUvNxO0Ee-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_eBUvOBO0Ee-4k7CzzL6IsA"/>
+            </children>
+            <children xmi:type="notation:Node" xmi:id="_eoD_HBO0Ee-4k7CzzL6IsA" type="3010" element="_enuA0BO0Ee-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_eoD_HRO0Ee-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_eoD_HhO0Ee-4k7CzzL6IsA"/>
+            </children>
+            <children xmi:type="notation:Node" xmi:id="_fGm8QBO0Ee-4k7CzzL6IsA" type="3010" element="_fGJCMBO0Ee-4k7CzzL6IsA">
+              <styles xmi:type="notation:FontStyle" xmi:id="_fGm8QRO0Ee-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+              <layoutConstraint xmi:type="notation:Location" xmi:id="_fGm8QhO0Ee-4k7CzzL6IsA"/>
+            </children>
+            <styles xmi:type="notation:SortingStyle" xmi:id="_Z2K9cRO0Ee-4k7CzzL6IsA"/>
+            <styles xmi:type="notation:FilteringStyle" xmi:id="_Z2K9chO0Ee-4k7CzzL6IsA"/>
+          </children>
+          <styles xmi:type="notation:ShapeStyle" xmi:id="_Z2K9bRO0Ee-4k7CzzL6IsA" fontName="Noto Sans" fontHeight="8"/>
+          <layoutConstraint xmi:type="notation:Bounds" xmi:id="_Z2K9bhO0Ee-4k7CzzL6IsA" x="2039" y="332" width="120" height="100"/>
+        </children>
         <styles xmi:type="notation:DiagramStyle" xmi:id="_CsZB8qA4EeuqkpDnuik1sg"/>
         <edges xmi:type="notation:Edge" xmi:id="_4eaYwKA8EeuqkpDnuik1sg" type="4001" element="_4eU5TqA8EeuqkpDnuik1sg" source="_D1D6MKA4EeuqkpDnuik1sg" target="_xsq_MKA8EeuqkpDnuik1sg">
           <children xmi:type="notation:Node" xmi:id="_4ea_06A8EeuqkpDnuik1sg" type="6001">
@@ -610,7 +672,7 @@
           <styles xmi:type="notation:ConnectorStyle" xmi:id="_onzXUaA6EeuqkpDnuik1sg" routing="Tree"/>
           <styles xmi:type="notation:FontStyle" xmi:id="_onzXUqA6EeuqkpDnuik1sg" fontName="Noto Sans" fontHeight="8"/>
           <bendpoints xmi:type="notation:RelativeBendpoints" xmi:id="_onzXU6A6EeuqkpDnuik1sg" points="[0, 0, 61, 191]$[0, -72, 61, 119]$[-60, -72, 1, 119]$[-60, -142, 1, 49]"/>
-          <sourceAnchor xmi:type="notation:IdentityAnchor" xmi:id="_on1MgKA6EeuqkpDnuik1sg" id="(0.2033898305084746,0.0)"/>
+          <sourceAnchor xmi:type="notation:IdentityAnchor" xmi:id="_on1MgKA6EeuqkpDnuik1sg" id="(0.31976744186046513,0.125)"/>
           <targetAnchor xmi:type="notation:IdentityAnchor" xmi:id="_on1MgaA6EeuqkpDnuik1sg" id="(0.5,0.5)"/>
         </edges>
         <edges xmi:type="notation:Edge" xmi:id="_vndkcCrcEeyyC-O0_LlY9w" type="4001" element="_Uy4bWaA6EeuqkpDnuik1sg" source="_A9YrQCrZEeyyC-O0_LlY9w" target="_QKLK0KA6EeuqkpDnuik1sg">
@@ -627,7 +689,7 @@
           <styles xmi:type="notation:FontStyle" xmi:id="_vndkcircEeyyC-O0_LlY9w" fontColor="7490599" fontName="Segoe UI" fontHeight="8"/>
           <bendpoints xmi:type="notation:RelativeBendpoints" xmi:id="_vndkcyrcEeyyC-O0_LlY9w" points="[-38, -41, 287, 48]$[-258, -41, 67, 48]"/>
           <sourceAnchor xmi:type="notation:IdentityAnchor" xmi:id="_vndkeircEeyyC-O0_LlY9w" id="(0.2602739726027397,0.9081632653061225)"/>
-          <targetAnchor xmi:type="notation:IdentityAnchor" xmi:id="_vneLgCrcEeyyC-O0_LlY9w" id="(0.4322033898305085,0.0)"/>
+          <targetAnchor xmi:type="notation:IdentityAnchor" xmi:id="_vneLgCrcEeyyC-O0_LlY9w" id="(0.47674418604651164,0.125)"/>
         </edges>
         <edges xmi:type="notation:Edge" xmi:id="_TuLToNbNEeuymriYTNxK2g" type="4001" element="_Tt9RRtbNEeuymriYTNxK2g" source="_jP6FkKA6EeuqkpDnuik1sg" target="_Kw-vINbNEeuymriYTNxK2g">
           <children xmi:type="notation:Node" xmi:id="_TuLTpNbNEeuymriYTNxK2g" type="6001">
@@ -1202,7 +1264,7 @@
           <styles xmi:type="notation:ConnectorStyle" xmi:id="_iXIY4WTzEe2qdtyPWAtoxA" routing="Rectilinear"/>
           <styles xmi:type="notation:FontStyle" xmi:id="_iXIY4mTzEe2qdtyPWAtoxA" fontColor="7490599" fontName="Noto Sans" fontHeight="8"/>
           <bendpoints xmi:type="notation:RelativeBendpoints" xmi:id="_iXIY42TzEe2qdtyPWAtoxA" points="[-72, 48, 1131, 5]$[-1144, 48, 59, 5]"/>
-          <sourceAnchor xmi:type="notation:IdentityAnchor" xmi:id="_iXIY6mTzEe2qdtyPWAtoxA" id="(0.6101694915254238,0.0)"/>
+          <sourceAnchor xmi:type="notation:IdentityAnchor" xmi:id="_iXIY6mTzEe2qdtyPWAtoxA" id="(0.5988372093023255,0.125)"/>
         </edges>
         <edges xmi:type="notation:Edge" xmi:id="_q7DhwGTzEe2qdtyPWAtoxA" type="4001" element="_q604amTzEe2qdtyPWAtoxA" source="_zaq8oKA9EeuqkpDnuik1sg" target="_dzfLYGTvEe2qdtyPWAtoxA">
           <children xmi:type="notation:Node" xmi:id="_q7EI0GTzEe2qdtyPWAtoxA" type="6001">
@@ -1532,10 +1594,34 @@
       <arrangeConstraints>KEEP_LOCATION</arrangeConstraints>
       <arrangeConstraints>KEEP_SIZE</arrangeConstraints>
       <arrangeConstraints>KEEP_RATIO</arrangeConstraints>
-      <ownedStyle xmi:type="diagram:FlatContainerStyle" uid="_Cr-9nBjHEe2_erjsEmF9GQ" borderSize="1" borderSizeComputationExpression="1" backgroundStyle="Liquid" foregroundColor="255,252,216">
+      <ownedStyle xmi:type="diagram:FlatContainerStyle" uid="_iG6EixO0Ee-4k7CzzL6IsA" borderSize="1" borderSizeComputationExpression="1" backgroundStyle="Liquid" foregroundColor="255,252,216">
         <description xmi:type="style:FlatContainerStyleDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@containerMappings[name='EC%20EClass']/@style"/>
       </ownedStyle>
       <actualMapping xmi:type="description_1:ContainerMapping" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@containerMappings[name='EC%20EClass']"/>
+      <ownedElements xmi:type="diagram:DNodeListElement" uid="_JRfVABOyEe-4k7CzzL6IsA" name="concreteness : Concreteness = PARTIAL" tooltipText="">
+        <target xmi:type="ecore:EAttribute" href="src/main/resources/model/problem.ecore#//Parameter/concreteness"/>
+        <semanticElements xmi:type="ecore:EAttribute" href="src/main/resources/model/problem.ecore#//Parameter/concreteness"/>
+        <ownedStyle xmi:type="diagram:BundledImage" uid="_KAVYBROyEe-4k7CzzL6IsA" labelAlignment="LEFT">
+          <description xmi:type="style:BundledImageDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@containerMappings[name='EC%20EClass']/@subNodeMappings[name='EC%20EAttribute']/@style"/>
+        </ownedStyle>
+        <actualMapping xmi:type="description_1:NodeMapping" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@containerMappings[name='EC%20EClass']/@subNodeMappings[name='EC%20EAttribute']"/>
+      </ownedElements>
+      <ownedElements xmi:type="diagram:DNodeListElement" uid="_LJG98BOyEe-4k7CzzL6IsA" name="modality : Modality = NONE" tooltipText="">
+        <target xmi:type="ecore:EAttribute" href="src/main/resources/model/problem.ecore#//Parameter/modality"/>
+        <semanticElements xmi:type="ecore:EAttribute" href="src/main/resources/model/problem.ecore#//Parameter/modality"/>
+        <ownedStyle xmi:type="diagram:BundledImage" uid="_LwmbwxOyEe-4k7CzzL6IsA" labelAlignment="LEFT">
+          <description xmi:type="style:BundledImageDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@containerMappings[name='EC%20EClass']/@subNodeMappings[name='EC%20EAttribute']/@style"/>
+        </ownedStyle>
+        <actualMapping xmi:type="description_1:NodeMapping" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@containerMappings[name='EC%20EClass']/@subNodeMappings[name='EC%20EAttribute']"/>
+      </ownedElements>
+      <ownedElements xmi:type="diagram:DNodeListElement" uid="_heTzcBO0Ee-4k7CzzL6IsA" name="binding : ParameterBinding = SINGLE" tooltipText="">
+        <target xmi:type="ecore:EAttribute" href="src/main/resources/model/problem.ecore#//Parameter/binding"/>
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+        <semanticElements xmi:type="ecore:EEnumLiteral" href="src/main/resources/model/problem.ecore#//ReferenceKind/PARTIAL"/>
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-      <semanticElements xmi:type="ecore:EReference" href="src/main/resources/model/problem.ecore#//Assertion/arguments"/>
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       <semanticElements xmi:type="ecore:EClass" href="src/main/resources/model/problem.ecore#//VariableOrNode"/>
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+        <endLabelStyle xmi:type="diagram:EndLabelStyle" uid="_wudFBRRqEe-4k7CzzL6IsA" labelSize="6" showIcon="false" labelColor="39,76,114"/>
+      </ownedStyle>
+      <actualMapping xmi:type="description_1:EdgeMapping" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@edgeMappings[name='EC_EReference']"/>
+    </ownedDiagramElements>
+    <ownedDiagramElements xmi:type="diagram:DEdge" uid="_xrullhRqEe-4k7CzzL6IsA" sourceNode="_x-t_EF4fEe2rXNsIDUvqhw" targetNode="_wuYMgBRqEe-4k7CzzL6IsA">
+      <target xmi:type="ecore:EClass" href="src/main/resources/model/problem.ecore#//AssertionAction"/>
+      <semanticElements xmi:type="ecore:EClass" href="src/main/resources/model/problem.ecore#//AssertionAction"/>
+      <ownedStyle xmi:type="diagram:EdgeStyle" uid="_xrullxRqEe-4k7CzzL6IsA" targetArrow="InputClosedArrow" routingStyle="tree">
+        <description xmi:type="style:EdgeStyleDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@edgeMappings[name='EC%20ESupertypes']/@style"/>
+        <beginLabelStyle xmi:type="diagram:BeginLabelStyle" uid="_xrulmBRqEe-4k7CzzL6IsA" showIcon="false">
+          <labelFormat>italic</labelFormat>
+        </beginLabelStyle>
+        <centerLabelStyle xmi:type="diagram:CenterLabelStyle" uid="_xrulmRRqEe-4k7CzzL6IsA" showIcon="false"/>
+      </ownedStyle>
+      <actualMapping xmi:type="description_1:EdgeMapping" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer/@edgeMappings[name='EC%20ESupertypes']"/>
+    </ownedDiagramElements>
     <description xmi:type="description_1:DiagramDescription" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']"/>
     <filterVariableHistory xmi:type="diagram:FilterVariableHistory" uid="_sCFBgV4fEe2rXNsIDUvqhw"/>
     <activatedLayers xmi:type="description_1:Layer" href="platform:/plugin/org.eclipse.emf.ecoretools.design/description/ecore.odesign#//@ownedViewpoints[name='Design']/@ownedRepresentations[name='Entities']/@defaultLayer"/>
diff --git a/subprojects/language-model/src/main/resources/model/problem.ecore b/subprojects/language-model/src/main/resources/model/problem.ecore
index 9a349490..e830c724 100644
--- a/subprojects/language-model/src/main/resources/model/problem.ecore
+++ b/subprojects/language-model/src/main/resources/model/problem.ecore
@@ -38,6 +38,9 @@
   </eClassifiers>
   <eClassifiers xsi:type="ecore:EClass" name="Parameter" eSuperTypes="#//Variable">
     <eStructuralFeatures xsi:type="ecore:EReference" name="parameterType" eType="#//Relation"/>
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="concreteness" eType="#//Concreteness"/>
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="modality" eType="#//Modality"/>
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="binding" eType="#//ParameterBinding"/>
   </eClassifiers>
   <eClassifiers xsi:type="ecore:EClass" name="Variable" abstract="true" eSuperTypes="#//VariableOrNode"/>
   <eClassifiers xsi:type="ecore:EClass" name="Atom" eSuperTypes="#//Expr">
@@ -52,11 +55,9 @@
     <eStructuralFeatures xsi:type="ecore:EReference" name="implicitVariables" upperBound="-1"
         eType="#//ImplicitVariable" transient="true" containment="true"/>
   </eClassifiers>
-  <eClassifiers xsi:type="ecore:EClass" name="Assertion" eSuperTypes="#//Statement">
+  <eClassifiers xsi:type="ecore:EClass" name="AbstractAssertion" abstract="true">
     <eStructuralFeatures xsi:type="ecore:EReference" name="arguments" upperBound="-1"
         eType="#//AssertionArgument" containment="true"/>
-    <eStructuralFeatures xsi:type="ecore:EAttribute" name="default" eType="ecore:EDataType http://www.eclipse.org/emf/2002/Ecore#//EBoolean"
-        defaultValueLiteral="false"/>
     <eStructuralFeatures xsi:type="ecore:EReference" name="relation" eType="#//Relation"/>
     <eStructuralFeatures xsi:type="ecore:EReference" name="value" eType="#//Expr"
         containment="true"/>
@@ -109,7 +110,7 @@
     <eStructuralFeatures xsi:type="ecore:EAttribute" name="stringValue" eType="ecore:EDataType http://www.eclipse.org/emf/2002/Ecore#//EString"/>
   </eClassifiers>
   <eClassifiers xsi:type="ecore:EClass" name="NodeAssertionArgument" eSuperTypes="#//AssertionArgument">
-    <eStructuralFeatures xsi:type="ecore:EReference" name="node" eType="#//Node"/>
+    <eStructuralFeatures xsi:type="ecore:EReference" name="node" eType="#//VariableOrNode"/>
   </eClassifiers>
   <eClassifiers xsi:type="ecore:EClass" name="AssertionArgument" abstract="true"/>
   <eClassifiers xsi:type="ecore:EClass" name="NodeDeclaration" eSuperTypes="#//Statement">
@@ -128,28 +129,14 @@
         eType="#//Consequent" containment="true"/>
     <eStructuralFeatures xsi:type="ecore:EReference" name="preconditions" upperBound="-1"
         eType="#//Conjunction" containment="true"/>
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="kind" eType="#//RuleKind"/>
   </eClassifiers>
   <eClassifiers xsi:type="ecore:EClass" name="Consequent">
     <eStructuralFeatures xsi:type="ecore:EReference" name="actions" upperBound="-1"
         eType="#//Action" containment="true"/>
   </eClassifiers>
-  <eClassifiers xsi:type="ecore:EClass" name="Action" abstract="true"/>
-  <eClassifiers xsi:type="ecore:EClass" name="AssertionAction" eSuperTypes="#//Action">
-    <eStructuralFeatures xsi:type="ecore:EReference" name="atom" eType="#//Atom" containment="true"/>
-    <eStructuralFeatures xsi:type="ecore:EAttribute" name="value" eType="#//LogicValue"
-        defaultValueLiteral="TRUE"/>
-    <eStructuralFeatures xsi:type="ecore:EAttribute" name="overwrite" eType="ecore:EDataType http://www.eclipse.org/emf/2002/Ecore#//EBoolean"
-        defaultValueLiteral="FALSE"/>
-  </eClassifiers>
-  <eClassifiers xsi:type="ecore:EClass" name="DeleteAction" eSuperTypes="#//Action">
-    <eStructuralFeatures xsi:type="ecore:EReference" name="variableOrNode" eType="#//VariableOrNode"/>
-  </eClassifiers>
-  <eClassifiers xsi:type="ecore:EClass" name="NewAction" eSuperTypes="#//Action">
-    <eStructuralFeatures xsi:type="ecore:EReference" name="variable" eType="#//NewVariable"
-        containment="true"/>
-    <eStructuralFeatures xsi:type="ecore:EReference" name="parent" eType="#//VariableOrNode"/>
-  </eClassifiers>
-  <eClassifiers xsi:type="ecore:EClass" name="NewVariable" eSuperTypes="#//Variable"/>
+  <eClassifiers xsi:type="ecore:EClass" name="Action" abstract="true" interface="true"/>
+  <eClassifiers xsi:type="ecore:EClass" name="AssertionAction" eSuperTypes="#//Action #//AbstractAssertion"/>
   <eClassifiers xsi:type="ecore:EEnum" name="ComparisonOp">
     <eLiterals name="LESS"/>
     <eLiterals name="LESS_EQ" value="1"/>
@@ -166,6 +153,7 @@
     <eLiterals name="REFERENCE" value="2"/>
     <eLiterals name="CONTAINMENT" value="3"/>
     <eLiterals name="CONTAINER" value="3"/>
+    <eLiterals name="PARTIAL" value="4"/>
   </eClassifiers>
   <eClassifiers xsi:type="ecore:EClass" name="Expr" abstract="true"/>
   <eClassifiers xsi:type="ecore:EClass" name="VariableOrNodeExpr" eSuperTypes="#//Expr">
@@ -264,4 +252,31 @@
   <eClassifiers xsi:type="ecore:EClass" name="AssignmentExpr" eSuperTypes="#//BinaryExpr"/>
   <eClassifiers xsi:type="ecore:EClass" name="InfiniteConstant" eSuperTypes="#//Constant"/>
   <eClassifiers xsi:type="ecore:EClass" name="AggregatorDeclaration" eSuperTypes="#//Statement #//NamedElement"/>
+  <eClassifiers xsi:type="ecore:EClass" name="ModalExpr" eSuperTypes="#//UnaryExpr">
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="concreteness" eType="#//Concreteness"/>
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="modality" eType="#//Modality"/>
+  </eClassifiers>
+  <eClassifiers xsi:type="ecore:EEnum" name="Modality">
+    <eLiterals name="NONE"/>
+    <eLiterals name="MUST" value="1"/>
+    <eLiterals name="MAY" value="2"/>
+  </eClassifiers>
+  <eClassifiers xsi:type="ecore:EEnum" name="Concreteness">
+    <eLiterals name="PARTIAL"/>
+    <eLiterals name="CANDIDATE" value="1"/>
+  </eClassifiers>
+  <eClassifiers xsi:type="ecore:EEnum" name="RuleKind">
+    <eLiterals name="REFINEMENT"/>
+    <eLiterals name="PROPAGATION" value="1"/>
+    <eLiterals name="DECISION" value="2"/>
+  </eClassifiers>
+  <eClassifiers xsi:type="ecore:EEnum" name="ParameterBinding">
+    <eLiterals name="SINGLE"/>
+    <eLiterals name="FOCUS" value="1"/>
+    <eLiterals name="MULTI" value="2"/>
+  </eClassifiers>
+  <eClassifiers xsi:type="ecore:EClass" name="Assertion" eSuperTypes="#//Statement #//AbstractAssertion">
+    <eStructuralFeatures xsi:type="ecore:EAttribute" name="default" eType="ecore:EDataType http://www.eclipse.org/emf/2002/Ecore#//EBoolean"
+        defaultValueLiteral="false"/>
+  </eClassifiers>
 </ecore:EPackage>
diff --git a/subprojects/language-model/src/main/resources/model/problem.genmodel b/subprojects/language-model/src/main/resources/model/problem.genmodel
index 2a1d8522..2ceb74a6 100644
--- a/subprojects/language-model/src/main/resources/model/problem.genmodel
+++ b/subprojects/language-model/src/main/resources/model/problem.genmodel
@@ -32,6 +32,7 @@
       <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ReferenceKind/REFERENCE"/>
       <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ReferenceKind/CONTAINMENT"/>
       <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ReferenceKind/CONTAINER"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ReferenceKind/PARTIAL"/>
     </genEnums>
     <genEnums typeSafeEnumCompatible="false" ecoreEnum="problem.ecore#//UnaryOp">
       <genEnumLiterals ecoreEnumLiteral="problem.ecore#//UnaryOp/PLUS"/>
@@ -60,6 +61,25 @@
       <genEnumLiterals ecoreEnumLiteral="problem.ecore#//LatticeBinaryOp/MEET"/>
       <genEnumLiterals ecoreEnumLiteral="problem.ecore#//LatticeBinaryOp/JOIN"/>
     </genEnums>
+    <genEnums typeSafeEnumCompatible="false" ecoreEnum="problem.ecore#//Modality">
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//Modality/NONE"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//Modality/MUST"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//Modality/MAY"/>
+    </genEnums>
+    <genEnums typeSafeEnumCompatible="false" ecoreEnum="problem.ecore#//Concreteness">
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//Concreteness/PARTIAL"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//Concreteness/CANDIDATE"/>
+    </genEnums>
+    <genEnums typeSafeEnumCompatible="false" ecoreEnum="problem.ecore#//RuleKind">
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//RuleKind/REFINEMENT"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//RuleKind/PROPAGATION"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//RuleKind/DECISION"/>
+    </genEnums>
+    <genEnums typeSafeEnumCompatible="false" ecoreEnum="problem.ecore#//ParameterBinding">
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ParameterBinding/SINGLE"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ParameterBinding/FOCUS"/>
+      <genEnumLiterals ecoreEnumLiteral="problem.ecore#//ParameterBinding/MULTI"/>
+    </genEnums>
     <genClasses ecoreClass="problem.ecore#//Problem">
       <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//Problem/nodes"/>
       <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//Problem/statements"/>
@@ -88,6 +108,9 @@
     </genClasses>
     <genClasses ecoreClass="problem.ecore#//Parameter">
       <genFeatures notify="false" createChild="false" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//Parameter/parameterType"/>
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//Parameter/concreteness"/>
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//Parameter/modality"/>
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//Parameter/binding"/>
     </genClasses>
     <genClasses ecoreClass="problem.ecore#//Variable"/>
     <genClasses ecoreClass="problem.ecore#//Atom">
@@ -99,11 +122,10 @@
     <genClasses ecoreClass="problem.ecore#//ExistentialQuantifier">
       <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//ExistentialQuantifier/implicitVariables"/>
     </genClasses>
-    <genClasses ecoreClass="problem.ecore#//Assertion">
-      <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//Assertion/arguments"/>
-      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//Assertion/default"/>
-      <genFeatures notify="false" createChild="false" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//Assertion/relation"/>
-      <genFeatures children="true" createChild="true" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//Assertion/value"/>
+    <genClasses ecoreClass="problem.ecore#//AbstractAssertion">
+      <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//AbstractAssertion/arguments"/>
+      <genFeatures notify="false" createChild="false" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//AbstractAssertion/relation"/>
+      <genFeatures children="true" createChild="true" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//AbstractAssertion/value"/>
     </genClasses>
     <genClasses ecoreClass="problem.ecore#//Node"/>
     <genClasses ecoreClass="problem.ecore#//ScopeDeclaration">
@@ -153,24 +175,13 @@
     <genClasses ecoreClass="problem.ecore#//RuleDefinition">
       <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//RuleDefinition/consequents"/>
       <genFeatures children="true" createChild="true" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//RuleDefinition/preconditions"/>
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//RuleDefinition/kind"/>
     </genClasses>
     <genClasses ecoreClass="problem.ecore#//Consequent">
       <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//Consequent/actions"/>
     </genClasses>
     <genClasses ecoreClass="problem.ecore#//Action"/>
-    <genClasses ecoreClass="problem.ecore#//AssertionAction">
-      <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//AssertionAction/atom"/>
-      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//AssertionAction/value"/>
-      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//AssertionAction/overwrite"/>
-    </genClasses>
-    <genClasses ecoreClass="problem.ecore#//DeleteAction">
-      <genFeatures notify="false" createChild="false" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//DeleteAction/variableOrNode"/>
-    </genClasses>
-    <genClasses ecoreClass="problem.ecore#//NewAction">
-      <genFeatures property="None" children="true" createChild="true" ecoreFeature="ecore:EReference problem.ecore#//NewAction/variable"/>
-      <genFeatures notify="false" createChild="false" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//NewAction/parent"/>
-    </genClasses>
-    <genClasses ecoreClass="problem.ecore#//NewVariable"/>
+    <genClasses ecoreClass="problem.ecore#//AssertionAction"/>
     <genClasses ecoreClass="problem.ecore#//Expr"/>
     <genClasses ecoreClass="problem.ecore#//VariableOrNodeExpr">
       <genFeatures notify="false" createChild="false" propertySortChoices="true" ecoreFeature="ecore:EReference problem.ecore#//VariableOrNodeExpr/variableOrNode"/>
@@ -232,5 +243,12 @@
     <genClasses ecoreClass="problem.ecore#//AssignmentExpr"/>
     <genClasses ecoreClass="problem.ecore#//InfiniteConstant"/>
     <genClasses ecoreClass="problem.ecore#//AggregatorDeclaration"/>
+    <genClasses ecoreClass="problem.ecore#//ModalExpr">
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//ModalExpr/concreteness"/>
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//ModalExpr/modality"/>
+    </genClasses>
+    <genClasses ecoreClass="problem.ecore#//Assertion">
+      <genFeatures createChild="false" ecoreFeature="ecore:EAttribute problem.ecore#//Assertion/default"/>
+    </genClasses>
   </genPackages>
 </genmodel:GenModel>
diff --git a/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ModelInitializer.java b/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ModelInitializer.java
index ccfb630f..486eb89b 100644
--- a/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ModelInitializer.java
+++ b/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ModelInitializer.java
@@ -6,6 +6,7 @@
 package tools.refinery.language.semantics;
 
