OpenCog in Pure Maude (mcog)

This project implements the core systems of the OpenCog cognitive architecture entirely in Pure Maude, leveraging rewriting logic to model hypergraphs, probabilistic reasoning, attention allocation, and evolutionary program search.

Overview

OpenCog's architecture revolves around a hypergraph database called the AtomSpace, where nodes and links (Atoms) represent knowledge, and cognitive processes (MindAgents) operate concurrently over this graph.

Maude is a high-performance reflective language and system supporting both equational and rewriting logic specification and programming. It turns out that Maude's algebraic data types and multiset rewriting rules are a highly natural fit for modeling OpenCog:

1. AtomSpace as a Multiset: The AtomSpace is simply a multiset ("soup") of annotated atoms (Atoms paired with TruthValues and AttentionValues).
2. MindAgents as Rewrite Rules: Cognitive processes like PLN inference, ECAN attention spreading, and MOSES mutation are expressed directly as conditional rewrite rules over the AtomSpace multiset.
3. Control via Strategy/Search: Maude's built-in search and strategy languages naturally map to the Unified Rule Engine's (URE) forward and backward chaining.

Architecture

The implementation consists of the following modules:

1. Core Representation

• truth-value.maude (OC-TRUTH-VALUE): Probabilistic truth values (Strength, Confidence) and their algebraic operations (And, Or, Negate, Revision).
• attention-value.maude (OC-ATTENTION-VALUE): Attention values (Short-Term Importance, Long-Term Importance, VLTI) for resource allocation.
• atom-types.maude (OC-ATOM-TYPES): The complete OpenCog Atom type hierarchy (180+ types) encoded as a Maude sort lattice.
• atom-space.maude (OC-ATOM-SPACE, OC-ATOM-SPACE-QUERY): The hypergraph store, modeled as an associative-commutative multiset of annotated atoms, with query and graph traversal operations.

2. Probabilistic Logic Networks (PLN)

• pln.maude (OC-PLN-FORMULAS, OC-PLN-RULES): The probabilistic reasoning engine. Implements PLN formulas (Deduction, Modus Ponens, Induction, Abduction) and the corresponding inference rules that derive new links from existing knowledge.

3. Economic Attention Networks (ECAN)

• ecan.maude (OC-ECAN-CONFIG, OC-ECAN): The attention allocation subsystem. Implements asymmetric and symmetric Hebbian importance spreading, rent collection, forgetting (garbage collection), and Hebbian learning (link weight updates based on co-activation).

4. Meta-Optimizing Semantic Evolutionary Search (MOSES)

• moses.maude (OC-COMBO, OC-COMBO-EVAL, OC-MOSES-POPULATION, OC-MOSES-EVOLVE): The program learning system. Implements the COMBO functional language (Boolean and Arithmetic expression trees), evaluation environments, populations (Demes), and evolutionary operators (mutation rules).

5. Orchestration

• ure.maude (OC-URE-RULE-BASE, OC-URE-FORWARD-CHAINER, OC-URE-BACKWARD-CHAINER, OC-COG-SERVER, OC-PATTERN-MATCHER, OPENCOG): The Unified Rule Engine (URE) for forward and backward chaining, pattern matching via substitutions, and the CogServer which rotates execution among the MindAgents.

6. Advanced Subsystems (Phase 2)

• execution-engine.maude (OC-EXECUTION-ENGINE): Atomese Execution Engine (Lambda calculus, beta-reduction, arithmetic eval, PutLink, CondLink, SequentialAnd).
• pattern-matcher.maude (OC-GRAPH-MATCH): Full first-order unification and graph pattern matching (BindLink, MeetLink, QueryLink, SatisfactionLink).
• pattern-miner.maude (OC-PATTERN-MINER): Frequent subgraph pattern mining with support counting and I-Surprisingness.
• spacetime.maude (OC-SPACETIME): Allen's 13 interval relations, TimeServer, temporal inference rules, and spatial bounding boxes.
• ghost-psi.maude (OC-OPENPSI-ENGINE): OpenPsi motivational system (demands, modulators, action-selection) and GHOST dialogue rules (responder, gambit, rejoinder).
• meta-opencog.maude (OC-META): Meta-level reflection for cognitive synergy (type introspection, strategy selection, self-modification, inference monitoring).

