AI Symbolic Neuro

Symbolic AI & Neuro-Symbolic Integration

Formal knowledge representation, symbolic reasoning, and their integration with neural methods for knowledge structuring and consolidation pipelines.

Routing

• USE FOR: Symbolic AI, neuro-symbolic integration, knowledge representation and reasoning (KRR), ontology engineering, description logics, and hybrid symbolic-neural architectures. Use for reasoning about formal knowledge structures, rule-based systems, logic programming, semantic web technologies, and their integration with neural approaches in knowledge graphs and structured reasoning pipelines.
• DO NOT USE FOR: formalising the ontology in Lean (use @lean-knowledge-formalization); commonsense reasoning (use @ai-commonsense-reasoning); agentic AI (use @ai-agentic-evolving).
• TRIGGERS: symbolic AI, neuro-symbolic, knowledge representation, KRR, ontology engineering, description logic, hybrid AI.

Workflow

1. Identify the integration question: symbolic-only, neural-only, or hybrid; pick the integration pattern (loose / tight / unified) from the body.
2. Pick the KRR formalism (description logic, RDF/OWL, conceptual graph, neural-symbolic embedding) that matches the application.
3. Apply the formalism; document where neural and symbolic components communicate + their semantic guarantees.
4. Hand off: to @lean-knowledge-formalization for Lean encoding, to @math-graph-knowledge for graph-theoretic foundations, to @lean-zettelkasten.

Recovery & STOP

• STOP if the question is purely commonsense-reasoning — delegate to @ai-commonsense-reasoning.
• STOP if the question is about causal/deontic logic — delegate to @ai-causal-deontic.
• STOP if the neural component requires empirical evaluation beyond methodological reasoning — escalate to @research-council.

Handoffs

• Predecessors: agent:gateway, skill:lean-research.
• Successors: skill:lean-knowledge-formalization, skill:ai-commonsense-reasoning, skill:math-graph-knowledge.

Part 1 — Knowledge Representation Foundations

1.1 Representation Languages

1.2 Ontology Engineering

Foundational ontologies:

• DOLCE (Descriptive Ontology for Linguistic and Cognitive Engineering)
• BFO (Basic Formal Ontology) — ISO 21838
• SUMO (Suggested Upper Merged Ontology)

Design patterns:

• Parthood and mereology
• Temporal entities (endurants vs perdurants)
• Roles and role-playing
• Quality and quality spaces

Common application: knowledge-graph quality gates validate ontological consistency:

• TBox coherence (no unsatisfiable concepts)
• ABox consistency (instances satisfy TBox constraints)
• Schema-instance alignment

1.3 Formal Reasoning Systems

Part 2 — Neuro-Symbolic Integration

2.1 Integration Spectrum (Kautz 2020)

2.2 Key Architectures

• Neural theorem proving: Neural guide for tactic selection (GPT-f, AlphaProof)
• Knowledge graph embeddings: TransE, RotatE, CompGCN — vector representations of KG
• Graph neural networks: Message passing on knowledge structures
• Neurosymbolic concept learner: Learn visual concepts as logical programs
• Logic tensor networks: Differentiable first-order logic

2.3 Typical Neuro-Symbolic Position

Many verification-oriented pipelines operate at Level 3-4:

• Ingest phase: neural perception, extraction, or embedding.
• Articulation: neural-to-symbolic conversion from natural language to structured claims.
• Structuring: symbolic knowledge graph construction and validation.
• Consolidation: hybrid formal verification plus neural synthesis.
• Application: symbolic-to-neural feedback from validated knowledge to new tasks.

Part 3 — Commonsense Reasoning

3.1 Commonsense Knowledge Types

3.2 Formal Approaches

• Circumscription (McCarthy): Minimize abnormality
• Default logic (Reiter): Default rules with exceptions
• Answer set programming: Stable models with negation-as-failure
• Probabilistic logic: Weight rules by confidence
• Large language models: Implicit commonsense from training data

3.3 Pipeline Integration

Commonsense reasoning commonly enters structured-AI pipelines in:

• Articulation: Interpreting tacit knowledge requires commonsense context
• Structuring: Default rules for knowledge graph completion
• Quality gates: Commonsense consistency checks on extracted knowledge
• Trust dynamics: Social commonsense for multi-agent coordination

Part 4 — Knowledge Graph Reasoning

4.1 Reasoning Tasks

4.2 Formal Quality Metrics

4.3 Knowledge Graph Architecture

Experience → Raw triples (LLM extraction)
  → Articulation → Candidate assertions with confidence
    → Structuring → Validated KG with ontological constraints
      → Consolidation → Proven properties (Lean formalization)
        → Innovation → Novel inferences from verified base

Quality gates at each transition enforce:

• Confidence thresholds (configurable per domain)
• Ontological consistency (TBox reasoning)
• Provenance tracking (W3C PROV-O)
• Temporal validity (assertions expire)

Part 5 — Host-Repository Lean Extension Points

Do not assume repository-local Lean modules, tactics, or namespaces exist unless the host repository explicitly provides them. When a repository has local knowledge-graph or quality-gate modules, map them to this generic checklist:

Part 6 — Research Connections

6.1 Epistemic Mapping Targets

6.2 Key References

• Brachman & Levesque (2004) — Knowledge Representation and Reasoning
• Hitzler et al. (2020) — Neuro-Symbolic AI: state of the art
• Marcus & Davis (2019) — Rebooting AI (commonsense perspective)
• Hogan et al. (2021) — Knowledge Graphs (comprehensive survey)
• Davis (2015) — Commonsense reasoning: an event calculus perspective