 import com.google.inject.Inject;
+import org.jetbrains.annotations.Nullable;
 import tools.refinery.language.library.BuiltinLibrary;
 import tools.refinery.language.model.problem.*;
 import tools.refinery.language.scoping.imports.ImportAdapterProvider;
@@ -13,10 +14,9 @@ import tools.refinery.language.scoping.imports.ImportCollector;
 import tools.refinery.language.semantics.internal.MutableSeed;
 import tools.refinery.language.utils.BuiltinSymbols;
 import tools.refinery.language.utils.ProblemUtil;
+import tools.refinery.language.validation.ActionTargetCollector;
 import tools.refinery.logic.Constraint;
-import tools.refinery.logic.dnf.InvalidClauseException;
-import tools.refinery.logic.dnf.Query;
-import tools.refinery.logic.dnf.RelationalQuery;
+import tools.refinery.logic.dnf.*;
 import tools.refinery.logic.literal.*;
 import tools.refinery.logic.term.NodeVariable;
 import tools.refinery.logic.term.Variable;
@@ -25,8 +25,18 @@ import tools.refinery.logic.term.cardinalityinterval.CardinalityIntervals;
 import tools.refinery.logic.term.truthvalue.TruthValue;
 import tools.refinery.logic.term.uppercardinality.UpperCardinalities;
 import tools.refinery.store.dse.propagation.PropagationBuilder;
+import tools.refinery.store.dse.transition.DesignSpaceExplorationBuilder;
+import tools.refinery.store.dse.transition.Rule;
+import tools.refinery.store.dse.transition.RuleBuilder;
+import tools.refinery.store.dse.transition.actions.ActionLiteral;
+import tools.refinery.store.dse.transition.actions.ActionLiterals;
 import tools.refinery.store.model.ModelStoreBuilder;
 import tools.refinery.store.reasoning.ReasoningAdapter;
+import tools.refinery.store.reasoning.actions.PartialActionLiterals;
+import tools.refinery.store.reasoning.literal.Concreteness;
+import tools.refinery.store.reasoning.literal.ModalConstraint;
+import tools.refinery.store.reasoning.literal.Modality;
+import tools.refinery.store.reasoning.literal.PartialLiterals;
 import tools.refinery.store.reasoning.representation.PartialRelation;
 import tools.refinery.store.reasoning.scope.ScopePropagator;
 import tools.refinery.store.reasoning.seed.ModelSeed;
@@ -59,6 +69,9 @@ public class ModelInitializer {
         @Inject
         private ImportAdapterProvider importAdapterProvider;
 
+        @Inject
+        private ActionTargetCollector actionTargetCollector;
+
         private Problem problem;
 
         private final Set<Problem> importedProblems = new HashSet<>();
@@ -87,6 +100,8 @@ public class ModelInitializer {
 
         private ModelSeed modelSeed;
 
+        private int ruleCount;
+
         public void readProblem(Problem problem) {
                 if (this.problem != null) {
                         throw new IllegalArgumentException("Problem was already set");
@@ -174,6 +189,7 @@ public class ModelInitializer {
                                 storeBuilder.with(scopePropagator);
                         }
                         collectPredicates(storeBuilder);
+                        collectRules(storeBuilder);
                 } catch (TranslationException e) {
                         throw problemTrace.wrapException(e);
                 }
@@ -336,6 +352,7 @@ public class ModelInitializer {
                 var target = getPartialRelation(referenceDeclaration.getReferenceType());
                 targetTypes.add(target);
                 boolean containment = referenceDeclaration.getKind() == ReferenceKind.CONTAINMENT;
+                boolean partial = referenceDeclaration.getKind() == ReferenceKind.PARTIAL;
                 var opposite = referenceDeclaration.getOpposite();
                 PartialRelation oppositeRelation = null;
                 if (opposite != null) {
@@ -356,6 +373,7 @@ public class ModelInitializer {
                                         .target(target)
                                         .opposite(oppositeRelation)
                                         .defaultValue(defaultValue)
+                                        .partial(partial)
                                         .build());
                 } catch (RuntimeException e) {
                         throw TracedException.addTrace(classDeclaration, e);
@@ -379,14 +397,16 @@ public class ModelInitializer {
 
         private static CardinalityInterval getCardinalityInterval(
                         tools.refinery.language.model.problem.Multiplicity problemMultiplicity) {
-                if (problemMultiplicity instanceof ExactMultiplicity exactMultiplicity) {
+                switch (problemMultiplicity) {
+                case ExactMultiplicity exactMultiplicity -> {
                         return CardinalityIntervals.exactly(exactMultiplicity.getExactValue());
-                } else if (problemMultiplicity instanceof RangeMultiplicity rangeMultiplicity) {
+                }
+                case RangeMultiplicity rangeMultiplicity -> {
                         var upperBound = rangeMultiplicity.getUpperBound();
                         return CardinalityIntervals.between(rangeMultiplicity.getLowerBound(),
                                         upperBound < 0 ? UpperCardinalities.UNBOUNDED : UpperCardinalities.atMost(upperBound));
-                } else {
-                        throw new TracedException(problemMultiplicity, "Unknown multiplicity");
+                }
+                default -> throw new TracedException(problemMultiplicity, "Unknown multiplicity");
                 }
         }
 
@@ -521,7 +541,12 @@ public class ModelInitializer {
                 for (int i = 0; i < arity; i++) {
                         var argument = arguments.get(i);
                         if (argument instanceof NodeAssertionArgument nodeArgument) {
-                                nodes[i] = getNodeId(nodeArgument.getNode());
+                                var variableOrNode = nodeArgument.getNode();
+                                if (variableOrNode instanceof Node node) {
+                                        nodes[i] = getNodeId(node);
+                                } else {
+                                        throw new TracedException(argument, "Invalid assertion argument: " + variableOrNode);
+                                }
                         } else if (argument instanceof WildcardAssertionArgument) {
                                 nodes[i] = -1;
                         } else {
@@ -573,7 +598,7 @@ public class ModelInitializer {
         private void collectPredicateDefinition(PredicateDefinition predicateDefinition, ModelStoreBuilder storeBuilder) {
                 var partialRelation = getPartialRelation(predicateDefinition);
                 var query = toQuery(partialRelation.name(), predicateDefinition);
-                boolean mutable = targetTypes.contains(partialRelation);
+                boolean mutable = targetTypes.contains(partialRelation) || isActionTarget(predicateDefinition);
                 TruthValue defaultValue;
                 if (predicateDefinition.isError()) {
                         defaultValue = TruthValue.FALSE;
@@ -588,6 +613,15 @@ public class ModelInitializer {
                 storeBuilder.with(translator);
         }
 
+        private boolean isActionTarget(PredicateDefinition predicateDefinition) {
+                for (var importedProblem : importedProblems) {
+                        if (actionTargetCollector.isActionTarget(importedProblem, predicateDefinition)) {
+                                return true;
+                        }
+                }
+                return false;
+        }
+
         private RelationalQuery toQuery(String name, PredicateDefinition predicateDefinition) {
                 var problemParameters = predicateDefinition.getParameters();
                 int arity = problemParameters.size();
@@ -607,23 +641,29 @@ public class ModelInitializer {
                 }
                 var builder = Query.builder(name).parameters(parameters);
                 for (var body : predicateDefinition.getBodies()) {
-                        try {
-                                var localScope = extendScope(parameterMap, body.getImplicitVariables());
-                                var problemLiterals = body.getLiterals();
-                                var literals = new ArrayList<>(commonLiterals);
-                                for (var problemLiteral : problemLiterals) {
-                                        toLiteralsTraced(problemLiteral, localScope, literals);
-                                }
-                                builder.clause(literals);
-                        } catch (RuntimeException e) {
-                                throw TracedException.addTrace(body, e);
-                        }
+                        buildConjunction(body, parameterMap, commonLiterals, builder);
                 }
                 return builder.build();
         }
 
-        private Map<tools.refinery.language.model.problem.Variable, Variable> extendScope(
-                        Map<tools.refinery.language.model.problem.Variable, Variable> existing,
+        private void buildConjunction(
+                        Conjunction body, HashMap<tools.refinery.language.model.problem.Variable, ? extends Variable> parameterMap,
+                        List<Literal> commonLiterals, AbstractQueryBuilder<?> builder) {
+                try {
+                        var localScope = extendScope(parameterMap, body.getImplicitVariables());
+                        var problemLiterals = body.getLiterals();
+                        var literals = new ArrayList<>(commonLiterals);
+                        for (var problemLiteral : problemLiterals) {
+                                toLiteralsTraced(problemLiteral, localScope, literals);
+                        }
+                        builder.clause(literals);
+                } catch (RuntimeException e) {
+                        throw TracedException.addTrace(body, e);
+                }
+        }
+
+        private Map<tools.refinery.language.model.problem.Variable, ? extends Variable> extendScope(
+                        Map<tools.refinery.language.model.problem.Variable, ? extends Variable> existing,
                         Collection<? extends tools.refinery.language.model.problem.Variable> newVariables) {
                 if (newVariables.isEmpty()) {
                         return existing;
@@ -637,8 +677,9 @@ public class ModelInitializer {
                 return localScope;
         }
 
-        private void toLiteralsTraced(Expr expr, Map<tools.refinery.language.model.problem.Variable, Variable> localScope,
-                                                                  List<Literal> literals) {
+        private void toLiteralsTraced(
+                        Expr expr, Map<tools.refinery.language.model.problem.Variable, ? extends Variable> localScope,
+                        List<Literal> literals) {
                 try {
                         toLiterals(expr, localScope, literals);
                 } catch (RuntimeException e) {
@@ -646,9 +687,12 @@ public class ModelInitializer {
                 }
         }
 
-        private void toLiterals(Expr expr, Map<tools.refinery.language.model.problem.Variable, Variable> localScope,
-                                                        List<Literal> literals) {
-                switch (expr) {
+        private void toLiterals(
+                        Expr expr, Map<tools.refinery.language.model.problem.Variable, ? extends Variable> localScope,
+                        List<Literal> literals) {
+                var extractedOuter = extractModalExpr(expr);
+                var outerModality = extractedOuter.modality();
+                switch (extractedOuter.body()) {
                 case LogicConstant logicConstant -> {
                         switch (logicConstant.getLogicValue()) {
                         case TRUE -> literals.add(BooleanLiteral.TRUE);
@@ -658,27 +702,22 @@ public class ModelInitializer {
                 }
                 case Atom atom -> {
                         var target = getPartialRelation(atom.getRelation());
-                        var polarity = atom.isTransitiveClosure() ? CallPolarity.TRANSITIVE : CallPolarity.POSITIVE;
+                        var constraint = atom.isTransitiveClosure() ? getTransitiveWrapper(target) : target;
                         var argumentList = toArgumentList(atom.getArguments(), localScope, literals);
-                        literals.add(target.call(polarity, argumentList));
+                        literals.add(extractedOuter.modality.wrapConstraint(constraint).call(CallPolarity.POSITIVE, argumentList));
                 }
                 case NegationExpr negationExpr -> {
                         var body = negationExpr.getBody();
-                        if (!(body instanceof Atom atom)) {
-                                throw new TracedException(body, "Cannot negate literal");
+                        var extractedInner = extractModalExpr(body);
+                        if (!(extractedInner.body() instanceof Atom atom)) {
+                                throw new TracedException(extractedInner.body(), "Cannot negate literal");
                         }
                         var target = getPartialRelation(atom.getRelation());
-                        Constraint constraint;
-                        if (atom.isTransitiveClosure()) {
-                                constraint = Query.of(target.name() + "#transitive", (builder, p1, p2) -> builder.clause(
-                                                target.callTransitive(p1, p2)
-                                )).getDnf();
-                        } else {
-                                constraint = target;
-                        }
+                        Constraint constraint = atom.isTransitiveClosure() ? getTransitiveWrapper(target) : target;
                         var negatedScope = extendScope(localScope, negationExpr.getImplicitVariables());
-                        var argumentList = toArgumentList(atom.getArguments(), negatedScope, literals);
-                        literals.add(constraint.call(CallPolarity.NEGATIVE, argumentList));
+                        List<Variable> argumentList = toArgumentList(atom.getArguments(), negatedScope, literals);
+                        var innerModality = extractedInner.modality().merge(outerModality.negate());
+                        literals.add(createNegationLiteral(innerModality, constraint, argumentList, localScope));
                 }
                 case ComparisonExpr comparisonExpr -> {
                         var argumentList = toArgumentList(List.of(comparisonExpr.getLeft(), comparisonExpr.getRight()),
@@ -689,14 +728,117 @@ public class ModelInitializer {
                                 default -> throw new TracedException(
                                                 comparisonExpr, "Unsupported operator");
                         };
-                        literals.add(new EquivalenceLiteral(positive, argumentList.get(0), argumentList.get(1)));
+                        literals.add(createEquivalenceLiteral(outerModality, positive, argumentList.get(0), argumentList.get(1),
+                                        localScope));
+                }
+                default -> throw new TracedException(extractedOuter.body(), "Unsupported literal");
+                }
+        }
+
+        private Constraint getTransitiveWrapper(Constraint target) {
+                return Query.of(target.name() + "#transitive", (builder, p1, p2) -> builder.clause(
+                                target.callTransitive(p1, p2)
+                )).getDnf();
+        }
+
+        private static Literal createNegationLiteral(
+                        ConcreteModality innerModality, Constraint constraint, List<Variable> argumentList,
+                        Map<tools.refinery.language.model.problem.Variable, ? extends Variable> localScope) {
+                if (innerModality.isSet()) {
+                        boolean needsQuantification = false;
+                        var filteredArguments = new LinkedHashSet<Variable>();
+                        for (var argument : argumentList) {
+                                if (localScope.containsValue(argument)) {
+                                        filteredArguments.add(argument);
+                                } else {
+                                        needsQuantification = true;
+                                }
+                        }
+                        // If there are any quantified arguments, set a helper pattern to be lifted so that the appropriate
+                        // {@code EXISTS} call are added by the {@code DnfLifter}.
+                        if (needsQuantification) {
+                                var filteredArgumentList = List.copyOf(filteredArguments);
+                                var quantifiedConstraint = Dnf.builder(constraint.name() + "#quantified")
+                                                .parameters(filteredArgumentList)
+                                                .clause(
+                                                                constraint.call(CallPolarity.POSITIVE, argumentList)
+                                                )
+                                                .build();
+                                return innerModality.wrapConstraint(quantifiedConstraint)
+                                                .call(CallPolarity.NEGATIVE, filteredArgumentList);
+                        }
                 }
-                default -> throw new TracedException(expr, "Unsupported literal");
+                return innerModality.wrapConstraint(constraint).call(CallPolarity.NEGATIVE, argumentList);
+        }
+
+        private Literal createEquivalenceLiteral(
+                        ConcreteModality outerModality, boolean positive, Variable left, Variable right,
+                        Map<tools.refinery.language.model.problem.Variable, ? extends Variable> localScope) {
+                if (!outerModality.isSet()) {
+                        return new EquivalenceLiteral(positive, left, right);
                 }
+                if (positive) {
+                        return outerModality.wrapConstraint(ReasoningAdapter.EQUALS_SYMBOL).call(left, right);
+                }
+                // Interpret {@code x != y} as {@code !equals(x, y)} at all times, even in modal operators.
+                return createNegationLiteral(outerModality.negate(), ReasoningAdapter.EQUALS_SYMBOL, List.of(left, right),
+                                localScope);
+        }
+
+        private record ConcreteModality(@Nullable Concreteness concreteness, @Nullable Modality modality) {
+                public static final ConcreteModality NULL = new ConcreteModality((Concreteness) null, null);
+
+                public ConcreteModality(tools.refinery.language.model.problem.Concreteness concreteness,
+                                                                tools.refinery.language.model.problem.Modality modality) {
+                        this(
+                                        switch (concreteness) {
+                                                case PARTIAL -> Concreteness.PARTIAL;
+                                                case CANDIDATE -> Concreteness.CANDIDATE;
+                                        },
+                                        switch (modality) {
+                                                case MUST -> Modality.MUST;
+                                                case MAY -> Modality.MAY;
+                                                case NONE -> throw new IllegalArgumentException("Invalid modality");
+                                        }
+                        );
+                }
+
+                public ConcreteModality negate() {
+                        var negatedModality = modality == null ? null : modality.negate();
+                        return new ConcreteModality(concreteness, negatedModality);
+                }
+
+                public ConcreteModality merge(ConcreteModality outer) {
+                        var mergedConcreteness = concreteness == null ? outer.concreteness() : concreteness;
+                        var mergedModality = modality == null ? outer.modality() : modality;
+                        return new ConcreteModality(mergedConcreteness, mergedModality);
+                }
+
+                public Constraint wrapConstraint(Constraint inner) {
+                        if (isSet()) {
+                                return new ModalConstraint(modality, concreteness, inner);
+                        }
+                        return inner;
+                }
+
+                public boolean isSet() {
+                        return concreteness != null || modality != null;
+                }
+        }
+
+        private record ExtractedModalExpr(ConcreteModality modality, Expr body) {
+        }
+
+        private ExtractedModalExpr extractModalExpr(Expr expr) {
+                if (expr instanceof ModalExpr modalExpr) {
+                        return new ExtractedModalExpr(new ConcreteModality(modalExpr.getConcreteness(), modalExpr.getModality()),
+                                        modalExpr.getBody());
+                }
+                return new ExtractedModalExpr(ConcreteModality.NULL, expr);
         }
 
