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AI","license":"MIT","homepage":"https://github.com/cogitator-ai/Cogitator-AI/tree/main/packages/neuro-symbolic#readme","keywords":["neuro-symbolic","ai","logic-programming","prolog","constraint-solving","sat","smt","z3","knowledge-graph","sparql","planning","pddl","formal-verification","llm","reasoning"],"repository":{"url":"https://github.com/cogitator-ai/Cogitator-AI.git","type":"git","directory":"packages/neuro-symbolic"},"description":"Neuro-symbolic AI for hybrid neural-symbolic reasoning","maintainers":[{"name":"el1fe","email":"piuro.pavel@gmail.com"}],"readme":"# @cogitator-ai/neuro-symbolic\n\nNeuro-symbolic AI package for hybrid neural-symbolic reasoning. Combines LLM-based understanding with formal methods for verifiable, explainable AI.\n\n## Installation\n\n```bash\npnpm add @cogitator-ai/neuro-symbolic\n```\n\nZ3 SMT support is an optional dependency. If it is not installed automatically, add it explicitly:\n\n```bash\npnpm add z3-solver\n```\n\nWithout Z3 the package falls back to the built-in solver (exact search for finite domains, local search otherwise).\n\nThe Postgres and Neo4j graph adapters need their drivers (optional peer dependencies):\n\n```bash\npnpm add pg            # createPostgresGraphAdapter\npnpm add neo4j-driver  # createNeo4jGraphAdapter\n```\n\nWebsite docs: [Neuro-Symbolic](https://cogitator.app/docs/advanced/neuro-symbolic).\n\n## Features\n\n- **Logic Programming** - Prolog engine with ISO operator precedence, cut, if-then-else, negation, `findall/3`, `between/3` and proof trees\n- **Knowledge Graph Queries** - SPARQL-like query language, natural language questions, path finding and rule-based inference\n- **Constraint Solving** - SAT/SMT solving with Z3 (WASM) or a pure-TS fallback, including optimisation and soft constraints\n- **Plan Verification** - PDDL-like action schemas with validation, ordering-threat detection, invariant checking and automatic repair\n\n---\n\n## Quick Start\n\n```typescript\nimport { createNeuroSymbolic } from '@cogitator-ai/neuro-symbolic';\n\nconst ns = createNeuroSymbolic();\n\nns.loadLogicProgram(`\n  parent(tom, mary).\n  parent(mary, ann).\n  grandparent(X, Z) :- parent(X, Y), parent(Y, Z).\n`);\n\nconst result = ns.queryLogic('grandparent(tom, X)?');\nconsole.log(result.data?.solutions[0].get('X')); // { type: 'atom', value: 'ann' }\nconsole.log(ns.getLogicSolutions('grandparent(tom, X)')); // \"X = ann.\"\n\nconst builder = ns.createConstraintProblem('sum');\nconst x = builder.int('x', 1, 10);\nconst y = builder.int('y', 1, 10);\nbuilder.assert(x.add(y).eq(15));\nbuilder.maximize(x);\n\nconst solution = await ns.solve(builder.build());\nif (solution.data?.status === 'sat') {\n  console.log(solution.data.model.assignments); // { x: 10, y: 5 }\n}\n```\n\n---\n\n## Logic Programming\n\nProlog-style logic programming with SLD resolution, unification and standard operator syntax.\n\n### Loading Programs\n\n```typescript\nns.loadLogicProgram(`\n  % Facts\n  human(socrates).\n  human(plato).\n\n  % Rules\n  mortal(X) :- human(X).\n\n  % Arithmetic uses ISO precedence: * binds tighter than +\n  total(Price, Qty, T) :- T is Price * Qty + 5.\n\n  % Cut is local to the clause that executes it\n  grade(S, a) :- S >= 90, !.\n  grade(S, b) :- S >= 75, !.\n  grade(_, c).\n\n  % If-then-else commits to the condition\n  label(S, L) :- ( S >= 50 -> L = pass ; L = fail ).\n`);\n```\n\n`loadLogicProgram` returns `{ success, errors }`; syntax errors include the line and column.\n\n### Querying\n\nQueries may be written with or without a trailing `.