7. AGI-Native Maude Capabilities (Phase 7)

• reflective-engine.maude (OC-REFLECTIVE-INFERENCE): Gödel Machine layer — rules-as-data with effectiveness tracking, adaptive pruning, and Maude META-LEVEL introspection.
• model-check-cog.maude (OC-COG-CHECK): LTL model-checking of cognitive safety and liveness properties over the AtomSpace as a Kripke structure.
• narrowing-abduce.maude (OC-NARROW-KB): Complete symbolic abduction via Maude narrowing — given a goal, find all explanatory initial states.
• parameterized-cog.maude (BIO-PLN, SOCIAL-PLN, PHYS-PLN): Algebraic transfer learning via parameterized PLN modules instantiated over Biology, Social, and Physics domains.
• cognitive-cycle.maude (OC-COGNITIVE-CYCLE): Strategy-controlled cognitive heartbeat — composable smod strategies for perceive, attend, reason, act, learn cycles.
• autogenesis.maude (OC-AUTOGENESIS): Emergent goal generation — the system introspects its own drives/metrics and generates new goals via seven autogenesis rules, with safety verification.

8. Cognitive Chemistry (Phase 8)

• cognitive-chemistry.maude (OC-ELEMENTS, OC-MOLECULES, OC-REACTIONS, OC-FIVE-STONES, OC-BOOTSTRAP): The Periodic Table of Cognition — atom types mapped to chemical elements with valence/bonding rules; molecular formation via reactions; alchemical transmutation of five emergent types (OpenCog, Wisdom, Philosophia, Monad, Yggdrasil) culminating in GNOSIS; bootstrap loop installing discovered types at runtime.

Usage

You need Maude 3.0+ installed to run the system.

To run the Phase 1 core integration test suite (48 assertions):

maude test-opencog.maude

To run the Phase 2 advanced subsystem test suite (56 assertions):

maude test-new-modules.maude

Both test suites perform equational reductions and state-space searches, verifying everything from truth value arithmetic to URE forward chaining derivations and full lambda beta-reduction.

Example: PLN Inference

In Maude, PLN inference rules are applied using the search command to find paths through the state space. For example, to perform a deduction:

search [1] in OC-PLN-RULES :
  [concept("cat"), stv(1.0, 0.9), defaultAV]
  [concept("animal"), stv(1.0, 0.9), defaultAV]
  [concept("living-thing"), stv(1.0, 0.9), defaultAV]
  [inheritance(concept("cat"), concept("animal")), stv(0.9, 0.8), defaultAV]
  [inheritance(concept("animal"), concept("living-thing")), stv(0.85, 0.7), defaultAV]
=>+ AS:AtomSpace
such that
  hasAtom(AS:AtomSpace, inheritance(concept("cat"), concept("living-thing"))) == true .

This searches for a state where the inheritance(cat, living-thing) link has been derived, successfully returning the AtomSpace containing the new link with its calculated truth value stv(1.0, 0.6996).

Example: OpenPsi Action Selection

The OpenPsi engine tracks demands (e.g., "energy") and selects actions based on urgency and context. As "energy" urgency increases over time, the system will eventually fire the highest-weight PsiRule that satisfies the demand (e.g., eating when hungry):

crl [psi-fire-rule] :
    psiState(
      [Ctx, TV, AV] AS,
      psiDemand(DN, DU, DT) ;; DS,
      MS,
      psiRule("r", Ctx, Act, DN, RW) ;; PRS,
      GRS, Topic, N)
  =>
    psiState(
      [Ctx, TV, AV] [Act, stv(1.0, 0.9), AV] AS,
      psiDemand(DN, clamp01(DU - 0.1), DT) ;; DS,
      MS,
      psiRule("r", Ctx, Act, DN, RW) ;; PRS,
      GRS, Topic, N + 1)
  if DU > 0.3 /\ tvStrength(TV) > 0.5 .