         private List<Variable> toArgumentList(
-                        List<Expr> expressions, Map<tools.refinery.language.model.problem.Variable, Variable> localScope,
+                        List<Expr> expressions, Map<tools.refinery.language.model.problem.Variable, ? extends Variable> localScope,
                         List<Literal> literals) {
                 var argumentList = new ArrayList<Variable>(expressions.size());
                 for (var expr : expressions) {
@@ -704,12 +846,14 @@ public class ModelInitializer {
                                 throw new TracedException(expr, "Unsupported argument");
                         }
                         var variableOrNode = variableOrNodeExpr.getVariableOrNode();
-                        if (variableOrNode instanceof Node node) {
+                        switch (variableOrNode) {
+                        case Node node -> {
                                 int nodeId = getNodeId(node);
                                 var tempVariable = Variable.of(semanticsUtils.getNameWithoutRootPrefix(node).orElse("_" + nodeId));
                                 literals.add(new ConstantLiteral(tempVariable, nodeId));
                                 argumentList.add(tempVariable);
-                        } else if (variableOrNode instanceof tools.refinery.language.model.problem.Variable problemVariable) {
+                        }
+                        case tools.refinery.language.model.problem.Variable problemVariable -> {
                                 if (variableOrNodeExpr.getSingletonVariable() == problemVariable) {
                                         argumentList.add(Variable.of(problemVariable.getName()));
                                 } else {
@@ -719,8 +863,8 @@ public class ModelInitializer {
                                         }
                                         argumentList.add(variable);
                                 }
-                        } else {
-                                throw new TracedException(variableOrNode, "Unknown argument");
+                        }
+                        default -> throw new TracedException(variableOrNode, "Unknown argument");
                         }
                 }
                 return argumentList;
@@ -796,4 +940,157 @@ public class ModelInitializer {
                         return defaultAssertions;
                 }
         }
+
+        private void collectRules(ModelStoreBuilder storeBuilder) {
+                for (var importedProblem : importedProblems) {
+                        for (var statement : importedProblem.getStatements()) {
+                                if (statement instanceof RuleDefinition ruleDefinition) {
+                                        collectRule(ruleDefinition, storeBuilder);
+                                }
+                        }
+                }
+        }
+
+        private void collectRule(RuleDefinition ruleDefinition, ModelStoreBuilder storeBuilder) {
+                try {
+                        var name = semanticsUtils.getNameWithoutRootPrefix(ruleDefinition)
+                                        .orElseGet(() -> "::rule" + ruleCount);
+                        ruleCount++;
+                        var rule = toRule(name, ruleDefinition);
+                        switch (ruleDefinition.getKind()) {
+                        case DECISION -> storeBuilder.tryGetAdapter(DesignSpaceExplorationBuilder.class)
+                                        .ifPresent(dseBuilder -> dseBuilder.transformation(rule));
+                        case PROPAGATION -> storeBuilder.tryGetAdapter(PropagationBuilder.class)
+                                        .ifPresent(propagationBuilder -> propagationBuilder.rule(rule));
+                        case REFINEMENT -> {
+                                // Rules not marked for decision or propagation are not invoked automatically.
+                        }
+                        }
+                } catch (InvalidClauseException e) {
+                        int clauseIndex = e.getClauseIndex();
+                        var bodies = ruleDefinition.getPreconditions();
+                        if (clauseIndex < bodies.size()) {
+                                throw new TracedException(bodies.get(clauseIndex), e);
+                        } else {
+                                throw new TracedException(ruleDefinition, e);
+                        }
+                } catch (RuntimeException e) {
+                        throw TracedException.addTrace(ruleDefinition, e);
+                }
+        }
+
+        private Rule toRule(String name, RuleDefinition ruleDefinition) {
+                var problemParameters = ruleDefinition.getParameters();
+                int arity = problemParameters.size();
+                var parameters = new NodeVariable[arity];
+                var parameterMap = HashMap.<tools.refinery.language.model.problem.Variable, NodeVariable>newHashMap(arity);
+                var commonLiterals = new ArrayList<Literal>();
+                var parametersToFocus = new ArrayList<tools.refinery.language.model.problem.Variable>();
+                for (int i = 0; i < arity; i++) {
+                        var problemParameter = problemParameters.get(i);
+                        var parameter = Variable.of(problemParameter.getName());
+                        parameters[i] = parameter;
+                        parameterMap.put(problemParameter, parameter);
+                        var parameterType = problemParameter.getParameterType();
+                        if (parameterType != null) {
+                                var partialType = getPartialRelation(parameterType);
+                                var modality = new ConcreteModality(problemParameter.getConcreteness(),
+                                                problemParameter.getModality());
+                                commonLiterals.add(modality.wrapConstraint(partialType).call(parameter));
+                        }
+                        if (ruleDefinition.getKind() == RuleKind.DECISION &&
+                                        problemParameter.getBinding() == ParameterBinding.SINGLE) {
+                                commonLiterals.add(MultiObjectTranslator.MULTI_VIEW.call(CallPolarity.NEGATIVE, parameter));
+                        }
+                        if (problemParameter.getBinding() == ParameterBinding.FOCUS) {
+                                parametersToFocus.add(problemParameter);
+                        }
+                }
+                toMonomorphicMatchingLiterals(parametersToFocus, parameterMap, commonLiterals);
+                var builder = Rule.builder(name).parameters(parameters);
+                var preconditions = ruleDefinition.getPreconditions();
+                if (preconditions.isEmpty()) {
+                        builder.clause(commonLiterals);
+                } else {
+                        for (var precondition : preconditions) {
+                                buildConjunction(precondition, parameterMap, commonLiterals, builder);
+                        }
+                }
+                for (var consequent : ruleDefinition.getConsequents()) {
+                        buildConsequent(consequent, parameterMap, parametersToFocus, builder);
+                }
+                return builder.build();
+        }
+
+        private static void toMonomorphicMatchingLiterals(
+                        ArrayList<tools.refinery.language.model.problem.Variable> parametersToFocus,
+                        HashMap<tools.refinery.language.model.problem.Variable, NodeVariable> parameterMap,
+                        ArrayList<Literal> commonLiterals) {
+                int focusCount = parametersToFocus.size();
+                for (int i = 0; i < focusCount; i++) {
+                        var leftFocus = parameterMap.get(parametersToFocus.get(i));
+                        for (int j = i + 1; j < focusCount; j++) {
+                                var rightFocus = parameterMap.get(parametersToFocus.get(j));
+                                commonLiterals.add(Literals.not(PartialLiterals.must(
+                                                ReasoningAdapter.EQUALS_SYMBOL.call(leftFocus, rightFocus))));
+                        }
+                }
+        }
+
+        private void buildConsequent(
+                        Consequent body, HashMap<tools.refinery.language.model.problem.Variable, NodeVariable> parameterMap,
+                        Collection<tools.refinery.language.model.problem.Variable> parametersToFocus, RuleBuilder builder) {
+                try {
+                        var actionLiterals = new ArrayList<ActionLiteral>();
+                        HashMap<tools.refinery.language.model.problem.Variable, NodeVariable> localScope;
+                        if (parametersToFocus.isEmpty()) {
+                                localScope = parameterMap;
+                        } else {
+                                localScope = new LinkedHashMap<>(parameterMap);
+                                for (var parameterToFocus : parametersToFocus) {
+                                        var originalParameter = parameterMap.get(parameterToFocus);
+                                        var focusedParameter = Variable.of(originalParameter.getName() + "#focused");
+                                        localScope.put(parameterToFocus, focusedParameter);
+                                        actionLiterals.add(PartialActionLiterals.focus(originalParameter, focusedParameter));
+                                }
+                        }
+                        for (var action : body.getActions()) {
+                                toActionLiterals(action, localScope, actionLiterals);
+                        }
+                        builder.action(actionLiterals);
+                } catch (RuntimeException e) {
+                        throw TracedException.addTrace(body, e);
+                }
+        }
+
+        private void toActionLiterals(
+                        Action action, HashMap<tools.refinery.language.model.problem.Variable, NodeVariable> localScope,
+                        List<ActionLiteral> actionLiterals) {
+                if (!(action instanceof AssertionAction assertionAction)) {
+                        throw new TracedException(action, "Unknown action");
+                }
+                var partialRelation = getPartialRelation(assertionAction.getRelation());
+                var truthValue = getTruthValue(assertionAction.getValue());
+                var problemArguments = assertionAction.getArguments();
+                var arguments = new NodeVariable[problemArguments.size()];
+                for (int i = 0; i < arguments.length; i++) {
+                        var problemArgument = problemArguments.get(i);
+                        if (!(problemArgument instanceof NodeAssertionArgument nodeAssertionArgument)) {
+                                throw new TracedException(problemArgument, "Invalid argument");
+                        }
+                        var variableOrNode = nodeAssertionArgument.getNode();
+                        switch (variableOrNode) {
+                        case tools.refinery.language.model.problem.Variable problemVariable ->
+                                        arguments[i] = localScope.get(problemVariable);
+                        case Node node -> {
+                                int nodeId = getNodeId(node);
+                                var tempVariable = Variable.of(semanticsUtils.getNameWithoutRootPrefix(node).orElse("_" + nodeId));
+                                actionLiterals.add(ActionLiterals.constant(tempVariable, nodeId));
+                                arguments[i] = tempVariable;
+                        }
+                        default -> throw new TracedException(problemArgument, "Invalid argument");
+                        }
+                }
+                actionLiterals.add(PartialActionLiterals.merge(partialRelation, truthValue, arguments));
+        }
 }
diff --git a/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ProblemTraceImpl.java b/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ProblemTraceImpl.java
index aef0fd89..3a979bf0 100644
--- a/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ProblemTraceImpl.java
+++ b/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/ProblemTraceImpl.java
@@ -152,7 +152,7 @@ class ProblemTraceImpl implements ProblemTrace {
 
         @Override
         public PartialRelation getPartialRelation(QualifiedName qualifiedName) {
-                var relationScope = scopeProvider.getScope(problem, ProblemPackage.Literals.ASSERTION__RELATION);
+                var relationScope = scopeProvider.getScope(problem, ProblemPackage.Literals.ABSTRACT_ASSERTION__RELATION);
                 return getPartialRelation(getElement(relationScope, qualifiedName, Relation.class));
         }
 
diff --git a/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/SolutionSerializer.java b/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/SolutionSerializer.java
index f097143f..ed4841c4 100644
--- a/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/SolutionSerializer.java
+++ b/subprojects/language-semantics/src/main/java/tools/refinery/language/semantics/SolutionSerializer.java
@@ -310,7 +310,7 @@ public class SolutionSerializer {
                 var relation = findPartialRelation(partialRelation);
                 var cursor = reasoningAdapter.getPartialInterpretation(Concreteness.CANDIDATE, partialRelation).getAll();
                 // Make sure to output assertions in a deterministic order.
-                var sortedTuples = new TreeSet<Tuple>();
+                var sortedTuples = new TreeMap<Tuple, LogicValue>();
                 while (cursor.move()) {
                         var tuple = cursor.getKey();
                         var from = nodes.get(tuple.get(0));
@@ -320,17 +320,20 @@ public class SolutionSerializer {
                                 continue;
                         }
                         var value = cursor.getValue();
-                        if (!value.isConcrete()) {
-                                throw new IllegalStateException("Invalid %s %s for tuple %s".formatted(partialRelation, value, tuple));
-                        }
-                        if (value.may()) {
-                                sortedTuples.add(tuple);
-                        }
+                        var logicValue = switch (value) {
+                                case TRUE -> LogicValue.TRUE;
+                                case FALSE -> throw new IllegalStateException("Invalid %s %s for tuple %s"
+                                                .formatted(partialRelation, value, tuple));
+                                case UNKNOWN -> LogicValue.UNKNOWN;
+                                case ERROR -> LogicValue.ERROR;
+                        };
+                        sortedTuples.put(tuple, logicValue);
                 }
-                for (var tuple : sortedTuples) {
+                for (var entry : sortedTuples.entrySet()) {
+                        var tuple = entry.getKey();
                         var from = nodes.get(tuple.get(0));
                         var to = nodes.get(tuple.get(1));
-                        addAssertion(relation, LogicValue.TRUE, from, to);
+                        addAssertion(relation, entry.getValue(), from, to);
                 }
         }
 
diff --git a/subprojects/language-web/src/main/java/tools/refinery/language/web/semantics/metadata/MetadataCreator.java b/subprojects/language-web/src/main/java/tools/refinery/language/web/semantics/metadata/MetadataCreator.java
index 91008919..29f8ab8b 100644
--- a/subprojects/language-web/src/main/java/tools/refinery/language/web/semantics/metadata/MetadataCreator.java
+++ b/subprojects/language-web/src/main/java/tools/refinery/language/web/semantics/metadata/MetadataCreator.java
@@ -51,7 +51,7 @@ public class MetadataCreator {
                 this.problemTrace = problemTrace;
                 var problem = problemTrace.getProblem();
                 nodeScope = scopeProvider.getScope(problem, ProblemPackage.Literals.NODE_ASSERTION_ARGUMENT__NODE);
-                relationScope = scopeProvider.getScope(problem, ProblemPackage.Literals.ASSERTION__RELATION);
+                relationScope = scopeProvider.getScope(problem, ProblemPackage.Literals.ABSTRACT_ASSERTION__RELATION);
         }
 
         public List<NodeMetadata> getNodesMetadata(Model model, Concreteness concreteness) {
diff --git a/subprojects/language/src/main/java/tools/refinery/language/Problem.xtext b/subprojects/language/src/main/java/tools/refinery/language/Problem.xtext
index 08f7a585..10e994a0 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/Problem.xtext
+++ b/subprojects/language/src/main/java/tools/refinery/language/Problem.xtext
@@ -18,7 +18,7 @@ enum ModuleKind:
 Statement:
         ImportStatement | Assertion | ClassDeclaration | EnumDeclaration |
         DatatypeDeclaration | AggregatorDeclaration | PredicateDefinition |
-        /* FunctionDefinition | RuleDefinition | */
+        /* FunctionDefinition | */ RuleDefinition |
         ScopeDeclaration | NodeDeclaration;
 
 ImportStatement:
@@ -45,7 +45,7 @@ AggregatorDeclaration:
         "extern" "aggregator" name=Identifier ".";
 
 enum ReferenceKind:
-        REFERENCE="refers" | CONTAINMENT="contains" | CONTAINER="container";
+        REFERENCE="refers" | CONTAINMENT="contains" | CONTAINER="container" | PARTIAL="partial";
 
 ReferenceDeclaration:
         (referenceType=[Relation|NonContainmentQualifiedName] |
@@ -75,35 +75,40 @@ Conjunction:
 //
 //Case:
 //      Conjunction ({Match.condition=current} "->" value=Expr)?;
-//RuleDefinition:
-//      "rule"
-//      name=Identifier
-//      "(" (parameters+=Parameter ("," parameters+=Parameter)*)? ")"
-//      (":" preconditions+=Conjunction (";" preconditions+=Conjunction)*)?
-//      "==>" consequents+=Consequent (";" consequents+=Consequent)*)?
-//      ".";
+
+enum RuleKind:
+        DECISION="decision" | PROPAGATION="propagation";
+
+RuleDefinition:
+        kind=RuleKind? "rule"
+        name=Identifier
+        "(" (parameters+=Parameter ("," parameters+=Parameter)*)? ")"
+        ("<->" preconditions+=Conjunction (";" preconditions+=Conjunction)*)?
+        ("==>" consequents+=Consequent (";" consequents+=Consequent)*)?
+        ".";
+
+enum ParameterBinding:
+        FOCUS="&" | MULTI="*";
 
 Parameter:
-        parameterType=[Relation|QualifiedName]? name=Identifier;
+        (
+                (concreteness=Concreteness? modality=Modality)?
+                parameterType=[Relation|QualifiedName]
+        )? binding=ParameterBinding? name=Identifier;
 
-//Consequent:
-//      actions+=Action ("," actions+=Action)*;
-//
-//Action:
-//      AssertionAction | DeleteAction | NewAction;
-//
-//AssertionAction:
-//      value=ShortLogicValue? atom=Atom |
-//      atom=Atom (overwrite?=":=" | "<:") value=LogicValue;
-//
-//DeleteAction:
-//      "delete" variableOrNode=[VariableOrNode|QualifiedName];
-//
-//NewAction:
-//      "new" variable=NewVariable ("<:" parent=[VariableOrNode|QualifiedName])?;
-//
-//NewVariable:
-//      name=Identifier;
+Consequent:
+        actions+=Action ("," actions+=Action)*;
+
+Action:
+        AssertionAction;
+
+AssertionAction:
+        relation=[Relation|QualifiedName]
+        "(" (arguments+=AssertionArgument ("," arguments+=AssertionArgument)*)? ")"
+        ":" value=Expr |
+        value=ShortLogicConstant
+        relation=[Relation|QualifiedName]
+        "(" (arguments+=AssertionArgument ("," arguments+=AssertionArgument)*)? ")";
 
 Expr:
         AssignmentExpr;
@@ -159,7 +164,7 @@ RangeExpr returns Expr:
 
 UnaryExpr returns Expr:
         ArithmeticUnaryExpr | NegationExpr |
-        CountExpr | AggregationExpr | CastExpr;
+        CountExpr | AggregationExpr | ModalExpr | CastExpr;
 
 enum UnaryOp:
         PLUS="+" | MINUS="-";
@@ -177,6 +182,15 @@ AggregationExpr:
         aggregator=[AggregatorDeclaration|QualifiedName]
         "{" value=Expr "|" condition=ComparisonExpr "}";
 
+enum Concreteness:
+        CANDIDATE="candidate";
+
+enum Modality:
+        MUST="must" | MAY="may";
+
+ModalExpr:
+        concreteness=Concreteness? modality=Modality body=UnaryExpr;
+
 CastExpr returns Expr:
         CastExprBody ({CastExpr.body=current} "as" targetType=[Relation|QualifiedName])?;
 
@@ -281,7 +295,7 @@ Identifier:
 
 NonContainmentIdentifier:
         ID | "atom" | "multi" | "contained" | "problem" | "module" |
-        "datatype" | "aggregator";
+        "datatype" | "aggregator" | "decision" | "propagation";
 
 Real returns ecore::EDouble:
         EXPONENTIAL | INT "." (INT | EXPONENTIAL);
diff --git a/subprojects/language/src/main/java/tools/refinery/language/formatting2/ProblemFormatter.java b/subprojects/language/src/main/java/tools/refinery/language/formatting2/ProblemFormatter.java
index d6ece1ea..c6fca89a 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/formatting2/ProblemFormatter.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/formatting2/ProblemFormatter.java
@@ -35,7 +35,7 @@ public class ProblemFormatter extends AbstractJavaFormatter {
                 surroundNewLines(doc, assertion, this::singleNewLine);
                 var region = regionFor(assertion);
                 doc.append(region.feature(ProblemPackage.Literals.ASSERTION__DEFAULT), this::oneSpace);
-                doc.append(region.feature(ProblemPackage.Literals.ASSERTION__RELATION), this::noSpace);
+                doc.append(region.feature(ProblemPackage.Literals.ABSTRACT_ASSERTION__RELATION), this::noSpace);
                 formatParenthesizedList(region, doc);
                 for (var argument : assertion.getArguments()) {
                         doc.format(argument);
diff --git a/subprojects/language/src/main/java/tools/refinery/language/resource/ProblemResourceDescriptionStrategy.java b/subprojects/language/src/main/java/tools/refinery/language/resource/ProblemResourceDescriptionStrategy.java
index 8fd60364..505c7787 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/resource/ProblemResourceDescriptionStrategy.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/resource/ProblemResourceDescriptionStrategy.java
@@ -154,6 +154,9 @@ public class ProblemResourceDescriptionStrategy extends DefaultResourceDescripti
                         if (ProblemUtil.isTypeLike(relation)) {
                                 builder.put(TYPE_LIKE, TYPE_LIKE_TRUE);
                         }
+                } else if (eObject instanceof RuleDefinition) {
+                        // Rule definitions and predicates live in the same namespace.
+                        builder.put(SHADOWING_KEY, SHADOWING_KEY_RELATION);
                 } else if (eObject instanceof AggregatorDeclaration) {
                         builder.put(SHADOWING_KEY, SHADOWING_KEY_AGGREGATOR);
                 }
diff --git a/subprojects/language/src/main/java/tools/refinery/language/scoping/ProblemScopeProvider.java b/subprojects/language/src/main/java/tools/refinery/language/scoping/ProblemScopeProvider.java
index d94c9a13..21f64236 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/scoping/ProblemScopeProvider.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/scoping/ProblemScopeProvider.java
@@ -31,11 +31,11 @@ public class ProblemScopeProvider extends AbstractProblemScopeProvider {
         public IScope getScope(EObject context, EReference reference) {
                 var scope = super.getScope(context, reference);
                 if (reference == ProblemPackage.Literals.NODE_ASSERTION_ARGUMENT__NODE) {
-                        return getNodesScope(context, scope);
+                        // On the right side of a rule, assertion arguments may refer to variables.
+                        var rule = EcoreUtil2.getContainerOfType(context, RuleDefinition.class);
+                        return rule == null ? getNodesScope(context, scope) : getVariableScope(context, scope);
                 }
-                if (reference == ProblemPackage.Literals.VARIABLE_OR_NODE_EXPR__VARIABLE_OR_NODE
-                                || reference == ProblemPackage.Literals.NEW_ACTION__PARENT
-                                || reference == ProblemPackage.Literals.DELETE_ACTION__VARIABLE_OR_NODE) {
+                if (reference == ProblemPackage.Literals.VARIABLE_OR_NODE_EXPR__VARIABLE_OR_NODE) {
                         return getVariableScope(context, scope);
                 }
                 if (reference == ProblemPackage.Literals.REFERENCE_DECLARATION__OPPOSITE) {
@@ -81,13 +81,6 @@ public class ProblemScopeProvider extends AbstractProblemScopeProvider {
                 switch (currentContext) {
                 case ExistentialQuantifier quantifier -> variables.addAll(quantifier.getImplicitVariables());
                 case Match match -> variables.addAll(match.getCondition().getImplicitVariables());
-                case Consequent consequent -> {
-                        for (var literal : consequent.getActions()) {
-                                if (literal instanceof NewAction newAction && newAction.getVariable() != null) {
-                                        variables.add(newAction.getVariable());
-                                }
-                        }
-                }
                 default -> {
                         // Nothing to add.
                 }
diff --git a/subprojects/language/src/main/java/tools/refinery/language/serializer/PreferShortAssertionsProblemSemanticSequencer.java b/subprojects/language/src/main/java/tools/refinery/language/serializer/PreferShortAssertionsProblemSemanticSequencer.java
index 3432b2d8..225bf49d 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/serializer/PreferShortAssertionsProblemSemanticSequencer.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/serializer/PreferShortAssertionsProblemSemanticSequencer.java
@@ -12,9 +12,11 @@ import org.eclipse.xtext.serializer.sequencer.ITransientValueService.ValueTransi
 import tools.refinery.language.model.problem.Assertion;
 import tools.refinery.language.model.problem.LogicConstant;
 import tools.refinery.language.model.problem.LogicValue;
-import tools.refinery.language.model.problem.ProblemPackage;
 import tools.refinery.language.services.ProblemGrammarAccess;
 