`/`?` and an optional `?-` prefix.\n\n```typescript\nconst result = ns.queryLogic('mortal(X)?');\nfor (const solution of result.data?.solutions ?? []) {\n  console.log(solution.get('X')); // socrates, plato\n}\n\nns.proveLogic('mortal(socrates)').data; // true\nns.getLogicSolutions('append(X, Y, [1, 2])');\n// \"X = [], Y = [1, 2] ;\\nX = [1], Y = [2] ;\\nX = [1, 2], Y = [].\"\n\nns.queryLogic('findall(X, human(X), L), length(L, N)', { maxSolutions: 1 });\n```\n\nVariables starting with `_` (including the anonymous `_`) are not reported in answers. When a query runs out of time or depth, `result.error` / `result.data.explanation` says so.\n\n### Proof Trees\n\nEnable `traceExecution` to capture the proof tree:\n\n```typescript\nimport {\n  createNeuroSymbolic,\n  formatProofTree,\n  proofTreeToMermaid,\n} from '@cogitator-ai/neuro-symbolic';\n\nconst traced = createNeuroSymbolic({ config: { logic: { traceExecution: true } } });\ntraced.loadLogicProgram(\n  'parent(tom, mary). parent(mary, ann). grandparent(X, Z) :- parent(X, Y), parent(Y, Z).'\n);\n\nconst proof = traced.queryLogic('grandparent(tom, X)').data?.proofTree;\nif (proof) {\n  console.log(formatProofTree(proof));\n  console.log(proofTreeToMermaid(proof));\n}\n```\n\n### Built-in Predicates\n\n| Category      | Predicates                                                                                                                                     |\n| ------------- | ---------------------------------------------------------------------------------------------------------------------------------------------- |\n| Control       | `,/2`, `;/2`, `->/2`, `!/0`, `\\+/1`, `not/1`, `call/1..8`, `findall/3`, `forall/2`, `between/3`                                                |\n| Unification   | `=/2`, `\\=/2`, `==/2`, `\\==/2`, `@</2`, `@>/2`, `@=</2`, `@>=/2`, `compare/3`                                                                  |\n| Arithmetic    | `is/2`, `=:=/2`, `=\\=/2`, `</2`, `>/2`, `=</2`, `>=/2`, `succ/2`, `plus/3`                                                                     |\n| Type checks   | `atom/1`, `number/1`, `integer/1`, `float/1`, `atomic/1`, `compound/1`, `var/1`, `nonvar/1`, `is_list/1`, `ground/1`, `string/1`, `callable/1` |\n| Lists         | `member/2`, `append/3`, `length/2`, `reverse/2`, `nth0/3`, `nth1/3`, `last/2`, `sort/2`, `msort/2`, `sum_list/2`, `max_list/2`, `min_list/2`   |\n| Terms & atoms | `functor/3`, `arg/3`, `=../2`, `copy_term/2`, `atom_length/2`, `atom_concat/3`                                                                 |\n| Logic         | `true/0`, `fail/0`, `false/0`                                                                                                                  |\n\nArithmetic follows ISO semantics (`-7 mod 3 =:= 2`, `-7 // 2 =:= -3`, `div`, bitwise `/\\ \\/ xor << >>`, `gcd`, `min`, `max`, `abs`, trigonometry, `pi`, `e`, ...). Undefined results such as `sqrt(-1)` fail instead of binding `NaN`. Use `getBuiltinList()` / `isControlConstruct()` to inspect support at runtime.\n\n---\n\n## Knowledge Graph Queries\n\nSPARQL-like query language with natural language interface. Works with any `GraphAdapter` (in-memory, Postgres, Neo4j, or adapters from `@cogitator-ai/memory`).\n\n### Query Builder\n\n```typescript\nimport {\n  GraphQueryBuilder,\n  graphVariable as variable,\n  executeQuery,\n} from '@cogitator-ai/neuro-symbolic';\n\nconst query = GraphQueryBuilder.select()\n  .where(variable('person'), 'works_at', variable('company'))\n  .where(variable('company'), 'located_in', 'Berlin')\n  .filter('person.name', 'startsWith', 'A')\n  .orderBy('person.name', 'asc')\n  .limit(10)\n  .build();\n\nconst result = await executeQuery(query, {\n  adapter: graphAdapter,\n  agentId: 'agent-1',\n  variables: new Map(),\n});\n```\n\n- Patterns join on shared variables; bidirectional edges match in both directions.