Testing

Run the full test suite (6 test files, 400+ assertions and searches):

# Phase 1 — core integration tests
python3 .github/scripts/validate-tests.py test-opencog.maude

# Phase 2 — advanced subsystem tests
python3 .github/scripts/validate-tests.py test-new-modules.maude

# Comprehensive coverage tests (all untested modules)
python3 .github/scripts/validate-tests.py test-coverage.maude

# Algebraic property tests (Phase 6.3)
python3 .github/scripts/validate-tests.py test-properties.maude

# Phase 7 AGI-native capability tests (reflection, model-checking, narrowing, etc.)
python3 .github/scripts/validate-tests.py test-phase3.maude

# Cognitive Chemistry tests (elements, bonds, molecules, alchemy, bootstrap)
python3 .github/scripts/validate-tests.py test-chemistry.maude

Benchmarks can be run directly with Maude (set show timing on reports rewrite-step counts):

maude bench-pln.maude            # PLN deduction chains of depth 1–4
maude bench-ecan.maude           # ECAN spreading and forgetting
maude bench-pattern-miner.maude  # pattern mining at various dataset sizes

New Modules (Phase 1–6 Roadmap)

Phase 1 — Correctness Hardening

• truth-value.maude: Added tvAnd/tvOr/tvRevision/tvNegate for ctv and itv variants. General [owise] fallbacks handle mixed-type operands by projecting to strength/confidence.
• attention-value.maude: Fixed non-linear setVLTI equation (was V = V; now uses distinct V2).
• atom-space.maude: Added mergeTV (applies PLN revision if atom already exists) and getAtomList (enumerates all atom keys in the space).
• pln.maude: Deduction rule now checks not hasAtom(…, inheritance(A,C)) to prevent duplicate derivation. Induction and abduction require minimum confidence ≥ 0.1.
• ecan.maude: Added totalSTI/normalizeSTI to the config module; new OC-ECAN-PARAM system module provides ecanState-wrapped, fully parameterised versions of every spreading, rent, forgetting, and Hebbian rule.

Phase 2 — Missing Core Features

• ure.maude: Added maxWeightRule for weighted rule selection; BC modus-ponens decomposition rule; emptyRB total-weight invariant.
• cogserver-full.maude: New OC-COG-SERVER-FULL module with CogServerFull — adds InferenceStrategy and AppRecordSet to the server state; csf-cycle records per-rule attempts; csf-switch-strategy rotates the strategy when success rate falls below 0.2.
• pattern-matcher.maude: Multi-clause BindLink matching via andLink patterns; new OC-TYPED-UNIFICATION module for TypedVariableLink type-constrained unification; new OC-GLOB-MATCH module for GlobNode sequence matching.
• moses.maude: New OC-MOSES-FITNESS module adds DataSet/DataPoint types and evalFitness : BoolExpr DataSet -> Float; OC-MOSES-FITNESS-EVOLVE wires fitness evaluation into the metapopulation loop.

Phase 3 — Advanced Cognitive Synergy

• ghost-psi.maude: psi-fire-rule now increments STI of Ctx and Act atoms (ECAN coupling); new psi-demand-decay homeostasis rule; new ghost-rejoinder and ghost-record-topic rules for multi-turn dialogue.
• pattern-miner.maude: mine-inh-pattern now injects a PLN InheritanceLink with TV derived from support fraction and I-Surprisingness; new OC-PATTERN-GENERALISE module provides generalise, extendPattern, and extendMinedPattern.

Phase 4 — Meta-Level and Reflection

• meta-opencog.maude: OC-SELF-MODIFY now carries a URRuleBase in SelfModState; register-type injects a corresponding PLN deduction rule into the base; new adapt-strategy removes under-performing rules (success rate < 0.1 after ≥ 10 attempts); new promote-rule boosts well-performing rules.
• meta-maude.maude (new): OC-META-MAUDE wraps Maude's built-in META-LEVEL (without importing OC-ATOM-SPACE to avoid _,_ conflicts); exposes doMetaReduce, doMetaApply, doMetaSearch. OC-META-QUOTE provides module qids and atom-quoting helpers.