+import static tools.refinery.language.model.problem.ProblemPackage.Literals.ABSTRACT_ASSERTION__ARGUMENTS;
+import static tools.refinery.language.model.problem.ProblemPackage.Literals.ABSTRACT_ASSERTION__RELATION;
+
 public class PreferShortAssertionsProblemSemanticSequencer extends ProblemSemanticSequencer {
         @Inject
         private ProblemGrammarAccess grammarAccess;
@@ -27,13 +29,13 @@ public class PreferShortAssertionsProblemSemanticSequencer extends ProblemSemant
                         return;
                 }
                 if (errorAcceptor != null) {
-                        if (transientValues.isValueTransient(semanticObject, ProblemPackage.Literals.ASSERTION__RELATION) == ValueTransient.YES) {
+                        if (transientValues.isValueTransient(semanticObject, ABSTRACT_ASSERTION__RELATION) == ValueTransient.YES) {
                                 errorAcceptor.accept(diagnosticProvider.createFeatureValueMissing(semanticObject,
-                                                ProblemPackage.Literals.ASSERTION__RELATION));
+                                                ABSTRACT_ASSERTION__RELATION));
                         }
-                        if (transientValues.isListTransient(semanticObject, ProblemPackage.Literals.ASSERTION__ARGUMENTS) == ListTransient.YES) {
+                        if (transientValues.isListTransient(semanticObject, ABSTRACT_ASSERTION__ARGUMENTS) == ListTransient.YES) {
                                 errorAcceptor.accept(diagnosticProvider.createFeatureValueMissing(semanticObject,
-                                                ProblemPackage.Literals.ASSERTION__ARGUMENTS));
+                                                ABSTRACT_ASSERTION__ARGUMENTS));
                         }
                 }
                 var feeder = createSequencerFeeder(context, semanticObject);
diff --git a/subprojects/language/src/main/java/tools/refinery/language/typesystem/ExprType.java b/subprojects/language/src/main/java/tools/refinery/language/typesystem/ExprType.java
index 9e44063d..65721924 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/typesystem/ExprType.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/typesystem/ExprType.java
@@ -8,6 +8,7 @@ package tools.refinery.language.typesystem;
 public sealed interface ExprType permits FixedType, MutableType {
         NodeType NODE = new NodeType();
         LiteralType LITERAL = new LiteralType();
+        ModalLiteralType MODAL_LITERAL = new ModalLiteralType();
         InvalidType INVALID = new InvalidType();
 
         FixedType getActualType();
diff --git a/subprojects/language/src/main/java/tools/refinery/language/typesystem/FixedType.java b/subprojects/language/src/main/java/tools/refinery/language/typesystem/FixedType.java
index 1b2ded48..f9e75f26 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/typesystem/FixedType.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/typesystem/FixedType.java
@@ -5,7 +5,8 @@
  */
 package tools.refinery.language.typesystem;
 
-public sealed interface FixedType extends ExprType permits NodeType, LiteralType, InvalidType, DataExprType {
+public sealed interface FixedType extends ExprType permits NodeType, LiteralType, ModalLiteralType, InvalidType,
+                DataExprType {
         @Override
         default FixedType getActualType() {
                 return this;
diff --git a/subprojects/language/src/main/java/tools/refinery/language/typesystem/ModalLiteralType.java b/subprojects/language/src/main/java/tools/refinery/language/typesystem/ModalLiteralType.java
new file mode 100644
index 00000000..6b44977a
--- /dev/null
+++ b/subprojects/language/src/main/java/tools/refinery/language/typesystem/ModalLiteralType.java
@@ -0,0 +1,16 @@
+/*
+ * SPDX-FileCopyrightText: 2024 The Refinery Authors <https://refinery.tools/>
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ */
+package tools.refinery.language.typesystem;
+
+public final class ModalLiteralType implements FixedType {
+        ModalLiteralType() {
+        }
+
+        @Override
+        public String toString() {
+                return "modal constraint";
+        }
+}
diff --git a/subprojects/language/src/main/java/tools/refinery/language/typesystem/TypedModule.java b/subprojects/language/src/main/java/tools/refinery/language/typesystem/TypedModule.java
index 6691f0ae..63815506 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/typesystem/TypedModule.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/typesystem/TypedModule.java
@@ -63,6 +63,7 @@ public class TypedModule {
                 for (var statement : problem.getStatements()) {
                         switch (statement) {
                         case PredicateDefinition predicateDefinition -> checkTypes(predicateDefinition);
+                        case RuleDefinition ruleDefinition -> checkTypes(ruleDefinition);
                         case Assertion assertion -> checkTypes(assertion);
                         default -> {
                                 // Nothing to type check.
@@ -79,13 +80,33 @@ public class TypedModule {
                 }
         }
 
+        private void checkTypes(RuleDefinition ruleDefinition) {
+                for (var conjunction : ruleDefinition.getPreconditions()) {
+                        for (var literal : conjunction.getLiterals()) {
+                                expectType(literal, ExprType.MODAL_LITERAL);
+                        }
+                }
+                for (var consequent : ruleDefinition.getConsequents()) {
+                        for (var action : consequent.getActions()) {
+                                if (action instanceof AssertionAction assertionAction) {
+                                        checkTypes(assertionAction);
+                                }
+                        }
+                }
+        }
+
         private void checkTypes(Assertion assertion) {
+                checkAssertionValueType(assertion);
+                checkNodeAssertionArgumentTypes(assertion, false);
+        }
+
+        private void checkAssertionValueType(AbstractAssertion assertion) {
                 var relation = assertion.getRelation();
-                var value = assertion.getValue();
                 if (relation == null) {
                         return;
                 }
                 var type = signatureProvider.getSignature(relation).resultType();
+                var value = assertion.getValue();
                 if (type == ExprType.LITERAL) {
                         if (value == null) {
                                 return;
@@ -95,11 +116,43 @@ public class TypedModule {
                 }
                 if (value == null) {
                         var message = "Assertion value of type %s is required.".formatted(type);
-                        error(message, assertion, ProblemPackage.Literals.ASSERTION__RELATION, 0, ProblemValidator.TYPE_ERROR);
+                        error(message, assertion, ProblemPackage.Literals.ABSTRACT_ASSERTION__VALUE, 0,
+                    ProblemValidator.TYPE_ERROR);
                 }
                 expectType(value, type);
         }
 
+        private void checkNodeAssertionArgumentTypes(AbstractAssertion assertion, boolean allowVariables) {
+                for (var argument : assertion.getArguments()) {
+                        if (argument instanceof NodeAssertionArgument nodeAssertionArgument) {
+                                checkNodeAssertionArgumentType(nodeAssertionArgument, allowVariables);
+                        }
+                }
+        }
+
+        private void checkNodeAssertionArgumentType(NodeAssertionArgument nodeAssertionArgument, boolean allowVariables) {
+                var variableOrNode = nodeAssertionArgument.getNode();
+                if (variableOrNode == null || variableOrNode.eIsProxy()) {
+                        return;
+                }
+                if (allowVariables && variableOrNode instanceof Variable variable) {
+                        var variableType = getVariableType(variable);
+                        if (variableType == ExprType.INVALID || variableType == ExprType.NODE) {
+                                return;
+                        }
+                }
+                if (variableOrNode instanceof Node) {
+                        return;
+                }
+                error("Assertion argument must be a node.", nodeAssertionArgument,
+                                ProblemPackage.Literals.NODE_ASSERTION_ARGUMENT__NODE, 0, ProblemValidator.TYPE_ERROR);
+        }
+
+        private void checkTypes(AssertionAction assertionAction) {
+                checkAssertionValueType(assertionAction);
+                checkNodeAssertionArgumentTypes(assertionAction, true);
+        }
+
         public List<FeatureBasedDiagnostic> getDiagnostics() {
                 return diagnostics;
         }
@@ -202,6 +255,7 @@ public class TypedModule {
                         case RangeExpr rangeExpr -> computeExpressionType(rangeExpr);
                         case ArithmeticBinaryExpr arithmeticBinaryExpr -> computeExpressionType(arithmeticBinaryExpr);
                         case CastExpr castExpr -> computeExpressionType(castExpr);
+                        case ModalExpr modalExpr -> computeExpressionType(modalExpr);
                         default -> {
                                 error("Unknown expression: " + expr.getClass().getSimpleName(), expr, null, 0,
                                                 ProblemValidator.UNKNOWN_EXPRESSION_ISSUE);
@@ -290,6 +344,9 @@ public class TypedModule {
                         // Negation of literals yields another (non-enumerable) literal.
                         return ExprType.LITERAL;
                 }
+                if (actualType == ExprType.MODAL_LITERAL) {
+                        return ExprType.MODAL_LITERAL;
+                }
                 if (actualType == ExprType.INVALID) {
                         return ExprType.INVALID;
                 }
@@ -507,6 +564,28 @@ public class TypedModule {
                 return ExprType.INVALID;
         }
 
+        @NotNull
+        private ExprType computeExpressionType(ModalExpr expr) {
+                var body = expr.getBody();
+                if (body == null) {
+                        return ExprType.INVALID;
+                }
+                var actualType = getExpressionType(body);
+                if (actualType == ExprType.LITERAL || BuiltinTermInterpreter.BOOLEAN_TYPE.equals(actualType)) {
+                        return ExprType.MODAL_LITERAL;
+                }
+                if (actualType == ExprType.INVALID) {
+                        return ExprType.INVALID;
+                }
+                if (actualType instanceof MutableType) {
+                        error(OPERAND_TYPE_ERROR_MESSAGE, body, null, 0, ProblemValidator.TYPE_ERROR);
+                        return ExprType.INVALID;
+                }
+                var message = "Data type %s does not support modal operators.".formatted(actualType);
+                error(message, expr, null, 0, ProblemValidator.TYPE_ERROR);
+                return ExprType.INVALID;
+        }
+
         private FixedType getCommonDataType(BinaryExpr expr) {
                 var commonType = getCommonType(expr);
                 if (!(commonType instanceof DataExprType) && commonType != ExprType.INVALID) {
diff --git a/subprojects/language/src/main/java/tools/refinery/language/utils/ProblemUtil.java b/subprojects/language/src/main/java/tools/refinery/language/utils/ProblemUtil.java
index 9daa8f61..e1820261 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/utils/ProblemUtil.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/utils/ProblemUtil.java
@@ -42,13 +42,11 @@ public final class ProblemUtil {
         }
 
         public static boolean isImplicit(EObject eObject) {
-                if (eObject instanceof Node node) {
-                        return isImplicitNode(node);
-                } else if (eObject instanceof Variable variable) {
-                        return isImplicitVariable(variable);
-                } else {
-                        return false;
-                }
+                return switch (eObject) {
+                        case Node node -> isImplicitNode(node);
+                        case Variable variable -> isImplicitVariable(variable);
+                        default -> false;
+                };
         }
 
         public static boolean isError(EObject eObject) {
@@ -119,7 +117,7 @@ public final class ProblemUtil {
                         return false;
                 }
                 return switch (kind) {
-                        case CONTAINMENT -> false;
+                        case CONTAINMENT, PARTIAL -> false;
                         case CONTAINER -> true;
                         case DEFAULT, REFERENCE -> {
                                 var opposite = referenceDeclaration.getOpposite();
diff --git a/subprojects/language/src/main/java/tools/refinery/language/validation/ActionTargetCollector.java b/subprojects/language/src/main/java/tools/refinery/language/validation/ActionTargetCollector.java
new file mode 100644
index 00000000..67cd5777
--- /dev/null
+++ b/subprojects/language/src/main/java/tools/refinery/language/validation/ActionTargetCollector.java
@@ -0,0 +1,73 @@
+/*
+ * SPDX-FileCopyrightText: 2024 The Refinery Authors <https://refinery.tools/>
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ */
+package tools.refinery.language.validation;
+
+import com.google.inject.Inject;
+import com.google.inject.Singleton;
+import org.eclipse.xtext.EcoreUtil2;
+import org.eclipse.xtext.util.IResourceScopeCache;
+import org.eclipse.xtext.util.Tuples;
+import tools.refinery.language.model.problem.*;
+
+import java.util.HashSet;
+import java.util.Set;
+
+@Singleton
+public class ActionTargetCollector {
+        private static final String ACTION_TARGETS =
+                        "tools.refinery.language.validation.ActionTargetCollector.ACTION_TARGETS";
+
+        @Inject
+        private IResourceScopeCache cache = IResourceScopeCache.NullImpl.INSTANCE;
+
+        public boolean isActionTarget(Relation relation) {
+                var problem = EcoreUtil2.getContainerOfType(relation, Problem.class);
+                return problem != null && isActionTarget(problem, relation);
+        }
+
+        public boolean isActionTarget(Problem problem, Relation relation) {
+                var targets = getActionTargets(problem);
+                if (targets.contains(relation)) {
+                        return true;
+                }
+                if (relation instanceof ReferenceDeclaration referenceDeclaration) {
+                        var opposite = referenceDeclaration.getOpposite();
+                        return opposite != null && targets.contains(opposite);
+                }
+                return false;
+        }
+
+        protected Set<Relation> getActionTargets(Problem problem) {
+                var resource = problem.eResource();
+                if (resource == null) {
+                        return doGetActionTargets(problem);
+                }
+                return cache.get(Tuples.create(problem, ACTION_TARGETS), resource, () -> doGetActionTargets(problem));
+        }
+
+        protected Set<Relation> doGetActionTargets(Problem problem) {
+                var targets = new HashSet<Relation>();
+                for (var statement : problem.getStatements()) {
+                        if (statement instanceof RuleDefinition ruleDefinition) {
+                                collectTargets(ruleDefinition, targets);
+                        }
+                }
+                return targets;
+        }
+
+        private static void collectTargets(RuleDefinition ruleDefinition, HashSet<Relation> targets) {
+                for (var consequent : ruleDefinition.getConsequents()) {
+                        for (var action : consequent.getActions()) {
+                                if (action instanceof AssertionAction assertionAction) {
+                                        var target = assertionAction.getRelation();
+                                        if (target != null) {
+                                                targets.add(target);
+                                        }
+                                }
+                        }
+                }
+        }
+}
diff --git a/subprojects/language/src/main/java/tools/refinery/language/validation/ExistsVariableCollector.java b/subprojects/language/src/main/java/tools/refinery/language/validation/ExistsVariableCollector.java
new file mode 100644
index 00000000..5812bdc4
--- /dev/null
+++ b/subprojects/language/src/main/java/tools/refinery/language/validation/ExistsVariableCollector.java
@@ -0,0 +1,75 @@
+/*
+ * SPDX-FileCopyrightText: 2024 The Refinery Authors <https://refinery.tools/>
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ */
+package tools.refinery.language.validation;
+
+import com.google.inject.Inject;
+import com.google.inject.Singleton;
+import org.eclipse.xtext.EcoreUtil2;
+import org.eclipse.xtext.util.IResourceScopeCache;
+import org.eclipse.xtext.util.Tuples;
+import tools.refinery.language.model.problem.*;
+import tools.refinery.language.scoping.imports.ImportAdapterProvider;
+import tools.refinery.language.utils.ProblemUtil;
+
+import java.util.HashSet;
+import java.util.Set;
+
+@Singleton
+public class ExistsVariableCollector {
+        private static final String EXISTS_VARIABLES =
+                        "tools.refinery.language.validation.ExistsVariableCollector.EXISTS_VARIABLES";
+
+        @Inject
+        private IResourceScopeCache cache = IResourceScopeCache.NullImpl.INSTANCE;
+
+        @Inject
+        private ImportAdapterProvider importAdapterProvider;
+
+        public boolean missingExistsConstraint(Variable variable) {
+                if (variable instanceof Parameter) {
+                        return false;
+                }
+                if (ProblemUtil.isImplicitVariable(variable)) {
+                        var negation = EcoreUtil2.getContainerOfType(variable, NegationExpr.class);
+                        if (negation != null) {
+                                // Negations are implicitly quantified.
+                                return false;
+                        }
+                }
+                var conjunction = EcoreUtil2.getContainerOfType(variable, Conjunction.class);
+                if (conjunction == null) {
+                        return true;
+                }
+                var variables = getExistsVariables(conjunction);
+                return !variables.contains(variable);
+        }
+
+        protected Set<Variable> getExistsVariables(Conjunction conjunction) {
+                var resource = conjunction.eResource();
+                if (resource == null) {
+                        return doGetExistsVariables(conjunction);
+                }
+                return cache.get(Tuples.create(conjunction, EXISTS_VARIABLES), resource,
+                                () -> doGetExistsVariables(conjunction));
+        }
+
+        protected Set<Variable> doGetExistsVariables(Conjunction conjunction) {
+                var builtinSymbols = importAdapterProvider.getBuiltinSymbols(conjunction);
+                var existsRelation = builtinSymbols.exists();
+                var set = new HashSet<Variable>();
+                for (var atom : EcoreUtil2.getAllContentsOfType(conjunction, Atom.class)) {
+                        if (existsRelation.equals(atom.getRelation())) {
+                                for (var argument : atom.getArguments()) {
+                                        if (argument instanceof VariableOrNodeExpr variableOrNodeExpr &&
+                                                        variableOrNodeExpr.getVariableOrNode() instanceof Variable variable) {
+                                                set.add(variable);
+                                        }
+                                }
+                        }
+                }
+                return set;
+        }
+}
diff --git a/subprojects/language/src/main/java/tools/refinery/language/validation/ProblemValidator.java b/subprojects/language/src/main/java/tools/refinery/language/validation/ProblemValidator.java
index 745e2d2b..84218f17 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/validation/ProblemValidator.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/validation/ProblemValidator.java
@@ -24,10 +24,7 @@ import tools.refinery.language.typesystem.ProblemTypeAnalyzer;
 import tools.refinery.language.typesystem.SignatureProvider;
 import tools.refinery.language.utils.ProblemUtil;
 
-import java.util.ArrayList;
-import java.util.LinkedHashMap;
-import java.util.LinkedHashSet;
-import java.util.Set;
+import java.util.*;
 
 /**
  * This class contains custom validation rules.
@@ -49,17 +46,26 @@ public class ProblemValidator extends AbstractProblemValidator {
         public static final String INVALID_SUPERTYPE_ISSUE = ISSUE_PREFIX + "INVALID_SUPERTYPE";
         public static final String INVALID_REFERENCE_TYPE_ISSUE = ISSUE_PREFIX + "INVALID_REFERENCE_TYPE";
         public static final String INVALID_ARITY_ISSUE = ISSUE_PREFIX + "INVALID_ARITY";
+        public static final String INVALID_MODALITY_ISSUE = ISSUE_PREFIX + "INVALID_MODALITY";
+        public static final String INVALID_RULE_ISSUE = ISSUE_PREFIX + "INVALID_RULE";
         public static final String INVALID_TRANSITIVE_CLOSURE_ISSUE = ISSUE_PREFIX + "INVALID_TRANSITIVE_CLOSURE";
-        public static final String INVALID_VALUE_ISSUE = ISSUE_PREFIX + "INVALID_VALUE";
         public static final String UNSUPPORTED_ASSERTION_ISSUE = ISSUE_PREFIX + "UNSUPPORTED_ASSERTION";
         public static final String UNKNOWN_EXPRESSION_ISSUE = ISSUE_PREFIX + "UNKNOWN_EXPRESSION";
         public static final String INVALID_ASSIGNMENT_ISSUE = ISSUE_PREFIX + "INVALID_ASSIGNMENT";
         public static final String TYPE_ERROR = ISSUE_PREFIX + "TYPE_ERROR";
+        public static final String VARIABLE_WITHOUT_EXISTS = ISSUE_PREFIX + "VARIABLE_WITHOUT_EXISTS";
+        public static final String UNUSED_PARTIAL_RELATION = ISSUE_PREFIX + "UNUSED_PARTIAL_RELATION";
 
         @Inject
         private ReferenceCounter referenceCounter;
 
         @Inject
+        private ExistsVariableCollector existsVariableCollector;
+
+        @Inject
+        private ActionTargetCollector actionTargetCollector;
+
+        @Inject
         private IQualifiedNameConverter qualifiedNameConverter;
 
         @Inject
@@ -128,6 +134,14 @@ public class ProblemValidator extends AbstractProblemValidator {
                 var variableOrNode = expr.getVariableOrNode();
                 if (variableOrNode instanceof Variable variable && ProblemUtil.isImplicitVariable(variable)
                                 && !ProblemUtil.isSingletonVariable(variable)) {
+                        if (EcoreUtil2.getContainerOfType(variable, ParametricDefinition.class) instanceof RuleDefinition &&
+                                        EcoreUtil2.getContainerOfType(variable, NegationExpr.class) == null &&
+                                        // If there is an exists constraint, it is the only constraint.
+                                        existsVariableCollector.missingExistsConstraint(variable)) {
+                                // Existentially quantified variables in rules should not be singletons,
+                                // because we have to add an {@code exists} constraint as well.
+                                return;
+                        }
                         var problem = EcoreUtil2.getContainerOfType(variable, Problem.class);
                         if (problem != null && referenceCounter.countReferences(problem, variable) <= 1) {
                                 var name = variable.getName();
@@ -152,13 +166,32 @@ public class ProblemValidator extends AbstractProblemValidator {
         }
 
         @Check
+        public void checkNodeAssertionArgumentConstants(NodeAssertionArgument argument) {
+                var rule = EcoreUtil2.getContainerOfType(argument, RuleDefinition.class);
+                if (rule == null) {
+                        return;
+                }
+                var variableOrNode = argument.getNode();
+                if (variableOrNode instanceof Node node && !ProblemUtil.isAtomNode(node)) {
+                        var name = node.getName();
+                        var message = ("Only atoms can be referenced in rule actions. " +
+                                        "Mark '%s' as an atom with the declaration 'atom %s.'").formatted(name, name);
+                        error(message, argument, ProblemPackage.Literals.NODE_ASSERTION_ARGUMENT__NODE,
+                                        INSIGNIFICANT_INDEX, NODE_CONSTANT_ISSUE);
+                }
+        }
+
+        @Check
         public void checkUniqueDeclarations(Problem problem) {
-                var relations = new ArrayList<Relation>();
+                var relations = new ArrayList<NamedElement>();
                 var nodes = new ArrayList<Node>();
                 var aggregators = new ArrayList<AggregatorDeclaration>();
                 for (var statement : problem.getStatements()) {
                         if (statement instanceof Relation relation) {
                                 relations.add(relation);
+                        } else if (statement instanceof RuleDefinition ruleDefinition) {
+                                // Rule definitions and predicates live in the same namespace.
+                                relations.add(ruleDefinition);
                         } else if (statement instanceof NodeDeclaration nodeDeclaration) {
                                 nodes.addAll(nodeDeclaration.getNodes());
                         } else if (statement instanceof AggregatorDeclaration aggregatorDeclaration) {
@@ -298,6 +331,22 @@ public class ProblemValidator extends AbstractProblemValidator {
                                                 referenceDeclaration, ProblemPackage.Literals.REFERENCE_DECLARATION__OPPOSITE, 0,
                                                 INVALID_OPPOSITE_ISSUE);
                         }
+                } else if (kind == ReferenceKind.PARTIAL && opposite != null && opposite.getKind() != ReferenceKind.PARTIAL) {
+                        acceptError("Opposite '%s' of partial reference '%s' is not a partial reference."
+                                                        .formatted(opposite.getName(), referenceDeclaration.getName()),
+                                        referenceDeclaration, ProblemPackage.Literals.REFERENCE_DECLARATION__OPPOSITE, 0,
+                                        INVALID_OPPOSITE_ISSUE);
+                }
+        }
+
+        @Check
+        public void checkPartialReference(ReferenceDeclaration referenceDeclaration) {
+                if (referenceDeclaration.getKind() == ReferenceKind.PARTIAL &&
+                                !actionTargetCollector.isActionTarget(referenceDeclaration)) {
+                        var message = "Add decision or propagation rules to refine partial relation '%s'."
+                                                        .formatted(referenceDeclaration.getName());
+                        acceptWarning(message, referenceDeclaration, ProblemPackage.Literals.REFERENCE_DECLARATION__KIND, 0,
+                                        UNUSED_PARTIAL_RELATION);
                 }
         }
 