\n- `?x a person` / `?x type person` matches node entity types.\n- `describe` queries match edges in either direction around the subject.\n- Filters can address nested properties: `person.properties.profile.level`.\n- `count('*', 'total')` counts all bindings.\n\n### Query Strings\n\n```typescript\nimport { parseQueryString } from '@cogitator-ai/neuro-symbolic';\n\nconst parsed = parseQueryString(`\n  SELECT ?p WHERE { ?p works_at ?c . ?c located_in Berlin }\n  FILTER(?p.confidence >= 0.5)\n  ORDER BY DESC(?p.name)\n  LIMIT 5\n`);\n```\n\nSupported filter operators: `= != > >= < <= contains startsWith endsWith regex in notIn`.\n\n### Natural Language Queries\n\n```typescript\nconst answer = await ns.askGraph('Who works at \"Acme\"?');\nconsole.log(answer.data?.naturalLanguageResponse);\n```\n\n`NeuroSymbolic` honours `config.knowledgeGraph.enableNaturalLanguage` and applies `defaultQueryLimit` to queries without an explicit limit.\n\n### Reasoning Engine\n\n```typescript\nimport { createReasoningEngine } from '@cogitator-ai/neuro-symbolic';\n\nconst engine = createReasoningEngine(graphAdapter, 'agent-1', { maxHops: 3, minConfidence: 0.5 });\n\nconst path = await engine.findPath(aliceId, companyId);\nconst hops = await engine.multiHopQuery(aliceId, ['works_at', 'located_in']);\nconst inferred = await engine.infer(); // transitive, inverse and composed relations, de-duplicated\n```\n\n---\n\n## Constraint Solving\n\nSAT/SMT solving with a fluent DSL. Variable declarations return expressions; constraints are added to the builder.\n\n### Building Constraints\n\n```typescript\nimport { ConstraintBuilder, allDifferent, solve } from '@cogitator-ai/neuro-symbolic';\n\nconst builder = ConstraintBuilder.create('example');\nconst a = builder.bool('a');\nconst b = builder.bool('b');\nconst x = builder.int('x', 0, 100);\nconst y = builder.int('y', 0, 100);\nconst z = builder.real('z', 0, 1);\n\nbuilder.assert(a.or(b));\nbuilder.assert(x.add(y).lte(50));\nbuilder.assert(z.mul(2).gt(0.5));\nbuilder.assert(allDifferent(x, y));\nbuilder.soft(x.eq(10), 2);\nbuilder.maximize(x.add(y));\n\nconst result = await solve(builder.build());\nif (result.status === 'sat') {\n  console.log(result.model.assignments, result.model.objectiveValue);\n}\n```\n\nDeclaring the same variable twice or an empty domain (`min > max`) throws.\n\n### Solver Selection\n\n`solve(problem, { solver: 'z3' })` (the default) uses Z3 when `z3-solver` can be loaded and otherwise falls back to the built-in solver.\n\n```typescript\nimport { isZ3Available, solveWithZ3, solveSAT } from '@cogitator-ai/neuro-symbolic';\n\nconst result = (await isZ3Available()) ? await solveWithZ3(problem) : solveSAT(problem);\n```\n\n- **Z3**: integers, reals, booleans and bit-vectors (unsigned semantics); mixed Int/Real expressions are coerced automatically; objectives and soft constraints use Z3's optimiser.\n- **Built-in solver**: exhaustive search when every variable has a finite domain (≤ 2^20 assignments) — exact `sat`/`unsat`, optimal objective, minimal soft-constraint violations; local search for real or unbounded variables (may return `unknown`).