Phase 5 — I/O and External Integration

• io-bridge.maude (new): OC-SCHEME-SERIAL serialises any OcAtom to Scheme S-expression or JSON strings; OC-EXTERNAL-SYNC provides a stub importAtoms hook for future REST/Python bridge integration; OC-ROBOTICS models sensor and actuator atoms (sensorSonar, motorMove, speechSay) and a tick-decay rule that ages short-lived atoms by −5 STI per cycle.

Phase 7 — AGI-Native Maude Capabilities

• reflective-engine.maude (new): OC-REFLECT-TERMS, OC-META-OPS, OC-REFLECTIVE-INFERENCE, OC-DERIVABILITY-CHECK — the Gödel Machine layer; rules reified as data with effectiveness tracking; mostEffective/leastEffective selection; adapt-rule pruning; Maude META-LEVEL introspection via cogModuleName.
• model-check-cog.maude (new): OC-COG-STATE, OC-COG-PREDS, OC-COG-TRANSITIONS, OC-COG-CHECK — cognitive Kripke structure for Maude's built-in LTL model checker; propositions noContradiction, budgetRespected, hasKnowledge; state-space transitions for PLN inference and ECAN spreading.
• narrowing-abduce.maude (new): OC-NARROW-KB — constructor-based knowledge base enabling Maude vu-narrow/search for complete symbolic abduction; deduction, modus-ponens, and similarity-to-inheritance rules over a narrowing-ready term algebra.
• parameterized-cog.maude (new): COGNITIVE-DOMAIN functional theory; PLN-CORE{D} parameterized PLN module; BIO-PLN, SOCIAL-PLN, PHYS-PLN instantiations via views — algebraic transfer learning across Biology, Social, and Physics domains.
• cognitive-cycle.maude (new): OC-CYCLE-STATE, OC-COGNITIVE-CYCLE — strategy-controlled cognitive cycle using Maude's smod; composable strategies perceive, attend, reason, act, learn, tick, basicCycle, deliberative, reactive, drainPercepts.
• autogenesis.maude (new): OC-INTROSPECTION, OC-GOAL-GENERATOR, OC-AUTOGENESIS — emergent goal generation; seven autogenesis rules (exploration, inference-boost, attention-rebalance, drive-satisfaction, meta-learning, social, creativity); six-phase autogenesis loop (introspect → analyze → generate → verify → install → execute) with bounded-iteration safety check.

Phase 8 — Cognitive Chemistry

• cognitive-chemistry.maude (new): OC-ELEMENTS, OC-MOLECULES, OC-REACTIONS, OC-FIVE-STONES, OC-BOOTSTRAP — the Periodic Table of Cognition; 20 cognitive elements (helium through gold) with atomic number, symbol, period, group, valence, and electronegativity; covalent/ionic/metallic bond classification; molecular formation via synthesis reactions; five alchemical stones (OpenCog, Wisdom, Philosophia, Monad, Yggdrasil); bootstrap loop that installs discovered emergent types into a TypeRegistry.

Phase 6 — Verification and Formal Properties

• test-properties.maude (new): Algebraic laws — tvAnd/tvOr commutativity and associativity, mergeTV idempotence, ECAN rent monotonicity, forgetting termination, normalizeSTI budget invariant, tvRevision commutativity, PLN duplicate-derivation guard.
• bench-pln.maude (new): PLN deduction benchmarks over taxonomy chains of depth 1–4.
• bench-ecan.maude (new): ECAN benchmarks — single-hop spreading, chain spreading, symmetric equilibration, parameterised ECAN.
• bench-pattern-miner.maude (new): Pattern miner benchmarks — small/medium datasets, mixed link types, support count accuracy, I-Surprisingness range.

License

AGPL-3.0 (following OpenCog).