@@ -336,8 +385,33 @@ public class ProblemValidator extends AbstractProblemValidator {
         }
 
         @Check
-        public void checkParameterType(Parameter parameter) {
+        public void checkParameter(Parameter parameter) {
                 checkArity(parameter, ProblemPackage.Literals.PARAMETER__PARAMETER_TYPE, 1);
+                var parametricDefinition = EcoreUtil2.getContainerOfType(parameter, ParametricDefinition.class);
+                if (parametricDefinition instanceof RuleDefinition rule) {
+                        if (parameter.getParameterType() != null && parameter.getModality() == Modality.NONE) {
+                                acceptError("Parameter type modality must be specified.", parameter,
+                                                ProblemPackage.Literals.PARAMETER__PARAMETER_TYPE, 0, INVALID_MODALITY_ISSUE);
+                        }
+                        var kind = rule.getKind();
+                        var binding = parameter.getBinding();
+                        if (kind == RuleKind.PROPAGATION && binding != ParameterBinding.SINGLE) {
+                                acceptError("Parameter binding annotations are not supported in propagation rules.", parameter,
+                                                ProblemPackage.Literals.PARAMETER__BINDING, 0, INVALID_MODALITY_ISSUE);
+                        } else if (kind != RuleKind.DECISION && binding == ParameterBinding.MULTI) {
+                                acceptError("Explicit multi-object bindings are only supported in decision rules.", parameter,
+                                                ProblemPackage.Literals.PARAMETER__BINDING, 0, INVALID_MODALITY_ISSUE);
+                        }
+                } else {
+                        if (parameter.getConcreteness() != Concreteness.PARTIAL || parameter.getModality() != Modality.NONE) {
+                                acceptError("Modal parameter types are only supported in rule definitions.", parameter, null, 0,
+                                                INVALID_MODALITY_ISSUE);
+                        }
+                        if (parameter.getBinding() != ParameterBinding.SINGLE) {
+                                acceptError("Parameter binding annotations are only supported in decision rules.", parameter,
+                                                ProblemPackage.PARAMETER__BINDING, 0, INVALID_MODALITY_ISSUE);
+                        }
+                }
         }
 
         @Check
@@ -353,16 +427,46 @@ public class ProblemValidator extends AbstractProblemValidator {
         }
 
         @Check
-        public void checkAssertion(Assertion assertion) {
+        public void checkRuleDefinition(RuleDefinition ruleDefinition) {
+                if (ruleDefinition.getConsequents().size() != 1) {
+                        acceptError("Rules must have exactly one consequent.", ruleDefinition,
+                                        ProblemPackage.Literals.NAMED_ELEMENT__NAME, 0, INVALID_RULE_ISSUE);
+                }
+                var unquantifiedVariables = new HashSet<Variable>();
+                for (var variable : EcoreUtil2.getAllContentsOfType(ruleDefinition, Variable.class)) {
+                        if (existsVariableCollector.missingExistsConstraint(variable)) {
+                                unquantifiedVariables.add(variable);
+                        }
+                }
+                for (var expr : EcoreUtil2.getAllContentsOfType(ruleDefinition, VariableOrNodeExpr.class)) {
+                        if (expr.getVariableOrNode() instanceof Variable variable && unquantifiedVariables.contains(variable)) {
+                                unquantifiedVariables.remove(variable);
+                                var name = variable.getName();
+                                String message;
+                                if (ProblemUtil.isSingletonVariable(variable)) {
+                                        message = ("Remove the singleton variable marker '_' and clarify the quantification of variable " +
+                            "'%s'.").formatted(name);
+                                } else {
+                                        message = ("Add a 'must exists(%s)', 'may exists(%s)', or 'may !exists(%s)' constraint to " +
+                                                        "clarify the quantification of variable '%s'.").formatted(name, name, name, name);
+                                }
+                                acceptWarning(message, expr, ProblemPackage.Literals.VARIABLE_OR_NODE_EXPR__VARIABLE_OR_NODE, 0,
+                                                VARIABLE_WITHOUT_EXISTS);
+                        }
+                }
+        }
+
+        @Check
+        public void checkAssertion(AbstractAssertion assertion) {
                 var relation = assertion.getRelation();
                 if (relation instanceof DatatypeDeclaration) {
                         var message = "Assertions for data types are not supported.";
-                        acceptError(message, assertion, ProblemPackage.Literals.ASSERTION__RELATION, 0,
+                        acceptError(message, assertion, ProblemPackage.Literals.ABSTRACT_ASSERTION__RELATION, 0,
                                         UNSUPPORTED_ASSERTION_ISSUE);
                         return;
                 }
                 int argumentCount = assertion.getArguments().size();
-                checkArity(assertion, ProblemPackage.Literals.ASSERTION__RELATION, argumentCount);
+                checkArity(assertion, ProblemPackage.Literals.ABSTRACT_ASSERTION__RELATION, argumentCount);
         }
 
         @Check
@@ -466,15 +570,17 @@ public class ProblemValidator extends AbstractProblemValidator {
 
         @Nullable
         private Node getNodeArgumentForMultiObjectAssertion(AssertionArgument argument) {
-                if (argument instanceof WildcardAssertionArgument) {
-                        acceptError("Wildcard arguments for 'exists' are not supported.", argument, null, 0,
-                                        UNSUPPORTED_ASSERTION_ISSUE);
-                        return null;
-                }
-                if (argument instanceof NodeAssertionArgument nodeAssertionArgument) {
-                        return nodeAssertionArgument.getNode();
-                }
-                throw new IllegalArgumentException("Unknown assertion argument: " + argument);
+                return switch (argument) {
+                        case null -> null;
+                        case WildcardAssertionArgument ignoredWildcardAssertionArgument -> {
+                                acceptError("Wildcard arguments for 'exists' are not supported.", argument, null, 0,
+                                                UNSUPPORTED_ASSERTION_ISSUE);
+                                yield null;
+                        }
+                        case NodeAssertionArgument nodeAssertionArgument ->
+                                        nodeAssertionArgument.getNode() instanceof Node node ? node : null;
+                        default -> throw new IllegalArgumentException("Unknown assertion argument: " + argument);
+                };
         }
 
         @Check
@@ -484,8 +590,10 @@ public class ProblemValidator extends AbstractProblemValidator {
                 }
                 for (var argument : assertion.getArguments()) {
                         if (argument instanceof NodeAssertionArgument nodeAssertionArgument) {
-                                var node = nodeAssertionArgument.getNode();
-                                if (node != null && !node.eIsProxy() && ProblemUtil.isImplicitNode(node)) {
+                                var variableOrNode = nodeAssertionArgument.getNode();
+                                if (variableOrNode instanceof Node node &&
+                                                !variableOrNode.eIsProxy() &&
+                                                ProblemUtil.isImplicitNode(node)) {
                                         var name = node.getName();
                                         var message = ("Implicit nodes are not allowed in modules. Explicitly declare '%s' as a node " +
                                                         "with the declaration 'declare %s.'").formatted(name, name);
diff --git a/subprojects/language/src/main/java/tools/refinery/language/validation/ReferenceCounter.java b/subprojects/language/src/main/java/tools/refinery/language/validation/ReferenceCounter.java
index 55cbd71d..40781168 100644
--- a/subprojects/language/src/main/java/tools/refinery/language/validation/ReferenceCounter.java
+++ b/subprojects/language/src/main/java/tools/refinery/language/validation/ReferenceCounter.java
@@ -5,20 +5,21 @@
  */
 package tools.refinery.language.validation;
 
-import java.util.HashMap;
-import java.util.Map;
-
+import com.google.inject.Inject;
+import com.google.inject.Singleton;
 import org.eclipse.emf.ecore.EObject;
 import org.eclipse.xtext.util.IResourceScopeCache;
 import org.eclipse.xtext.util.Tuples;
-
-import com.google.inject.Inject;
-import com.google.inject.Singleton;
-
 import tools.refinery.language.model.problem.Problem;
 
+import java.util.HashMap;
+import java.util.Map;
+
 @Singleton
 public class ReferenceCounter {
+        private static final String REFERENCE_COUNTS =
+                        "tools.refinery.language.validation.ReferenceCounter.REFERENCE_COUNTS";
+
         @Inject
         private IResourceScopeCache cache = IResourceScopeCache.NullImpl.INSTANCE;
 
@@ -35,7 +36,7 @@ public class ReferenceCounter {
                 if (resource == null) {
                         return doGetReferenceCounts(problem);
                 }
-                return cache.get(Tuples.create(problem, "referenceCounts"), resource, () -> doGetReferenceCounts(problem));
+                return cache.get(Tuples.create(problem, REFERENCE_COUNTS), resource, () -> doGetReferenceCounts(problem));
         }
 
         protected Map<EObject, Integer> doGetReferenceCounts(Problem problem) {
diff --git a/subprojects/language/src/test/java/tools/refinery/language/tests/rules/RuleParsingTest.java b/subprojects/language/src/test/java/tools/refinery/language/tests/rules/RuleParsingTest.java
index 56e65550..15636483 100644
--- a/subprojects/language/src/test/java/tools/refinery/language/tests/rules/RuleParsingTest.java
+++ b/subprojects/language/src/test/java/tools/refinery/language/tests/rules/RuleParsingTest.java
@@ -9,7 +9,6 @@ import com.google.inject.Inject;
 import org.eclipse.xtext.testing.InjectWith;
 import org.eclipse.xtext.testing.extensions.InjectionExtension;
 import org.junit.jupiter.api.Disabled;
-import org.junit.jupiter.api.Test;
 import org.junit.jupiter.api.extension.ExtendWith;
 import org.junit.jupiter.params.ParameterizedTest;
 import org.junit.jupiter.params.provider.ValueSource;
@@ -17,7 +16,7 @@ import tools.refinery.language.model.tests.utils.ProblemParseHelper;
 import tools.refinery.language.tests.ProblemInjectorProvider;
 
 import static org.hamcrest.MatcherAssert.assertThat;
-import static org.hamcrest.Matchers.*;
+import static org.hamcrest.Matchers.empty;
 
 @Disabled("TODO: Rework transformation rules")
 @ExtendWith(InjectionExtension.class)
@@ -29,62 +28,13 @@ class RuleParsingTest {
         @ParameterizedTest
         @ValueSource(strings = { """
                         pred Person(p).
-                        rule r(p1): must Person(p1) ==> Person(p1) := false.
-                        """, """
-                        pred Person(p).
-                        rule r(p1): must Person(p1) ==> Person(p1) <: false.
+                        rule r(p1): must Person(p1) ==> Person(p1): false.
                         """, """
                         pred Person(p).
                         rule r(p1): must Person(p1) ==> !Person(p1).
-                        """, """
-                        pred Person(p).
-                        rule r(p1): must Person(p1) ==> delete p1.
                         """ })
         void simpleTest(String text) {
                 var problem = parseHelper.parse(text);
                 assertThat(problem.getResourceErrors(), empty());
         }
-
-        @Test
-        void newNodeTest() {
-                var problem = parseHelper.parse("""
-                                pred Person(p).
-                                rule r(p1): must Person(p1) ==> new p2, Person(p2) := unknown.
-                                """);
-                assertThat(problem.getResourceErrors(), empty());
-                assertThat(problem.rule("r").param(0), equalTo(problem.rule("r").conj(0).lit(0).arg(0).variable()));
-                assertThat(problem.rule("r").consequent(0).action(0).newVar(),
-                                equalTo(problem.rule("r").consequent(0).action(1).assertedAtom().arg(0).variable()));
-        }
-
-        @Test
-        void differentScopeTest() {
-                var problem = parseHelper.parse("""
-                                pred Friend(a, b).
-                                rule r(p1): !may Friend(p1, p2) ==> new p2, Friend(p1, p2) := true.
-                                """);
-                assertThat(problem.getResourceErrors(), empty());
-                assertThat(problem.rule("r").conj(0).lit(0).negated().arg(1).variable(),
-                                not(equalTo(problem.rule("r").consequent(0).action(1).assertedAtom().arg(1).variable())));
-        }
-
-        @Test
-        void parameterShadowingTest() {
-                var problem = parseHelper.parse("""
-                                pred Friend(a, b).
-                                rule r(p1, p2): !may Friend(p1, p2) ==> new p2, Friend(p1, p2) := true.
-                                """);
-                assertThat(problem.getResourceErrors(), empty());
-                assertThat(problem.rule("r").param(1),
-                                not(equalTo(problem.rule("r").consequent(0).action(1).assertedAtom().arg(1).variable())));
-        }
-
-        @Test
-        void deleteDifferentScopeNodeTest() {
-                var problem = parseHelper.parse("""
-                                pred Person(p).
-                                rule r(p1): must Friend(p1, p2) ==> delete p2.
-                                """);
-                assertThat(problem.getResourceErrors(), not(empty()));
-        }
 }
diff --git a/subprojects/language/src/test/java/tools/refinery/language/tests/validation/OppositeValidationTest.java b/subprojects/language/src/test/java/tools/refinery/language/tests/validation/OppositeValidationTest.java
index 57602377..d73ef8e7 100644
--- a/subprojects/language/src/test/java/tools/refinery/language/tests/validation/OppositeValidationTest.java
+++ b/subprojects/language/src/test/java/tools/refinery/language/tests/validation/OppositeValidationTest.java
@@ -57,6 +57,18 @@ class OppositeValidationTest {
                         class Foo {
                                 Foo foo[] opposite foo
                         }
+                        """, """
+                        class Foo {
+                                partial Bar bar opposite foo
+                        }
+
+                        class Bar {
+                                partial Foo foo opposite bar
+                        }
+                        """, """
+                        class Foo {
+                                partial Foo foo[] opposite foo
+                        }
                         """})
         void validOppositeTest(String text) {
                 var problem = parseHelper.parse(text);
@@ -188,7 +200,7 @@ class OppositeValidationTest {
         }
 
         @ParameterizedTest
-        @ValueSource(strings = {"Foo foo", "container Foo foo"})
+        @ValueSource(strings = {"Foo foo", "container Foo foo", "partial Foo foo"})
         void containerInvalidOppositeTest(String reference) {
                 var problem = parseHelper.parse("""
                                 class Foo {
@@ -203,7 +215,27 @@ class OppositeValidationTest {
                 assertThat(issues, hasItem(allOf(
                                 hasProperty("severity", is(Diagnostic.ERROR)),
                                 hasProperty("issueCode", is(ProblemValidator.INVALID_OPPOSITE_ISSUE)),
-                                hasProperty("message", stringContainsInOrder("foo", "bar"))
+                                hasProperty("message", stringContainsInOrder("foo", "container", "bar"))
+                )));
+        }
+
+        @ParameterizedTest
+        @ValueSource(strings = {"Foo foo", "contains Foo foo", "container Foo foo"})
+        void partialWithConcreteOppositeTest(String reference) {
+                var problem = parseHelper.parse("""
+                                class Foo {
+                                        partial Bar bar opposite foo
+                                }
+
+                                class Bar {
+                                        %s opposite bar
+                                }
+                                """.formatted(reference));
+                var issues = problem.validate();
+                assertThat(issues, hasItem(allOf(
+                                hasProperty("severity", is(Diagnostic.ERROR)),
+                                hasProperty("issueCode", is(ProblemValidator.INVALID_OPPOSITE_ISSUE)),
+                                hasProperty("message", stringContainsInOrder("foo", "partial", "bar"))
                 )));
         }
 }
diff --git a/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAction.java b/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAction.java
index 3a49a0b9..4987cb89 100644
--- a/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAction.java
+++ b/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAction.java
@@ -6,25 +6,9 @@
 package tools.refinery.language.model.tests.utils;
 
 import tools.refinery.language.model.problem.Action;
-import tools.refinery.language.model.problem.AssertionAction;
-import tools.refinery.language.model.problem.DeleteAction;
-import tools.refinery.language.model.problem.NewAction;
-import tools.refinery.language.model.problem.VariableOrNode;
 
 public record WrappedAction(Action action) {
         public Action get() {
                 return action;
         }
-        
-        public VariableOrNode newVar() {
-                return ((NewAction) action).getVariable();
-        }
-        
-        public VariableOrNode deleteVar() {
-                return ((DeleteAction) action).getVariableOrNode();
-        }
-        
-        public WrappedAtom assertedAtom() {
-                return new WrappedAtom(((AssertionAction) action).getAtom());
-        }
 }
diff --git a/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAssertionArgument.java b/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAssertionArgument.java
index b36f2506..50cb958d 100644
--- a/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAssertionArgument.java
+++ b/subprojects/language/src/testFixtures/java/tools/refinery/language/model/tests/utils/WrappedAssertionArgument.java
@@ -15,6 +15,6 @@ public record WrappedAssertionArgument(AssertionArgument assertionArgument) {
         }
 
         public Node node() {
-                return ((NodeAssertionArgument) assertionArgument).getNode();
+                return (Node) ((NodeAssertionArgument) assertionArgument).getNode();
         }
 }
diff --git a/subprojects/logic/src/main/java/tools/refinery/logic/literal/ConstantLiteral.java b/subprojects/logic/src/main/java/tools/refinery/logic/literal/ConstantLiteral.java
index 688ddfa0..36cf4226 100644
--- a/subprojects/logic/src/main/java/tools/refinery/logic/literal/ConstantLiteral.java
+++ b/subprojects/logic/src/main/java/tools/refinery/logic/literal/ConstantLiteral.java
@@ -14,6 +14,8 @@ import tools.refinery.logic.term.Variable;
 import java.util.Objects;
 import java.util.Set;
 
+// {@link Object#equals(Object)} is implemented by {@link AbstractLiteral}.
+@SuppressWarnings("squid:S2160")
 public class ConstantLiteral extends AbstractLiteral {
         private final NodeVariable variable;
         private final int nodeId;
@@ -31,7 +33,6 @@ public class ConstantLiteral extends AbstractLiteral {
                 return nodeId;
         }
 
-
         @Override
         public Set<Variable> getOutputVariables() {
                 return Set.of(variable);
diff --git a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/propagation/impl/rule/BoundPropagationRule.java b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/propagation/impl/rule/BoundPropagationRule.java
index a70292ad..5f69b7a2 100644
--- a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/propagation/impl/rule/BoundPropagationRule.java
+++ b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/propagation/impl/rule/BoundPropagationRule.java
@@ -9,31 +9,54 @@ import tools.refinery.store.dse.propagation.PropagationResult;
 import tools.refinery.store.dse.transition.Rule;
 import tools.refinery.store.dse.transition.actions.BoundAction;
 import tools.refinery.store.model.Model;
+import tools.refinery.store.model.ModelListener;
 import tools.refinery.store.query.ModelQueryAdapter;
 import tools.refinery.store.query.resultset.ResultSet;
+import tools.refinery.store.tuple.Tuple;
+
+import java.util.HashSet;
 
 class BoundPropagationRule {
         private final Model model;
+        private final Rule rule;
         private final ResultSet<Boolean> resultSet;
         private final BoundAction action;
+        private final HashSet<Tuple> firedActivations = new HashSet<>();
 
         public BoundPropagationRule(Model model, Rule rule) {
                 this.model = model;
+                this.rule = rule;
                 resultSet = model.getAdapter(ModelQueryAdapter.class).getResultSet(rule.getPrecondition());
                 action = rule.createAction(model);
+                model.addListener(new ModelListener() {
+                        @Override
+                        public void afterRestore() {
+                                firedActivations.clear();
+                        }
+                });
+                resultSet.addListener((key, fromValue, toValue) -> {
+                        if (Boolean.FALSE.equals(toValue)) {
+                                firedActivations.remove(key);
+                        }
+                });
         }
 
         public PropagationResult fireAll() {
+                if (!firedActivations.isEmpty()) {
+                        throw new IllegalStateException("Stuck propagation rule '%s'.".formatted(rule.getName()));
+                }
                 if (resultSet.size() == 0) {
                         return PropagationResult.UNCHANGED;
                 }
                 var cursor = resultSet.getAll();
                 while (cursor.move()) {
                         model.checkCancelled();
-                        var result = action.fire(cursor.getKey());
+                        var tuple = cursor.getKey();
+                        var result = action.fire(tuple);
                         if (!result) {
                                 return PropagationResult.REJECTED;
                         }
+                        firedActivations.add(tuple);
                 }
                 return PropagationResult.PROPAGATED;
         }
diff --git a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/Action.java b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/Action.java
index 0ce0c3a4..edcf9526 100644
--- a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/Action.java
+++ b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/Action.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -67,7 +67,7 @@ public class Action {
                 var outputVariables = actionLiteral.getOutputVariables();
                 int size = outputVariables.size();
                 if (size == 0) {
-                        // Identity mappings use a {@code null} allocation to avoid iterating over the output tuple.
+                        // Empty mappings use a {@code null} allocation to avoid iterating over the output tuple.
                         return;
                 }
                 if (size >= 2 && new HashSet<>(outputVariables).size() != size) {
diff --git a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ActionLiterals.java b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ActionLiterals.java
index d06e2479..6bd5075b 100644
--- a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ActionLiterals.java
+++ b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ActionLiterals.java
@@ -16,6 +16,10 @@ public final class ActionLiterals {
                 throw new IllegalArgumentException("This is a static utility class and should not be instantiated directly");
         }
 