\n\n### Expression Types\n\n```typescript\nx.add(y);\nx.sub(5);\nx.mul(2);\nx.div(3);\nx.mod(7);\nx.pow(2);\nx.abs();\nx.min(y);\nx.max(y);\na.and(b);\na.or(b);\na.not();\na.implies(b);\na.iff(b);\nx.eq(10);\nx.neq(y);\nx.gt(0);\nx.gte(0);\nx.lt(100);\nx.lte(100);\n\nite(a, x, y);\nsum(x, y, z);\nallDifferent(x, y, z);\natMost(2, a, b, c);\natLeast(1, a, b, c);\nexactly(1, a, b, c);\n```\n\n---\n\n## Plan Verification\n\nPDDL-like planning with verification and repair. Parameter references use the `?name` syntax.\n\n### Action Schemas\n\n```typescript\nimport { ActionSchemaBuilder, ActionRegistry } from '@cogitator-ai/neuro-symbolic';\n\nconst move = ActionSchemaBuilder.create('move')\n  .describe('Move robot from one location to another')\n  .param('from', 'string')\n  .param('to', 'string')\n  .preSimple('robotAt', '?from')\n  .preCompare('battery', 'gt', 10)\n  .assign('robotAt', '?to')\n  .decrement('battery', 5)\n  .setCost(5)\n  .build();\n\nconst registry = new ActionRegistry();\nregistry.register(move);\n```\n\nPrecondition equality is structural (arrays and objects compare by value). Conditional effects evaluate their condition against the state _before_ the action.\n\n### Plan Validation\n\n```typescript\nimport { createAction, validatePlan, formatValidationResult } from '@cogitator-ai/neuro-symbolic';\n\nconst plan = {\n  id: 'plan-1',\n  actions: [\n    createAction('move', { from: 'A', to: 'B' }),\n    createAction('move', { from: 'B', to: 'C' }),\n  ],\n  initialState: { id: 's0', variables: { robotAt: 'A', battery: 100 } },\n  goalConditions: [{ type: 'simple' as const, variable: 'robotAt', value: 'C' }],\n};\n\nconst result = validatePlan(plan, registry, { maxSteps: 50 });\nconsole.log(formatValidationResult(result));\n```\n\nValidation reports precondition violations, missing/unknown parameters, unmet goals, redundant actions and ordering threats (an action deleting a variable a later action requires).\n\n### Invariant Checking\n\n```typescript\nimport { createInvariantChecker, formatInvariantResults } from '@cogitator-ai/neuro-symbolic';\n\nconst checker = createInvariantChecker(registry);\nchecker.addInvariant('battery-non-negative', {\n  type: 'comparison',\n  variable: 'battery',\n  operator: 'gte',\n  value: 0,\n});\nchecker.addNever('danger', { type: 'simple', variable: 'robotAt', value: 'danger-zone' });\nchecker.addEventually('arrived', { type: 'simple', variable: 'robotAt', value: 'C' });\n\nconsole.log(formatInvariantResults(checker.checkPlan(plan)));\n```\n\nThe trajectory stops at the first action whose preconditions do not hold.\n\n### Plan Repair\n\n```typescript\nimport { createPlanRepairer, formatRepairResult } from '@cogitator-ai/neuro-symbolic';\n\nconst repairer = createPlanRepairer(registry, { maxInsertions: 3, maxRemovals: 2 });\nconst repair = repairer.repair(plan);\n\nif (repair.success) {\n  console.log('Repaired plan:', repair.repairedPlan);\n} else {\n  console.log(formatRepairResult(repair));\n}\n```\n\nInsertion suggestions are verified by simulation (an action is only suggested if applying it establishes the failed condition); missing parameters are filled from defaults or the current state.\n\n---\n\n## Main Orchestrator\n\nThe `NeuroSymbolic` class integrates all modules. Every method returns a `NeuroSymbolicResult` (`{ success, data?, error?, duration }`) instead of throwing.