+        public static ConstantActionLiteral constant(NodeVariable variable, int nodeId) {
+                return new ConstantActionLiteral(variable, nodeId);
+        }
+
         public static <T> PutActionLiteral<T> put(Symbol<T> symbol, T value, NodeVariable... parameters) {
                 return new PutActionLiteral<>(symbol, value, List.of(parameters));
         }
diff --git a/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ConstantActionLiteral.java b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ConstantActionLiteral.java
new file mode 100644
index 00000000..fecb2960
--- /dev/null
+++ b/subprojects/store-dse/src/main/java/tools/refinery/store/dse/transition/actions/ConstantActionLiteral.java
@@ -0,0 +1,45 @@
+/*
+ * SPDX-FileCopyrightText: 2024 The Refinery Authors <https://refinery.tools/>
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ */
+package tools.refinery.store.dse.transition.actions;
+
+import tools.refinery.logic.term.NodeVariable;
+import tools.refinery.store.model.Model;
+import tools.refinery.store.tuple.Tuple;
+
+import java.util.List;
+
+public class ConstantActionLiteral extends AbstractActionLiteral {
+        private final NodeVariable variable;
+        private final int nodeId;
+
+        public ConstantActionLiteral(NodeVariable variable, int nodeId) {
+                this.variable = variable;
+                this.nodeId = nodeId;
+        }
+
+        public NodeVariable getVariable() {
+                return variable;
+        }
+
+        public int getNodeId() {
+                return nodeId;
+        }
+
+        @Override
+        public List<NodeVariable> getInputVariables() {
+                return List.of();
+        }
+
+        @Override
+        public List<NodeVariable> getOutputVariables() {
+                return List.of(variable);
+        }
+
+        @Override
+        public BoundActionLiteral bindToModel(Model model) {
+                return ignoredTuple -> Tuple.of(nodeId);
+        }
+}
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/internal/PartialClauseRewriter.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/internal/PartialClauseRewriter.java
index dc508a7b..f7e86c44 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/internal/PartialClauseRewriter.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/internal/PartialClauseRewriter.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -53,38 +53,30 @@ class PartialClauseRewriter {
                         markAsDone(literal);
                         return;
                 }
-                if (callLiteral instanceof CountLowerBoundLiteral countLowerBoundLiteral) {
-                        rewriteCountLowerBound(countLowerBoundLiteral);
-                        return;
-                }
-                if (callLiteral instanceof CountUpperBoundLiteral countUpperBoundLiteral) {
-                        rewriteCountUpperBound(countUpperBoundLiteral);
-                        return;
-                }
-                if (callLiteral instanceof CountCandidateLowerBoundLiteral countCandidateLowerBoundLiteral) {
-                        rewriteCountCandidateLowerBound(countCandidateLowerBoundLiteral);
-                        return;
-                }
-                if (callLiteral instanceof CountCandidateUpperBoundLiteral countCandidateUpperBoundLiteral) {
-                        rewriteCountCandidateUpperBound(countCandidateUpperBoundLiteral);
-                        return;
-                }
-                var target = callLiteral.getTarget();
-                if (target instanceof Dnf dnf) {
-                        rewriteRecursively(callLiteral, dnf);
-                } else if (target instanceof ModalConstraint modalConstraint) {
-                        var modality = modalConstraint.modality();
-                        var concreteness = modalConstraint.concreteness();
-                        var constraint = modalConstraint.constraint();
-                        if (constraint instanceof Dnf dnf) {
-                                rewriteRecursively(callLiteral, modality, concreteness, dnf);
-                        } else if (constraint instanceof PartialRelation partialRelation) {
-                                rewrite(callLiteral, modality, concreteness, partialRelation);
-                        } else {
-                                throw new IllegalArgumentException("Cannot interpret modal constraint: " + modalConstraint);
+                switch (callLiteral) {
+                case CountLowerBoundLiteral countLowerBoundLiteral -> rewriteCountLowerBound(countLowerBoundLiteral);
+                case CountUpperBoundLiteral countUpperBoundLiteral -> rewriteCountUpperBound(countUpperBoundLiteral);
+                case CountCandidateLowerBoundLiteral countCandidateLowerBoundLiteral ->
+                                rewriteCountCandidateLowerBound(countCandidateLowerBoundLiteral);
+                case CountCandidateUpperBoundLiteral countCandidateUpperBoundLiteral ->
+                                rewriteCountCandidateUpperBound(countCandidateUpperBoundLiteral);
+                default -> {
+                        var target = callLiteral.getTarget();
+                        switch (target) {
+                        case Dnf dnf -> rewriteRecursively(callLiteral, dnf);
+                        case ModalConstraint modalConstraint -> {
+                                var modality = modalConstraint.modality();
+                                var concreteness = modalConstraint.concreteness();
+                                var constraint = modalConstraint.constraint();
+                                switch (constraint) {
+                                case Dnf dnf -> rewriteRecursively(callLiteral, modality, concreteness, dnf);
+                                case PartialRelation partialRelation -> rewrite(callLiteral, modality, concreteness, partialRelation);
+                                default -> throw new IllegalArgumentException("Cannot interpret modal constraint: " + modalConstraint);
+                                }
                         }
-                } else {
-                        markAsDone(literal);
+                        default -> markAsDone(literal);
+                        }
+                }
                 }
         }
 
@@ -111,11 +103,11 @@ class PartialClauseRewriter {
                                 .call(CallPolarity.POSITIVE, countResult.rewrittenArguments()));
                 switch (variablesToCount.size()) {
                 case 0 -> literals.add(outputVariable.assign(new ConstantTerm<>(type, one)));
-                case 1 -> literals.add(view.call(variablesToCount.get(0),
+                case 1 -> literals.add(view.call(variablesToCount.getFirst(),
                                 outputVariable));
                 default -> {
                         var firstCount = Variable.of(type);
-                        literals.add(view.call(variablesToCount.get(0), firstCount));
+                        literals.add(view.call(variablesToCount.getFirst(), firstCount));
                         int length = variablesToCount.size();
                         Term<T> accumulator = firstCount;
                         for (int i = 1; i < length; i++) {
@@ -137,11 +129,11 @@ class PartialClauseRewriter {
         }
 
         private void rewriteCountCandidateLowerBound(CountCandidateLowerBoundLiteral literal) {
-                rewriteCandidateCount(literal, "lower", Modality.MAY);
+                rewriteCandidateCount(literal, "lower", Modality.MUST);
         }
 
         private void rewriteCountCandidateUpperBound(CountCandidateUpperBoundLiteral literal) {
-                rewriteCandidateCount(literal, "upper", Modality.MUST);
+                rewriteCandidateCount(literal, "upper", Modality.MAY);
         }
 
         private void rewriteCandidateCount(AbstractCountLiteral<Integer> literal, String name, Modality modality) {
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/interpretation/PartialNeighbourhoodCalculator.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/interpretation/PartialNeighbourhoodCalculator.java
new file mode 100644
index 00000000..859cf7c1
--- /dev/null
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/interpretation/PartialNeighbourhoodCalculator.java
@@ -0,0 +1,63 @@
+/*
+ * SPDX-FileCopyrightText: 2024 The Refinery Authors <https://refinery.tools/>
+ *
+ * SPDX-License-Identifier: EPL-2.0
+ */
+package tools.refinery.store.reasoning.interpretation;
+
+import org.eclipse.collections.api.set.primitive.IntSet;
+import tools.refinery.store.map.Cursor;
+import tools.refinery.store.model.Model;
+import tools.refinery.store.query.ModelQueryAdapter;
+import tools.refinery.store.reasoning.ReasoningAdapter;
+import tools.refinery.store.reasoning.literal.Concreteness;
+import tools.refinery.store.reasoning.representation.PartialSymbol;
+import tools.refinery.store.statecoding.StateCodeCalculatorFactory;
+import tools.refinery.store.statecoding.StateCoderResult;
+import tools.refinery.store.statecoding.neighbourhood.AbstractNeighbourhoodCalculator;
+import tools.refinery.store.tuple.Tuple;
+
+import java.util.List;
+
+public class PartialNeighbourhoodCalculator extends AbstractNeighbourhoodCalculator<PartialInterpretation<?, ?>> {
+        private final ModelQueryAdapter queryAdapter;
+
+        public static final StateCodeCalculatorFactory FACTORY =
+                        (model, ignoredInterpretations, individuals) -> new PartialNeighbourhoodCalculator(model, individuals);
+
+        protected PartialNeighbourhoodCalculator(Model model, IntSet individuals) {
+                super(model, individuals);
+                queryAdapter = model.getAdapter(ModelQueryAdapter.class);
+        }
+
+        @Override
+        public StateCoderResult calculateCodes() {
+                queryAdapter.flushChanges();
+                return super.calculateCodes();
+        }
+
+        @Override
+        protected List<PartialInterpretation<?, ?>> getInterpretations() {
+                var adapter = getModel().getAdapter(ReasoningAdapter.class);
+                var partialSymbols = adapter.getStoreAdapter().getPartialSymbols();
+                return partialSymbols.stream()
+                                .<PartialInterpretation<?, ?>>map(partialSymbol ->
+                                                adapter.getPartialInterpretation(Concreteness.PARTIAL, (PartialSymbol<?, ?>) partialSymbol))
+                                .toList();
+        }
+
+        @Override
+        protected int getArity(PartialInterpretation<?, ?> interpretation) {
+                return interpretation.getPartialSymbol().arity();
+        }
+
+        @Override
+        protected Object getNullValue(PartialInterpretation<?, ?> interpretation) {
+                return interpretation.get(Tuple.of());
+        }
+
+        @Override
+        protected Cursor<Tuple, ?> getCursor(PartialInterpretation<?, ?> interpretation) {
+                return interpretation.getAll();
+        }
+}
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/PartialRelationTranslator.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/PartialRelationTranslator.java
index 75fb3397..a9031f4c 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/PartialRelationTranslator.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/PartialRelationTranslator.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -52,6 +52,8 @@ public final class PartialRelationTranslator extends PartialSymbolTranslator<Tru
         private RelationalQuery must;
         private RelationalQuery candidateMay;
         private RelationalQuery candidateMust;
+        private RelationalQuery candidateMayMerged;
+        private RelationalQuery candidateMustMerged;
         private RoundingMode roundingMode;
 
         private PartialRelationTranslator(PartialRelation partialRelation) {
@@ -202,6 +204,7 @@ public final class PartialRelationTranslator extends PartialSymbolTranslator<Tru
                 liftQueries(storeBuilder);
                 createFallbackQueriesFromSymbol();
                 setFallbackCandidateQueries();
+                mergeCandidateQueries();
                 createFallbackRewriter();
                 createFallbackInterpretation();
                 createFallbackRefiner();
@@ -272,9 +275,11 @@ public final class PartialRelationTranslator extends PartialSymbolTranslator<Tru
                 }
                 if (candidateMay == null) {
                         candidateMay = queryBasedRelationRewriter.getCandidateMay();
+                        candidateMayMerged = candidateMay;
                 }
                 if (candidateMust == null) {
                         candidateMust = queryBasedRelationRewriter.getCandidateMust();
+                        candidateMustMerged = candidateMust;
                 }
         }
 
@@ -290,7 +295,7 @@ public final class PartialRelationTranslator extends PartialSymbolTranslator<Tru
                         candidateMay = reasoningBuilder.lift(Modality.MAY, Concreteness.CANDIDATE, query);
                 }
                 if (candidateMust == null) {
-                        candidateMust = reasoningBuilder.lift(Modality.MAY, Concreteness.CANDIDATE, query);
+                        candidateMust = reasoningBuilder.lift(Modality.MUST, Concreteness.CANDIDATE, query);
                 }
         }
 
@@ -309,15 +314,31 @@ public final class PartialRelationTranslator extends PartialSymbolTranslator<Tru
                 }
         }
 
+        private void mergeCandidateQueries() {
+                if (candidateMayMerged == null) {
+                        candidateMayMerged = createQuery("candidateMayMerged", (builder, arguments) -> builder
+                                        .clause(
+                                                        candidateMay.call(arguments),
+                                                        may.call(arguments)
+                                        ));
+                }
+                if (candidateMustMerged == null) {
+                        candidateMustMerged = createQuery("candidateMustMerged", (builder, arguments) -> builder
+                                        .clause(candidateMust.call(arguments))
+                                        .clause(must.call(arguments)));
+                }
+        }
+
         private void createFallbackRewriter() {
                 if (rewriter == null) {
-                        rewriter = new QueryBasedRelationRewriter(may, must, candidateMay, candidateMust);
+                        rewriter = new QueryBasedRelationRewriter(may, must, candidateMayMerged, candidateMustMerged);
                 }
         }
 
         private void createFallbackInterpretation() {
                 if (interpretationFactory == null) {
-                        interpretationFactory = new QueryBasedRelationInterpretationFactory(may, must, candidateMay, candidateMust);
+                        interpretationFactory = new QueryBasedRelationInterpretationFactory(may, must, candidateMayMerged,
+                                        candidateMustMerged);
                 }
         }
 
@@ -354,14 +375,6 @@ public final class PartialRelationTranslator extends PartialSymbolTranslator<Tru
                                 .clause(
                                                 PartialLiterals.candidateMust(partialRelation.call(parameters)),
                                                 not(PartialLiterals.candidateMay(partialRelation.call(parameters)))
-                                )
-                                .clause(
-                                                PartialLiterals.candidateMust(partialRelation.call(parameters)),
-                                                not(PartialLiterals.may(partialRelation.call(parameters)))
-                                )
-                                .clause(
-                                                PartialLiterals.must(partialRelation.call(parameters)),
-                                                not(PartialLiterals.candidateMay(partialRelation.call(parameters)))
                                 ));
                 var reject = createQuery("reject", (builder, parameters) -> {
                         var literals = new ArrayList<Literal>(parameters.length + 1);
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/CrossReferenceUtils.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/CrossReferenceUtils.java
index 26449df5..56c9d682 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/CrossReferenceUtils.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/CrossReferenceUtils.java
@@ -1,16 +1,18 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
 package tools.refinery.store.reasoning.translator.crossreference;
 
 import tools.refinery.logic.dnf.Query;
+import tools.refinery.logic.dnf.QueryBuilder;
 import tools.refinery.logic.dnf.RelationalQuery;
 import tools.refinery.logic.literal.Literal;
 import tools.refinery.logic.term.NodeVariable;
 import tools.refinery.logic.term.Variable;
 import tools.refinery.logic.term.uppercardinality.FiniteUpperCardinality;
+import tools.refinery.store.reasoning.literal.CountCandidateLowerBoundLiteral;
 import tools.refinery.store.reasoning.literal.CountLowerBoundLiteral;
 import tools.refinery.store.reasoning.representation.PartialRelation;
 import tools.refinery.store.reasoning.translator.multiplicity.Multiplicity;
@@ -21,6 +23,7 @@ import java.util.List;
 import static tools.refinery.logic.literal.Literals.check;
 import static tools.refinery.logic.term.int_.IntTerms.constant;
 import static tools.refinery.logic.term.int_.IntTerms.less;
+import static tools.refinery.store.reasoning.literal.PartialLiterals.candidateMay;
 import static tools.refinery.store.reasoning.literal.PartialLiterals.may;
 
 class CrossReferenceUtils {
@@ -30,6 +33,34 @@ class CrossReferenceUtils {
 
         public static RelationalQuery createMayHelper(PartialRelation linkType, PartialRelation type,
                                                                                                   Multiplicity multiplicity, boolean inverse) {
+                var preparedBuilder = prepareBuilder(linkType, inverse);
+                var literals = new ArrayList<Literal>();
+                literals.add(may(type.call(preparedBuilder.variable())));
+                if (multiplicity.multiplicity().upperBound() instanceof FiniteUpperCardinality(var finiteUpperBound)) {
+                        var existingLinks = Variable.of("existingLinks", Integer.class);
+                        literals.add(new CountLowerBoundLiteral(existingLinks, linkType, preparedBuilder.arguments()));
+                        literals.add(check(less(existingLinks, constant(finiteUpperBound))));
+                }
+                return preparedBuilder.builder().clause(literals).build();
+        }
+
+        public static RelationalQuery createCandidateMayHelper(PartialRelation linkType, PartialRelation type,
+                                                                                                                   Multiplicity multiplicity, boolean inverse) {
+                var preparedBuilder = prepareBuilder(linkType, inverse);
+                var literals = new ArrayList<Literal>();
+                literals.add(candidateMay(type.call(preparedBuilder.variable())));
+                if (multiplicity.multiplicity().upperBound() instanceof FiniteUpperCardinality(var finiteUpperBound)) {
+                        var existingLinks = Variable.of("existingLinks", Integer.class);
+                        literals.add(new CountCandidateLowerBoundLiteral(existingLinks, linkType, preparedBuilder.arguments()));
+                        literals.add(check(less(existingLinks, constant(finiteUpperBound))));
+                }
+                return preparedBuilder.builder().clause(literals).build();
+        }
+
+        private record PreparedBuilder(QueryBuilder builder, NodeVariable variable, List<Variable> arguments) {
+        }
+
+        private static PreparedBuilder prepareBuilder(PartialRelation linkType, boolean inverse) {
                 String name;
                 NodeVariable variable;
                 List<Variable> arguments;
@@ -44,14 +75,6 @@ class CrossReferenceUtils {
                 }
                 var builder = Query.builder(linkType.name() + "#mayNew" + name);
                 builder.parameter(variable);
-                var literals = new ArrayList<Literal>();
-                literals.add(may(type.call(variable)));
-                if (multiplicity.multiplicity().upperBound() instanceof FiniteUpperCardinality finiteUpperCardinality) {
-                        var existingLinks = Variable.of("existingLinks", Integer.class);
-                        literals.add(new CountLowerBoundLiteral(existingLinks, linkType, arguments));
-                        literals.add(check(less(existingLinks, constant(finiteUpperCardinality.finiteUpperBound()))));
-                }
-                builder.clause(literals);
-                return builder.build();
+                return new PreparedBuilder(builder, variable, arguments);
         }
 }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceInfo.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceInfo.java
index 982f835f..ef5bcebb 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceInfo.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceInfo.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -11,7 +11,7 @@ import tools.refinery.logic.term.truthvalue.TruthValue;
 
 public record DirectedCrossReferenceInfo(PartialRelation sourceType, Multiplicity sourceMultiplicity,
                                                                                  PartialRelation targetType, Multiplicity targetMultiplicity,
-                                                                                 TruthValue defaultValue) {
+                                                                                 TruthValue defaultValue, boolean partial) {
         public boolean isConstrained() {
                 return sourceMultiplicity.isConstrained() || targetMultiplicity.isConstrained();
         }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceTranslator.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceTranslator.java
index 5bf1f5ab..1985a43f 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceTranslator.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/DirectedCrossReferenceTranslator.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -18,6 +18,7 @@ import tools.refinery.store.reasoning.literal.Concreteness;
 import tools.refinery.store.reasoning.literal.Modality;
 import tools.refinery.store.reasoning.representation.PartialRelation;
 import tools.refinery.store.reasoning.translator.PartialRelationTranslator;
+import tools.refinery.store.reasoning.translator.RoundingMode;
 import tools.refinery.store.reasoning.translator.TranslationException;
 import tools.refinery.store.reasoning.translator.multiplicity.InvalidMultiplicityErrorTranslator;
 import tools.refinery.store.reasoning.translator.multiplicity.Multiplicity;
@@ -42,27 +43,77 @@ public class DirectedCrossReferenceTranslator implements ModelStoreConfiguration
 
         @Override
         public void apply(ModelStoreBuilder storeBuilder) {
-                var name = linkType.name();
                 var sourceType = info.sourceType();
                 var targetType = info.targetType();
-                var mayNewSource = createMayHelper(sourceType, info.sourceMultiplicity(), false);
-                var mayNewTarget = createMayHelper(targetType, info.targetMultiplicity(), true);
-                var mayName = DnfLifter.decorateName(name, Modality.MAY, Concreteness.PARTIAL);
-
                 var defaultValue = info.defaultValue();
                 if (defaultValue.must()) {
                         throw new TranslationException(linkType, "Unsupported default value %s for directed cross references %s"
                                         .formatted(defaultValue, linkType));
                 }
-
                 var translator = PartialRelationTranslator.of(linkType);
                 translator.symbol(symbol);
                 if (defaultValue.may()) {
-                        var forbiddenView = new ForbiddenView(symbol);
-                        translator.may(Query.of(mayName, (builder, source, target) -> {
+                        configureWithDefaultUnknown(translator);
+                } else {
+                        configureWithDefaultFalse(storeBuilder);
+                }
+                translator.refiner(DirectedCrossReferenceRefiner.of(symbol, sourceType, targetType));
+                translator.initializer(new DirectedCrossReferenceInitializer(linkType, sourceType, targetType, symbol));
+                if (info.partial()) {
+                        translator.roundingMode(RoundingMode.NONE);
+                } else {
+                        translator.decision(Rule.of(linkType.name(), (builder, source, target) -> builder
+                                        .clause(
+                                                        may(linkType.call(source, target)),
+                                                        not(candidateMust(linkType.call(source, target))),
+                                                        not(MULTI_VIEW.call(source)),
+                                                        not(MULTI_VIEW.call(target))
+                                        )
+                                        .action(
+                                                        add(linkType, source, target)
+                                        )));
+                }
+                storeBuilder.with(translator);
+                storeBuilder.with(new InvalidMultiplicityErrorTranslator(sourceType, linkType, false,
+                                info.sourceMultiplicity()));
+                storeBuilder.with(new InvalidMultiplicityErrorTranslator(targetType, linkType, true,
+                                info.targetMultiplicity()));
+        }
+
+        private void configureWithDefaultUnknown(PartialRelationTranslator translator) {
+                var name = linkType.name();
+                var sourceType = info.sourceType();
+                var targetType = info.targetType();
+                var mayNewSource = createMayHelper(sourceType, info.sourceMultiplicity(), false);
+                var mayNewTarget = createMayHelper(targetType, info.targetMultiplicity(), true);
+                var mayName = DnfLifter.decorateName(name, Modality.MAY, Concreteness.PARTIAL);
+                var forbiddenView = new ForbiddenView(symbol);
+                translator.may(Query.of(mayName, (builder, source, target) -> {
+                        builder.clause(
+                                        mayNewSource.call(source),
+                                        mayNewTarget.call(target),
+                                        not(forbiddenView.call(source, target))
+                        );
+                        if (info.isConstrained()) {
+                                // Violation of monotonicity:
+                                // Edges violating upper multiplicity will not be marked as {@code ERROR}, but the
+                                // corresponding error pattern will already mark the node as invalid.
+                                builder.clause(
+                                                must(linkType.call(source, target)),
+                                                not(forbiddenView.call(source, target)),
+                                                may(sourceType.call(source)),
+                                                may(targetType.call(target))
+                                );
+                        }
+                }));
+                if (info.partial()) {
+                        var candidateMayNewSource = createCandidateMayHelper(sourceType, info.sourceMultiplicity(), false);
+                        var candidateMayNewTarget = createCandidateMayHelper(targetType, info.targetMultiplicity(), true);
+                        var candidateMayName = DnfLifter.decorateName(name, Modality.MAY, Concreteness.CANDIDATE);
+                        translator.candidateMay(Query.of(candidateMayName, (builder, source, target) -> {
                                 builder.clause(
-                                                mayNewSource.call(source),
-                                                mayNewTarget.call(target),
+                                                candidateMayNewSource.call(source),
+                                                candidateMayNewTarget.call(target),
                                                 not(forbiddenView.call(source, target))
                                 );
                                 if (info.isConstrained()) {
@@ -70,63 +121,56 @@ public class DirectedCrossReferenceTranslator implements ModelStoreConfiguration
                                         // Edges violating upper multiplicity will not be marked as {@code ERROR}, but the
                                         // corresponding error pattern will already mark the node as invalid.
                                         builder.clause(
-                                                        must(linkType.call(source, target)),
+                                                        candidateMust(linkType.call(source, target)),
                                                         not(forbiddenView.call(source, target)),
-                                                        may(sourceType.call(source)),
-                                                        may(targetType.call(target))
+                                                        candidateMay(sourceType.call(source)),
+                                                        candidateMay(targetType.call(target))
                                         );
                                 }
                         }));
-                } else {
-                        var propagationBuilder = storeBuilder.getAdapter(PropagationBuilder.class);
-                        propagationBuilder.rule(Rule.of(name + "#invalidLink", (builder, p1, p2) -> {
+                }
+        }
+
+        private RelationalQuery createMayHelper(PartialRelation type, Multiplicity multiplicity, boolean inverse) {
+                return CrossReferenceUtils.createMayHelper(linkType, type, multiplicity, inverse);
+        }
+
+        private RelationalQuery createCandidateMayHelper(PartialRelation type, Multiplicity multiplicity, boolean inverse) {
+                return CrossReferenceUtils.createCandidateMayHelper(linkType, type, multiplicity, inverse);
+        }
+
+        private void configureWithDefaultFalse(ModelStoreBuilder storeBuilder) {
+                var name = linkType.name();
+                var sourceType = info.sourceType();
+                var targetType = info.targetType();
+                var mayNewSource = createMayHelper(sourceType, info.sourceMultiplicity(), false);
+                var mayNewTarget = createMayHelper(targetType, info.targetMultiplicity(), true);
+                var propagationBuilder = storeBuilder.getAdapter(PropagationBuilder.class);
+                propagationBuilder.rule(Rule.of(name + "#invalidLink", (builder, p1, p2) -> {
+                        builder.clause(
+                                        may(linkType.call(p1, p2)),
+                                        not(may(sourceType.call(p1)))
+                        );
+                        builder.clause(
+                                        may(linkType.call(p1, p2)),
+                                        not(may(targetType.call(p2)))
+                        );
+                        if (info.isConstrained()) {
                                 builder.clause(
                                                 may(linkType.call(p1, p2)),
-                                                not(may(sourceType.call(p1)))
+                                                not(must(linkType.call(p1, p2))),
+                                                not(mayNewSource.call(p1))
                                 );
                                 builder.clause(
                                                 may(linkType.call(p1, p2)),
-                                                not(may(targetType.call(p2)))
+                                                not(must(linkType.call(p1, p2))),
+                                                not(mayNewTarget.call(p2))
                                 );
-                                if (info.isConstrained()) {
-                                        builder.clause(
-                                                        may(linkType.call(p1, p2)),
-                                                        not(must(linkType.call(p1, p2))),
-                                                        not(mayNewSource.call(p1))
-                                        );
-                                        builder.clause(
-                                                        may(linkType.call(p1, p2)),
-                                                        not(must(linkType.call(p1, p2))),
-                                                        not(mayNewTarget.call(p2))
-                                        );
-                                }
-                                builder.action(
-                                                merge(linkType, TruthValue.FALSE, p1, p2)
-                                );
-                        }));
-                }
-                translator.refiner(DirectedCrossReferenceRefiner.of(symbol, sourceType, targetType));
-                translator.initializer(new DirectedCrossReferenceInitializer(linkType, sourceType, targetType, symbol));
-                translator.decision(Rule.of(linkType.name(), (builder, source, target) -> builder
-                                .clause(
-                                                may(linkType.call(source, target)),
-                                                not(candidateMust(linkType.call(source, target))),
-                                                not(MULTI_VIEW.call(source)),
-                                                not(MULTI_VIEW.call(target))
-                                )
-                                .action(
-                                                add(linkType, source, target)
-                                )));
-                storeBuilder.with(translator);
-
-                storeBuilder.with(new InvalidMultiplicityErrorTranslator(sourceType, linkType, false,
-                                info.sourceMultiplicity()));
-
-                storeBuilder.with(new InvalidMultiplicityErrorTranslator(targetType, linkType, true,
-                                info.targetMultiplicity()));
+                        }
+                        builder.action(
+                                        merge(linkType, TruthValue.FALSE, p1, p2)
+                        );
+                }));
         }
 
-        private RelationalQuery createMayHelper(PartialRelation type, Multiplicity multiplicity, boolean inverse) {
-                return CrossReferenceUtils.createMayHelper(linkType, type, multiplicity, inverse);
-        }
 }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceInfo.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceInfo.java
index 560eb04a..78b9cd86 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceInfo.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceInfo.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -9,7 +9,8 @@ import tools.refinery.store.reasoning.representation.PartialRelation;
 import tools.refinery.store.reasoning.translator.multiplicity.Multiplicity;
 import tools.refinery.logic.term.truthvalue.TruthValue;
 
-public record UndirectedCrossReferenceInfo(PartialRelation type, Multiplicity multiplicity, TruthValue defaultValue) {
+public record UndirectedCrossReferenceInfo(PartialRelation type, Multiplicity multiplicity, TruthValue defaultValue,
+                                                                                   boolean partial) {
         public boolean isConstrained() {
                 return multiplicity.isConstrained();
         }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceTranslator.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceTranslator.java
index 97c0b800..af0ddd2e 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceTranslator.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/crossreference/UndirectedCrossReferenceTranslator.java
@@ -1,25 +1,26 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
 package tools.refinery.store.reasoning.translator.crossreference;
 
+import tools.refinery.logic.dnf.Query;
+import tools.refinery.logic.term.truthvalue.TruthValue;
 import tools.refinery.store.dse.propagation.PropagationBuilder;
 import tools.refinery.store.dse.transition.Rule;
 import tools.refinery.store.model.ModelStoreBuilder;
 import tools.refinery.store.model.ModelStoreConfiguration;
-import tools.refinery.logic.dnf.Query;
 import tools.refinery.store.query.view.ForbiddenView;
 import tools.refinery.store.reasoning.lifting.DnfLifter;
 import tools.refinery.store.reasoning.literal.Concreteness;
 import tools.refinery.store.reasoning.literal.Modality;
 import tools.refinery.store.reasoning.representation.PartialRelation;
 import tools.refinery.store.reasoning.translator.PartialRelationTranslator;
+import tools.refinery.store.reasoning.translator.RoundingMode;
 import tools.refinery.store.reasoning.translator.TranslationException;
 import tools.refinery.store.reasoning.translator.multiplicity.InvalidMultiplicityErrorTranslator;
 import tools.refinery.store.representation.Symbol;
-import tools.refinery.logic.term.truthvalue.TruthValue;
 
 import static tools.refinery.logic.literal.Literals.not;
 import static tools.refinery.store.reasoning.actions.PartialActionLiterals.add;
@@ -40,73 +41,106 @@ public class UndirectedCrossReferenceTranslator implements ModelStoreConfigurati
 
         @Override
         public void apply(ModelStoreBuilder storeBuilder) {
-                var name = linkType.name();
                 var type = info.type();
-                var mayName = DnfLifter.decorateName(name, Modality.MAY, Concreteness.PARTIAL);
-
                 var defaultValue = info.defaultValue();
                 if (defaultValue.must()) {
                         throw new TranslationException(linkType, "Unsupported default value %s for directed cross references %s"
                                         .formatted(defaultValue, linkType));
                 }
-
-                var mayNewSource = CrossReferenceUtils.createMayHelper(linkType, type, info.multiplicity(), false);
-
                 var translator = PartialRelationTranslator.of(linkType);
                 translator.symbol(symbol);
                 if (defaultValue.may()) {
-                        var forbiddenView = new ForbiddenView(symbol);
-                        translator.may(Query.of(mayName, (builder, source, target) -> {
+                        configureWithDefaultUnknown(translator);
+                } else {
+                        configureWithDefaultFalse(storeBuilder);
+                }
+                translator.refiner(UndirectedCrossReferenceRefiner.of(symbol, type));
+                translator.initializer(new UndirectedCrossReferenceInitializer(linkType, type, symbol));
+                if (info.partial()) {
+                        translator.roundingMode(RoundingMode.NONE);
+                } else {
+                        translator.decision(Rule.of(linkType.name(), (builder, source, target) -> builder
+                                        .clause(
+                                                        may(linkType.call(source, target)),
+                                                        not(candidateMust(linkType.call(source, target))),
+                                                        not(MULTI_VIEW.call(source)),
+                                                        not(MULTI_VIEW.call(target))
+                                        )
+                                        .action(
+                                                        add(linkType, source, target)
+                                        )));
+                }
+                storeBuilder.with(translator);
+                storeBuilder.with(new InvalidMultiplicityErrorTranslator(type, linkType, false, info.multiplicity()));
+        }
+
+        private void configureWithDefaultUnknown(PartialRelationTranslator translator) {
+                var name = linkType.name();
+                var type = info.type();
+                var multiplicity = info.multiplicity();
+                var mayName = DnfLifter.decorateName(name, Modality.MAY, Concreteness.PARTIAL);
+                var mayNewSource = CrossReferenceUtils.createMayHelper(linkType, type, multiplicity, false);
+                var forbiddenView = new ForbiddenView(symbol);
+                translator.may(Query.of(mayName, (builder, source, target) -> {
+                        builder.clause(
+                                        mayNewSource.call(source),
+                                        mayNewSource.call(target),
+                                        not(forbiddenView.call(source, target))
+                        );
+                        if (info.isConstrained()) {
+                                // Violation of monotonicity:
+                                // Edges violating upper multiplicity will not be marked as {@code ERROR}, but the
+                                // corresponding error pattern will already mark the node as invalid.
+                                builder.clause(
+                                                must(linkType.call(source, target)),
+                                                not(forbiddenView.call(source, target)),
+                                                may(type.call(source)),
+                                                may(type.call(target))
+                                );
+                        }
+                }));
+                if (info.partial()) {
+                        var candidateMayName = DnfLifter.decorateName(name, Modality.MAY, Concreteness.CANDIDATE);
+                        var candidateMayNewSource = CrossReferenceUtils.createCandidateMayHelper(linkType, type, multiplicity,
+                                        false);
+                        translator.candidateMay(Query.of(candidateMayName, (builder, source, target) -> {
                                 builder.clause(
-                                                mayNewSource.call(source),
-                                                mayNewSource.call(target),
+                                                candidateMayNewSource.call(source),
+                                                candidateMayNewSource.call(target),
                                                 not(forbiddenView.call(source, target))
                                 );
                                 if (info.isConstrained()) {
-                                        // Violation of monotonicity:
-                                        // Edges violating upper multiplicity will not be marked as {@code ERROR}, but the
-                                        // corresponding error pattern will already mark the node as invalid.
                                         builder.clause(
-                                                        must(linkType.call(source, target)),
+                                                        candidateMust(linkType.call(source, target)),
                                                         not(forbiddenView.call(source, target)),
-                                                        may(type.call(source)),
-                                                        may(type.call(target))
+                                                        candidateMay(type.call(source)),
+                                                        candidateMay(type.call(target))
                                         );
                                 }
                         }));
-                } else {
-                        var propagationBuilder = storeBuilder.getAdapter(PropagationBuilder.class);
-                        propagationBuilder.rule(Rule.of(name + "#invalidLink", (builder, p1, p2) -> {
+                }
+        }
+
+        private void configureWithDefaultFalse(ModelStoreBuilder storeBuilder) {
+                var name = linkType.name();
+                var type = info.type();
+                var mayNewSource = CrossReferenceUtils.createMayHelper(linkType, type, info.multiplicity(), false);
+                var propagationBuilder = storeBuilder.getAdapter(PropagationBuilder.class);
+                propagationBuilder.rule(Rule.of(name + "#invalidLink", (builder, p1, p2) -> {
+                        builder.clause(
+                                        may(linkType.call(p1, p2)),
+                                        not(may(type.call(p1)))
+                        );
+                        if (info.isConstrained()) {
                                 builder.clause(
                                                 may(linkType.call(p1, p2)),
-                                                not(may(type.call(p1)))
-                                );
-                                if (info.isConstrained()) {
-                                        builder.clause(
-                                                        may(linkType.call(p1, p2)),
-                                                        not(must(linkType.call(p1, p2))),
-                                                        not(mayNewSource.call(p1))
-                                        );
-                                }
-                                builder.action(
-                                                merge(linkType, TruthValue.FALSE, p1, p2)
+                                                not(must(linkType.call(p1, p2))),
+                                                not(mayNewSource.call(p1))
                                 );
-                        }));
-                }
-                translator.refiner(UndirectedCrossReferenceRefiner.of(symbol, type));
-                translator.initializer(new UndirectedCrossReferenceInitializer(linkType, type, symbol));
-                translator.decision(Rule.of(linkType.name(), (builder, source, target) -> builder
-                                .clause(
-                                                may(linkType.call(source, target)),
-                                                not(candidateMust(linkType.call(source, target))),
-                                                not(MULTI_VIEW.call(source)),
-                                                not(MULTI_VIEW.call(target))
-                                )
-                                .action(
-                                                add(linkType, source, target)
-                                )));
-                storeBuilder.with(translator);
-
-                storeBuilder.with(new InvalidMultiplicityErrorTranslator(type, linkType, false, info.multiplicity()));
+                        }
+                        builder.action(
+                                        merge(linkType, TruthValue.FALSE, p1, p2)
+                        );
+                }));
         }
 }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/MetamodelBuilder.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/MetamodelBuilder.java
index d1979b8c..94bf1c5d 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/MetamodelBuilder.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/MetamodelBuilder.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -143,7 +143,7 @@ public class MetamodelBuilder {
                                                                         targetType, linkType, sourceType));
                                 }
                                 undirectedCrossReferences.put(linkType, new UndirectedCrossReferenceInfo(sourceType,
-                                                info.multiplicity(), defaultValue));
+                                                info.multiplicity(), defaultValue, info.partial()));
                                 return;
                         }
                         oppositeReferences.put(opposite, linkType);
@@ -153,7 +153,7 @@ public class MetamodelBuilder {
                         return;
                 }
                 directedCrossReferences.put(linkType, new DirectedCrossReferenceInfo(sourceType, info.multiplicity(),
-                                targetType, targetMultiplicity, defaultValue));
+                                targetType, targetMultiplicity, defaultValue, info.partial()));
         }
 
         private void processContainmentInfo(PartialRelation linkType, ReferenceInfo info,
@@ -197,5 +197,9 @@ public class MetamodelBuilder {
                         throw new TranslationException(opposite, "Opposite %s of containment %s cannot be containment"
                                         .formatted(opposite, linkType));
                 }
+                if (info.partial() != oppositeInfo.partial()) {
+                        throw new TranslationException(opposite, "Either both %s and %s have to be partial or neither of them"
+                                        .formatted(opposite, linkType));
+                }
         }
 }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfo.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfo.java
index 47a2e95f..94050dc0 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfo.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfo.java
@@ -10,7 +10,14 @@ import tools.refinery.store.reasoning.translator.multiplicity.Multiplicity;
 import tools.refinery.logic.term.truthvalue.TruthValue;
 
 public record ReferenceInfo(boolean containment, PartialRelation sourceType, Multiplicity multiplicity,
-                                                        PartialRelation targetType, PartialRelation opposite, TruthValue defaultValue) {
+                                                        PartialRelation targetType, PartialRelation opposite, TruthValue defaultValue,
+                                                        boolean partial) {
+        public ReferenceInfo {
+                if (containment && partial) {
+                        throw new IllegalArgumentException("Containment references cannot be partial");
+                }
+        }
+
         public static ReferenceInfoBuilder builder() {
                 return new ReferenceInfoBuilder();
         }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfoBuilder.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfoBuilder.java
index 39240d6b..90fb22b5 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfoBuilder.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/metamodel/ReferenceInfoBuilder.java
@@ -21,6 +21,7 @@ public final class ReferenceInfoBuilder {
         private PartialRelation targetType;
         private PartialRelation opposite;
         private TruthValue defaultValue = TruthValue.UNKNOWN;
+        private boolean partial;
 
         ReferenceInfoBuilder() {
         }
@@ -72,6 +73,11 @@ public final class ReferenceInfoBuilder {
                 return this;
         }
 
+        public ReferenceInfoBuilder partial(boolean partial) {
+                this.partial = partial;
+                return this;
+        }
+
         public ReferenceInfo build() {
                 if (sourceType == null) {
                         throw new IllegalStateException("Source type is required");
@@ -79,6 +85,6 @@ public final class ReferenceInfoBuilder {
                 if (targetType == null) {
                         throw new IllegalStateException("Target type is required");
                 }
-                return new ReferenceInfo(containment, sourceType, multiplicity, targetType, opposite, defaultValue);
+                return new ReferenceInfo(containment, sourceType, multiplicity, targetType, opposite, defaultValue, partial);
         }
 }
diff --git a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/multiplicity/InvalidMultiplicityErrorTranslator.java b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/multiplicity/InvalidMultiplicityErrorTranslator.java
index 0ca6eac2..e2eff921 100644
--- a/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/multiplicity/InvalidMultiplicityErrorTranslator.java
+++ b/subprojects/store-reasoning/src/main/java/tools/refinery/store/reasoning/translator/multiplicity/InvalidMultiplicityErrorTranslator.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 20232-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -52,12 +52,11 @@ public class InvalidMultiplicityErrorTranslator implements ModelStoreConfigurati
 
         @Override
         public void apply(ModelStoreBuilder storeBuilder) {
-                if (!(multiplicity instanceof ConstrainedMultiplicity constrainedMultiplicity)) {
+                if (!(multiplicity instanceof ConstrainedMultiplicity(var cardinalityInterval, var errorSymbol))) {
                         return;
                 }
 
-                var name = constrainedMultiplicity.errorSymbol().name();
-                var cardinalityInterval = constrainedMultiplicity.multiplicity();
+                var name = errorSymbol.name();
                 var node = Variable.of("node");
                 var other = Variable.of("other");
                 List<Variable> arguments = inverse ? List.of(other, node) : List.of(node, other);
@@ -98,8 +97,7 @@ public class InvalidMultiplicityErrorTranslator implements ModelStoreConfigurati
                         ));
                 }
 
-                if (cardinalityInterval.upperBound() instanceof FiniteUpperCardinality finiteUpperCardinality) {
-                        int upperBound = finiteUpperCardinality.finiteUpperBound();
+                if (cardinalityInterval.upperBound() instanceof FiniteUpperCardinality(int upperBound)) {
                         mustBuilder.clause(Integer.class, existingContents -> List.of(
                                         must(nodeType.call(node)),
                                         new CountLowerBoundLiteral(existingContents, linkType, arguments),
@@ -128,7 +126,7 @@ public class InvalidMultiplicityErrorTranslator implements ModelStoreConfigurati
                                 output.assign(missingBuilder.build().aggregate(INT_SUM, Variable.of()))
                 ));
 
-                storeBuilder.with(PartialRelationTranslator.of(constrainedMultiplicity.errorSymbol())
+                storeBuilder.with(PartialRelationTranslator.of(errorSymbol)
                                 .mayNever()
                                 .must(mustBuilder.build())
                                 .candidateMay(candidateMayBuilder.build())
diff --git a/subprojects/store-reasoning/src/test/java/tools/refinery/store/reasoning/translator/typehierarchy/TypeHierarchyPartialModelTest.java b/subprojects/store-reasoning/src/test/java/tools/refinery/store/reasoning/translator/typehierarchy/TypeHierarchyPartialModelTest.java
index e87b2684..85147921 100644
--- a/subprojects/store-reasoning/src/test/java/tools/refinery/store/reasoning/translator/typehierarchy/TypeHierarchyPartialModelTest.java
+++ b/subprojects/store-reasoning/src/test/java/tools/refinery/store/reasoning/translator/typehierarchy/TypeHierarchyPartialModelTest.java
@@ -149,7 +149,7 @@ class TypeHierarchyPartialModelTest {
 
                 var personCandidateInterpretation = reasoningAdapter.getPartialInterpretation(Concreteness.CANDIDATE, person);
                 assertThat(personCandidateInterpretation.get(Tuple.of(1)), is(TruthValue.TRUE));
-                assertThat(personCandidateInterpretation.get(Tuple.of(3)), is(TruthValue.FALSE));
+                assertThat(personCandidateInterpretation.get(Tuple.of(3)), is(TruthValue.ERROR));
 
                 var memberInterpretation = reasoningAdapter.getPartialInterpretation(Concreteness.PARTIAL, member);
                 assertThat(memberInterpretation.get(Tuple.of(1)), is(TruthValue.TRUE));
@@ -157,7 +157,7 @@ class TypeHierarchyPartialModelTest {
 
                 var memberCandidateInterpretation = reasoningAdapter.getPartialInterpretation(Concreteness.CANDIDATE, member);
                 assertThat(memberCandidateInterpretation.get(Tuple.of(1)), is(TruthValue.TRUE));
-                assertThat(memberCandidateInterpretation.get(Tuple.of(3)), is(TruthValue.FALSE));
+                assertThat(memberCandidateInterpretation.get(Tuple.of(3)), is(TruthValue.ERROR));
 
                 var studentInterpretation = reasoningAdapter.getPartialInterpretation(Concreteness.PARTIAL, student);
                 assertThat(studentInterpretation.get(Tuple.of(1)), is(TruthValue.FALSE));
@@ -165,7 +165,7 @@ class TypeHierarchyPartialModelTest {
 
                 var studentCandidateInterpretation = reasoningAdapter.getPartialInterpretation(Concreteness.CANDIDATE, student);
                 assertThat(studentCandidateInterpretation.get(Tuple.of(1)), is(TruthValue.FALSE));
-                assertThat(studentCandidateInterpretation.get(Tuple.of(3)), is(TruthValue.FALSE));
+                assertThat(studentCandidateInterpretation.get(Tuple.of(3)), is(TruthValue.ERROR));
 
                 var teacherInterpretation = reasoningAdapter.getPartialInterpretation(Concreteness.PARTIAL, teacher);
                 assertThat(teacherInterpretation.get(Tuple.of(1)), is(TruthValue.TRUE));
diff --git a/subprojects/store/build.gradle.kts b/subprojects/store/build.gradle.kts
index f96922a9..e48c0088 100644
--- a/subprojects/store/build.gradle.kts
+++ b/subprojects/store/build.gradle.kts
@@ -10,6 +10,6 @@ plugins {
 }
 
 dependencies {
-        implementation(libs.eclipseCollections.api)
+        api(libs.eclipseCollections.api)
         runtimeOnly(libs.eclipseCollections)
 }
diff --git a/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/AbstractNeighbourhoodCalculator.java b/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/AbstractNeighbourhoodCalculator.java
index 4cef6786..5bfc4725 100644
--- a/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/AbstractNeighbourhoodCalculator.java
+++ b/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/AbstractNeighbourhoodCalculator.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -8,39 +8,87 @@ package tools.refinery.store.statecoding.neighbourhood;
 import org.eclipse.collections.api.factory.primitive.IntLongMaps;
 import org.eclipse.collections.api.map.primitive.MutableIntLongMap;
 import org.eclipse.collections.api.set.primitive.IntSet;
-import tools.refinery.store.model.AnyInterpretation;
-import tools.refinery.store.model.Interpretation;
+import tools.refinery.store.map.Cursor;
 import tools.refinery.store.model.Model;
 import tools.refinery.store.statecoding.ObjectCode;
+import tools.refinery.store.statecoding.StateCodeCalculator;
+import tools.refinery.store.statecoding.StateCoderResult;
 import tools.refinery.store.tuple.Tuple;
-import tools.refinery.store.tuple.Tuple0;
 
 import java.util.*;
 