\n\n```typescript\nimport { createNeuroSymbolic } from '@cogitator-ai/neuro-symbolic';\n\nconst ns = createNeuroSymbolic({\n  graphAdapter: myGraphAdapter,\n  agentId: 'agent-1',\n  config: {\n    knowledgeGraph: { enableNaturalLanguage: true, defaultQueryLimit: 100 },\n    logic: { maxDepth: 50, maxSolutions: 10, timeout: 5000 },\n    constraints: { timeout: 10000, solver: 'z3' },\n    planning: { maxPlanLength: 100, enableRepair: true, verifyInvariants: true },\n  },\n});\n\nns.loadLogicProgram('...');\nns.queryLogic('...');\n\nawait ns.solve(problem);\n\nawait ns.queryGraph(query);\nawait ns.askGraph('natural language question');\nawait ns.findPath(startNodeId, endNodeId);\n\nns.registerAction(actionSchema);\nns.validatePlan(plan);\nns.repairPlan(plan);\nns.checkInvariants(plan);\nawait ns.validateAndRepair(plan);\n```\n\n| Method              | `success` means                                                |\n| ------------------- | -------------------------------------------------------------- |\n| `queryLogic`        | the query has at least one solution                            |\n| `validatePlan`      | validation ran (see `data.valid`)                              |\n| `repairPlan`        | the plan was repaired (suggestions are in `data` either way)   |\n| `checkInvariants`   | all safety properties hold                                     |\n| `validateAndRepair` | the (repaired) plan is valid **and** all invariants hold on it |\n\n`ns.getConfig()` returns a `ResolvedNeuroSymbolicConfig`: every section (`logic`, `constraints`, `planning`, `knowledgeGraph`) is present with its defaults filled in, so no optional chaining is needed. `ns.updateConfig(partial)` merges changes into the running instance.\n\n```typescript\nconst { logic, constraints } = ns.getConfig();\nconsole.log(logic.maxDepth, constraints.timeout);\n\nns.updateConfig({ logic: { maxSolutions: 5 } });\n```\n\n---\n\n## Agent Tools\n\nExpose neuro-symbolic capabilities as tools for AI agents.\n\n```typescript\nimport { createNeuroSymbolicTools, MemoryGraphAdapter } from '@cogitator-ai/neuro-symbolic';\nimport { Agent, Cogitator } from '@cogitator-ai/core';\n\nconst nsTools = createNeuroSymbolicTools({ graphAdapter: new MemoryGraphAdapter() });\n\nnsTools.instance.loadLogicProgram(`\n  parent(tom, mary).\n  parent(mary, ann).\n  grandparent(X, Z) :- parent(X, Y), parent(Y, Z).\n`);\n\nconst agent = new Agent({\n  name: 'reasoning-agent',\n  model: 'openai/gpt-6.1-sol',\n  tools: nsTools.all,\n  instructions:\n    'Use query_logic for Prolog queries, solve_constraints for SAT/SMT problems and validate_plan to verify action sequences.',\n});\n\nconst cogitator = new Cogitator({\n  llm: { providers: { openai: { apiKey: process.env.OPENAI_API_KEY! } } },\n});\nconst result = await cogitator.run(agent, { input: 'Who are the grandparents of ann?' });\n```\n\n### Available Tools\n\n| Property           | Tool name            | Description                                    |\n| ------------------ | -------------------- | ---------------------------------------------- |\n| `queryLogic`       | `query_logic`        | Run a Prolog query against the knowledge base  |\n| `assertFact`       | `assert_fact`        | Add facts or rules                             |\n| `loadProgram`      | `load_logic_program` | Load a Prolog program (optionally clearing)    |\n| `solveConstraints` | `solve_constraints`  | Solve SAT/SMT problems with optional objective |\n| `validatePlan`     | `validate_plan`      | Validate a plan against action schemas         |\n| `repairPlan`       | `repair_plan`        | Repair an invalid plan                         |\n| `registerAction`   | `register_action`    | Register an action schema                      |\n| `findPath`\\*       | `find_graph_path`    | Shortest path between graph nodes              |\n| `queryGraph`\\*     | `query_graph`        | Query nodes (and optionally their edges)       |\n| `addGraphNode`\\*   | `add_graph_node`     | Add a node                                     |\n| `addGraphEdge`\\*   | `add_graph_edge`     | Add an edge                                    |\n\n\\*Graph tools are available when a `graphAdapter` is passed or the provided `instance` has one.