-public abstract class AbstractNeighbourhoodCalculator {
-        protected final Model model;
-        protected final List<AnyInterpretation> nullImpactValues;
-        protected final LinkedHashMap<AnyInterpretation, long[]> impactValues;
-        protected final MutableIntLongMap individualHashValues = IntLongMaps.mutable.empty();
+public abstract class AbstractNeighbourhoodCalculator<T> implements StateCodeCalculator {
+        private final Model model;
+        private final IntSet individuals;
+        private List<T> nullImpactValues;
+        private LinkedHashMap<T, long[]> impactValues;
+        private MutableIntLongMap individualHashValues;
+        private ObjectCodeImpl previousObjectCode = new ObjectCodeImpl();
+        private ObjectCodeImpl nextObjectCode = new ObjectCodeImpl();
 
         protected static final long PRIME = 31;
 
-        protected AbstractNeighbourhoodCalculator(Model model, List<? extends AnyInterpretation> interpretations,
-                                                                                          IntSet individuals) {
+        protected AbstractNeighbourhoodCalculator(Model model, IntSet individuals) {
                 this.model = model;
-                this.nullImpactValues = new ArrayList<>();
-                this.impactValues = new LinkedHashMap<>();
+                this.individuals = individuals;
+        }
+
+        protected Model getModel() {
+                return model;
+        }
+
+        protected abstract List<T> getInterpretations();
+
+        protected abstract int getArity(T interpretation);
+
+        protected abstract Object getNullValue(T interpretation);
+
+        // We need the wildcard here, because we don't know the value type.
+        @SuppressWarnings("squid:S1452")
+        protected abstract Cursor<Tuple, ?> getCursor(T interpretation);
+
+        @Override
+        public StateCoderResult calculateCodes() {
+                model.checkCancelled();
+                ensureInitialized();
+                previousObjectCode.clear();
+                nextObjectCode.clear();
+                initializeWithIndividuals(previousObjectCode);
+
+                int rounds = 0;
+                do {
+                        model.checkCancelled();
+                        constructNextObjectCodes(previousObjectCode, nextObjectCode);
+                        var tempObjectCode = previousObjectCode;
+                        previousObjectCode = nextObjectCode;
+                        nextObjectCode = tempObjectCode;
+                        nextObjectCode.clear();
+                        rounds++;
+                } while (rounds <= 7 && rounds <= previousObjectCode.getEffectiveSize());
+
+                long result = calculateLastSum(previousObjectCode);
+                return new StateCoderResult((int) result, previousObjectCode);
+        }
+
+        private void ensureInitialized() {
+                if (impactValues != null) {
+                        return;
+                }
+
+                nullImpactValues = new ArrayList<>();
+                impactValues = new LinkedHashMap<>();
+                individualHashValues = IntLongMaps.mutable.empty();
                 // Random isn't used for cryptographical purposes but just to assign distinguishable identifiers to symbols.
                 @SuppressWarnings("squid:S2245")
                 Random random = new Random(1);
 
                 var individualsInOrder = individuals.toSortedList(Integer::compare);
-                for(int i = 0; i<individualsInOrder.size(); i++) {
+                for (int i = 0; i < individualsInOrder.size(); i++) {
                         individualHashValues.put(individualsInOrder.get(i), random.nextLong());
                 }
 
-                for (AnyInterpretation interpretation : interpretations) {
-                        int arity = interpretation.getSymbol().arity();
+                for (var interpretation : getInterpretations()) {
+                        int arity = getArity(interpretation);
                         if (arity == 0) {
                                 nullImpactValues.add(interpretation);
                         } else {
@@ -50,6 +98,88 @@ public abstract class AbstractNeighbourhoodCalculator {
                                 }
                                 impactValues.put(interpretation, impact);
                         }
+
+                }
+        }
+
+        private long calculateLastSum(ObjectCode codes) {
+                long result = 0;
+                for (var nullImpactValue : nullImpactValues) {
+                        result = result * PRIME + Objects.hashCode(getNullValue(nullImpactValue));
+                }
+
+                for (int i = 0; i < codes.getSize(); i++) {
+                        final long hash = codes.get(i);
+                        result += hash*PRIME;
+                }
+
+                return result;
+        }
+
+        private void constructNextObjectCodes(ObjectCodeImpl previous, ObjectCodeImpl next) {
+                for (var impactValueEntry : this.impactValues.entrySet()) {
+                        model.checkCancelled();
+                        var interpretation = impactValueEntry.getKey();
+                        var cursor = getCursor(interpretation);
+                        int arity = getArity(interpretation);
+                        long[] impactValue = impactValueEntry.getValue();
+                        impactCalculation(previous, next, impactValue, cursor, arity);
+                }
+        }
+
+        protected void impactCalculation(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValue,
+                                                                         Cursor<Tuple, ?> cursor, int arity) {
+                switch (arity) {
+                case 1 -> {
+                        while (cursor.move()) {
+                                impactCalculation1(previous, next, impactValue, cursor);
+                        }
+                }
+                case 2 -> {
+                        while (cursor.move()) {
+                                impactCalculation2(previous, next, impactValue, cursor);
+                        }
+                }
+                default -> {
+                        while (cursor.move()) {
+                                impactCalculationN(previous, next, impactValue, cursor);
+                        }
+                }
+                }
+        }
+
+        private void impactCalculation1(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValues,
+                                                                        Cursor<Tuple, ?> cursor) {
+
+                Tuple tuple = cursor.getKey();
+                int o = tuple.get(0);
+                Object value = cursor.getValue();
+                long tupleHash = getTupleHash1(tuple, value, previous);
+                addHash(next, o, impactValues[0], tupleHash);
+        }
+
+        private void impactCalculation2(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValues,
+                                                                        Cursor<Tuple, ?> cursor) {
+                final Tuple tuple = cursor.getKey();
+                final int o1 = tuple.get(0);
+                final int o2 = tuple.get(1);
+
+                Object value = cursor.getValue();
+                long tupleHash = getTupleHash2(tuple, value, previous);
+
+                addHash(next, o1, impactValues[0], tupleHash);
+                addHash(next, o2, impactValues[1], tupleHash);
+        }
+
+        private void impactCalculationN(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValues,
+                                                                        Cursor<Tuple, ?> cursor) {
+                final Tuple tuple = cursor.getKey();
+
+                Object value = cursor.getValue();
+                long tupleHash = getTupleHashN(tuple, value, previous);
+
+                for (int i = 0; i < tuple.getSize(); i++) {
+                        addHash(next, tuple.get(i), impactValues[i], tupleHash);
                 }
         }
 
@@ -88,13 +218,4 @@ public abstract class AbstractNeighbourhoodCalculator {
                 long x = tupleHash * impact;
                 objectCodeImpl.set(o, objectCodeImpl.get(o) + x);
         }
-
-        protected long calculateModelCode(long lastSum) {
-                long result = 0;
-                for (var nullImpactValue : nullImpactValues) {
-                        result = result * PRIME + Objects.hashCode(((Interpretation<?>) nullImpactValue).get(Tuple0.INSTANCE));
-                }
-                result += lastSum;
-                return result;
-        }
 }
diff --git a/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/LazyNeighbourhoodCalculator.java b/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/LazyNeighbourhoodCalculator.java
deleted file mode 100644
index 04335141..00000000
--- a/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/LazyNeighbourhoodCalculator.java
+++ /dev/null
@@ -1,195 +0,0 @@
-/*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
- *
- * SPDX-License-Identifier: EPL-2.0
- */
-package tools.refinery.store.statecoding.neighbourhood;
-
-import org.eclipse.collections.api.factory.primitive.LongIntMaps;
-import org.eclipse.collections.api.map.primitive.LongIntMap;
-import org.eclipse.collections.api.map.primitive.MutableLongIntMap;
-import org.eclipse.collections.api.set.primitive.IntSet;
-import tools.refinery.store.map.Cursor;
-import tools.refinery.store.model.AnyInterpretation;
-import tools.refinery.store.model.Interpretation;
-import tools.refinery.store.model.Model;
-import tools.refinery.store.statecoding.StateCodeCalculator;
-import tools.refinery.store.statecoding.StateCoderResult;
-import tools.refinery.store.tuple.Tuple;
-
-import java.util.List;
-
-public class LazyNeighbourhoodCalculator extends AbstractNeighbourhoodCalculator implements StateCodeCalculator {
-        public LazyNeighbourhoodCalculator(Model model, List<? extends AnyInterpretation> interpretations,
-                                                                           IntSet individuals) {
-                super(model, interpretations, individuals);
-        }
-
-        public StateCoderResult calculateCodes() {
-                ObjectCodeImpl previousObjectCode = new ObjectCodeImpl();
-                MutableLongIntMap prevHash2Amount = LongIntMaps.mutable.empty();
-
-                long lastSum;
-                // All hash code is 0, except to the individuals.
-                int lastSize = 1;
-                boolean first = true;
-
-                boolean grows;
-                int rounds = 0;
-                do {
-                        final ObjectCodeImpl nextObjectCode;
-                        if (first) {
-                                nextObjectCode = new ObjectCodeImpl();
-                                initializeWithIndividuals(nextObjectCode);
-                        } else {
-                                nextObjectCode = new ObjectCodeImpl(previousObjectCode);
-                        }
-                        constructNextObjectCodes(previousObjectCode, nextObjectCode, prevHash2Amount);
-
-                        MutableLongIntMap nextHash2Amount = LongIntMaps.mutable.empty();
-                        lastSum = calculateLastSum(previousObjectCode, nextObjectCode, prevHash2Amount, nextHash2Amount);
-
-                        int nextSize = nextHash2Amount.size();
-                        grows = nextSize > lastSize;
-                        lastSize = nextSize;
-                        first = false;
-
-                        previousObjectCode = nextObjectCode;
-                        prevHash2Amount = nextHash2Amount;
-                } while (grows && rounds++ < 4/*&& lastSize < previousObjectCode.getSize()*/);
-
-                long result = calculateModelCode(lastSum);
-
-                return new StateCoderResult((int) result, previousObjectCode);
-        }
-
-        private long calculateLastSum(ObjectCodeImpl previous, ObjectCodeImpl next, LongIntMap hash2Amount,
-                                                                  MutableLongIntMap nextHash2Amount) {
-                long lastSum = 0;
-                for (int i = 0; i < next.getSize(); i++) {
-                        final long hash;
-                        if (isUnique(hash2Amount, previous, i)) {
-                                hash = previous.get(i);
-                                next.set(i, hash);
-                        } else {
-                                hash = next.get(i);
-                        }
-
-                        final int amount = nextHash2Amount.get(hash);
-                        nextHash2Amount.put(hash, amount + 1);
-
-                        final long shifted1 = hash >>> 8;
-                        final long shifted2 = hash << 8;
-                        final long shifted3 = hash >> 2;
-                        lastSum += shifted1 * shifted3 + shifted2;
-                }
-                return lastSum;
-        }
-
-        private void constructNextObjectCodes(ObjectCodeImpl previous, ObjectCodeImpl next, LongIntMap hash2Amount) {
-                for (var impactValueEntry : this.impactValues.entrySet()) {
-                        Interpretation<?> interpretation = (Interpretation<?>) impactValueEntry.getKey();
-                        var cursor = interpretation.getAll();
-                        int arity = interpretation.getSymbol().arity();
-                        long[] impactValue = impactValueEntry.getValue();
-
-                        if (arity == 1) {
-                                while (cursor.move()) {
-                                        lazyImpactCalculation1(hash2Amount, previous, next, impactValue, cursor);
-                                }
-                        } else if (arity == 2) {
-                                while (cursor.move()) {
-                                        lazyImpactCalculation2(hash2Amount, previous, next, impactValue, cursor);
-                                }
-                        } else {
-                                while (cursor.move()) {
-                                        lazyImpactCalculationN(hash2Amount, previous, next, impactValue, cursor);
-                                }
-                        }
-                }
-        }
-
-        private boolean isUnique(LongIntMap hash2Amount, ObjectCodeImpl objectCodeImpl, int object) {
-                final long hash = objectCodeImpl.get(object);
-                if (hash == 0) {
-                        return false;
-                }
-                final int amount = hash2Amount.get(hash);
-                return amount == 1;
-        }
-
-        private void lazyImpactCalculation1(LongIntMap hash2Amount, ObjectCodeImpl previous, ObjectCodeImpl next,
-                                                                                long[] impactValues, Cursor<Tuple, ?> cursor) {
-
-                Tuple tuple = cursor.getKey();
-                int o = tuple.get(0);
-
-                if (isUnique(hash2Amount, previous, o)) {
-                        next.ensureSize(o);
-                } else {
-                        Object value = cursor.getValue();
-                        long tupleHash = getTupleHash1(tuple, value, previous);
-
-                        addHash(next, o, impactValues[0], tupleHash);
-                }
-        }
-
-        private void lazyImpactCalculation2(LongIntMap hash2Amount, ObjectCodeImpl previous, ObjectCodeImpl next,
-                                                                                long[] impactValues, Cursor<Tuple, ?> cursor) {
-                final Tuple tuple = cursor.getKey();
-                final int o1 = tuple.get(0);
-                final int o2 = tuple.get(1);
-
-                final boolean u1 = isUnique(hash2Amount, previous, o1);
-                final boolean u2 = isUnique(hash2Amount, previous, o2);
-
-                if (u1 && u2) {
-                        next.ensureSize(o1);
-                        next.ensureSize(o2);
-                } else {
-                        Object value = cursor.getValue();
-                        long tupleHash = getTupleHash2(tuple, value, previous);
-
-                        if (!u1) {
-                                addHash(next, o1, impactValues[0], tupleHash);
-                                next.ensureSize(o2);
-                        }
-                        if (!u2) {
-                                next.ensureSize(o1);
-                                addHash(next, o2, impactValues[1], tupleHash);
-                        }
-                }
-        }
-
-        private void lazyImpactCalculationN(LongIntMap hash2Amount, ObjectCodeImpl previous, ObjectCodeImpl next,
-                                                                                long[] impactValues, Cursor<Tuple, ?> cursor) {
-                final Tuple tuple = cursor.getKey();
-
-                final boolean[] uniques = new boolean[tuple.getSize()];
-                boolean allUnique = true;
-                for (int i = 0; i < tuple.getSize(); i++) {
-                        final boolean isUnique = isUnique(hash2Amount, previous, tuple.get(i));
-                        uniques[i] = isUnique;
-                        allUnique &= isUnique;
-                }
-
-                if (allUnique) {
-                        for (int i = 0; i < tuple.getSize(); i++) {
-                                next.ensureSize(tuple.get(i));
-                        }
-                } else {
-                        Object value = cursor.getValue();
-                        long tupleHash = getTupleHashN(tuple, value, previous);
-
-                        for (int i = 0; i < tuple.getSize(); i++) {
-                                int o = tuple.get(i);
-                                if (!uniques[i]) {
-                                        addHash(next, o, impactValues[i], tupleHash);
-                                } else {
-                                        next.ensureSize(o);
-                                }
-                        }
-                }
-        }
-
-}
diff --git a/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/NeighbourhoodCalculator.java b/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/NeighbourhoodCalculator.java
index 5e6de53b..f6071c5b 100644
--- a/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/NeighbourhoodCalculator.java
+++ b/subprojects/store/src/main/java/tools/refinery/store/statecoding/neighbourhood/NeighbourhoodCalculator.java
@@ -1,5 +1,5 @@
 /*
- * SPDX-FileCopyrightText: 2023 The Refinery Authors <https://refinery.tools/>
+ * SPDX-FileCopyrightText: 2023-2024 The Refinery Authors <https://refinery.tools/>
  *
  * SPDX-License-Identifier: EPL-2.0
  */
@@ -9,115 +9,36 @@ import org.eclipse.collections.api.set.primitive.IntSet;
 import tools.refinery.store.map.Cursor;
 import tools.refinery.store.model.Interpretation;
 import tools.refinery.store.model.Model;
-import tools.refinery.store.statecoding.ObjectCode;
-import tools.refinery.store.statecoding.StateCodeCalculator;
-import tools.refinery.store.statecoding.StateCoderResult;
 import tools.refinery.store.tuple.Tuple;
-import tools.refinery.store.tuple.Tuple0;
 
 import java.util.List;
-import java.util.Objects;
 
-public class NeighbourhoodCalculator extends AbstractNeighbourhoodCalculator implements StateCodeCalculator {
-        private ObjectCodeImpl previousObjectCode = new ObjectCodeImpl();
-        private ObjectCodeImpl nextObjectCode = new ObjectCodeImpl();
+public class NeighbourhoodCalculator extends AbstractNeighbourhoodCalculator<Interpretation<?>> {
+        private final List<Interpretation<?>> interpretations;
 
-        public NeighbourhoodCalculator(Model model, List<? extends Interpretation<?>> interpretations, IntSet individuals) {
-                super(model, interpretations, individuals);
+        public NeighbourhoodCalculator(Model model, List<? extends Interpretation<?>> interpretations,
+                                                                   IntSet individuals) {
+                super(model, individuals);
+                this.interpretations = List.copyOf(interpretations);
         }
 
-        public StateCoderResult calculateCodes() {
-                model.checkCancelled();
-                previousObjectCode.clear();
-                nextObjectCode.clear();
-                initializeWithIndividuals(previousObjectCode);
-
-                int rounds = 0;
-                do {
-                        model.checkCancelled();
-                        constructNextObjectCodes(previousObjectCode, nextObjectCode);
-                        var tempObjectCode = previousObjectCode;
-                        previousObjectCode = nextObjectCode;
-                        nextObjectCode = tempObjectCode;
-                        nextObjectCode.clear();
-                        rounds++;
-                } while (rounds <= 7 && rounds <= previousObjectCode.getEffectiveSize());
-
-                long result = calculateLastSum(previousObjectCode);
-                return new StateCoderResult((int) result, previousObjectCode);
+        @Override
+        public List<Interpretation<?>> getInterpretations() {
+                return interpretations;
         }
 
-        private long calculateLastSum(ObjectCode codes) {
-                long result = 0;
-                for (var nullImpactValue : nullImpactValues) {
-                        result = result * PRIME + Objects.hashCode(((Interpretation<?>) nullImpactValue).get(Tuple0.INSTANCE));
-                }
-
-                for (int i = 0; i < codes.getSize(); i++) {
-                        final long hash = codes.get(i);
-                        result += hash*PRIME;
-                }
-
-                return result;
+        @Override
+        protected int getArity(Interpretation<?> interpretation) {
+                return interpretation.getSymbol().arity();
         }
 
-        private void constructNextObjectCodes(ObjectCodeImpl previous, ObjectCodeImpl next) {
-                for (var impactValueEntry : this.impactValues.entrySet()) {
-                        model.checkCancelled();
-                        Interpretation<?> interpretation = (Interpretation<?>) impactValueEntry.getKey();
-                        var cursor = interpretation.getAll();
-                        int arity = interpretation.getSymbol().arity();
-                        long[] impactValue = impactValueEntry.getValue();
-
-                        if (arity == 1) {
-                                while (cursor.move()) {
-                                        impactCalculation1(previous, next, impactValue, cursor);
-                                }
-                        } else if (arity == 2) {
-                                while (cursor.move()) {
-                                        impactCalculation2(previous, next, impactValue, cursor);
-                                }
-                        } else {
-                                while (cursor.move()) {
-                                        impactCalculationN(previous, next, impactValue, cursor);
-                                }
-                        }
-                }
+        @Override
+        protected Object getNullValue(Interpretation<?> interpretation) {
+                return interpretation.get(Tuple.of());
         }
 
-
-        private void impactCalculation1(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValues,
-                                                                        Cursor<Tuple, ?> cursor) {
-
-                Tuple tuple = cursor.getKey();
-                int o = tuple.get(0);
-                Object value = cursor.getValue();
-                long tupleHash = getTupleHash1(tuple, value, previous);
-                addHash(next, o, impactValues[0], tupleHash);
-        }
-
-        private void impactCalculation2(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValues,
-                                                                        Cursor<Tuple, ?> cursor) {
-                final Tuple tuple = cursor.getKey();
-                final int o1 = tuple.get(0);
-                final int o2 = tuple.get(1);
-
-                Object value = cursor.getValue();
-                long tupleHash = getTupleHash2(tuple, value, previous);
-
-                addHash(next, o1, impactValues[0], tupleHash);
-                addHash(next, o2, impactValues[1], tupleHash);
-        }
-
-        private void impactCalculationN(ObjectCodeImpl previous, ObjectCodeImpl next, long[] impactValues,
-                                                                        Cursor<Tuple, ?> cursor) {
-                final Tuple tuple = cursor.getKey();
-
-                Object value = cursor.getValue();
-                long tupleHash = getTupleHashN(tuple, value, previous);
-
-                for (int i = 0; i < tuple.getSize(); i++) {
-                        addHash(next, tuple.get(i), impactValues[i], tupleHash);
-                }
+        @Override
+        protected Cursor<Tuple, ?> getCursor(Interpretation<?> interpretation) {
+                return interpretation.getAll();
         }
 }