\n\n### Factory Options\n\n```typescript\ninterface NeuroSymbolicToolsOptions {\n  instance?: NeuroSymbolic;\n  graphAdapter?: GraphAdapter;\n  config?: Partial<NeuroSymbolicConfig>;\n  agentId?: string;\n}\n```\n\nWhen `agentId` is set, graph tools read and write that agent's graph; otherwise they use the calling agent's id from the tool context. `createGraphTools(adapter, { agentId })` can be used on its own.\n\n### Graph Adapters\n\n```typescript\nimport {\n  MemoryGraphAdapter,\n  createPostgresGraphAdapter,\n  createNeo4jGraphAdapter,\n} from '@cogitator-ai/neuro-symbolic';\n\nconst memory = new MemoryGraphAdapter();\nawait memory.addNode({\n  agentId: 'agent-1',\n  name: 'Alice',\n  type: 'person',\n  aliases: [],\n  properties: { age: 30 },\n  confidence: 1,\n  source: 'user',\n});\n\nconst postgres = createPostgresGraphAdapter({ connectionString: process.env.DATABASE_URL! });\nawait postgres.connect();\n\nconst neo4j = createNeo4jGraphAdapter({\n  uri: 'bolt://localhost:7687',\n  username: 'neo4j',\n  password: 'secret',\n});\nawait neo4j.connect();\n```\n\nAll adapters scope traversal and shortest-path search to the requesting agent, treat bidirectional edges as traversable in both directions and reject merges into a node listed among its own sources.\n\nThe Postgres adapter uses the pgvector extension for `searchNodesSemantic()`. It indexes node embeddings with HNSW, which needs no training data, so the index built on the empty table finds every node as the graph grows. Earlier versions built an `ivfflat` index there, which missed nodes once Postgres used it (a search for 60 nodes in a graph of 3000 returned 31). The first `connect()` after upgrading replaces that index with HNSW, which takes a while on a large graph. To avoid the wait, build the index ahead of the deploy with `CREATE INDEX CONCURRENTLY idx_graph_nodes_embedding_new ON cogitator_graph.graph_nodes USING hnsw (embedding vector_cosine_ops)`, then drop the old index and rename the new one to `idx_graph_nodes_embedding`. An existing HNSW index is kept as it is. Each search raises `hnsw.ef_search` to the requested `limit` (up to 1000) and, on pgvector 0.8 or later, turns on iterative scans, so a large limit or an `entityTypes` filter still gets every matching node. Equally similar nodes are ordered by id.\n\n---\n\n## Module Imports\n\nEach module can be imported separately:\n\n```typescript\nimport {\n  KnowledgeBase,\n  SLDResolver,\n  parseQuery,\n  formatSolutions,\n} from '@cogitator-ai/neuro-symbolic/logic';\nimport {\n  GraphQueryBuilder,\n  executeQuery,\n  ReasoningEngine,\n} from '@cogitator-ai/neuro-symbolic/knowledge-graph';\nimport { ConstraintBuilder, solve, Z3WASMSolver } from '@cogitator-ai/neuro-symbolic/constraints';\nimport {\n  ActionSchemaBuilder,\n  PlanValidator,\n  InvariantChecker,\n} from '@cogitator-ai/neuro-symbolic/planning';\nimport { createNeuroSymbolicTools } from '@cogitator-ai/neuro-symbolic/tools';\n```\n\n---\n\n## Type Reference\n\n```typescript\nimport type {\n  Term,\n  Clause,\n  Substitution,\n  ProofTree,\n  LogicQueryResult,\n  GraphQuery,\n  GraphQueryResult,\n  NaturalLanguageQueryResult,\n  ConstraintProblem,\n  ConstraintVariable,\n  SolverResult,\n  ActionSchema,\n  Plan,\n  PlanState,\n  PlanValidationResult,\n  SafetyProperty,\n  InvariantCheckResult,\n} from '@cogitator-ai/types';\n```\n\n---\n\n## License\n\nMIT\n","readmeFilename":""}