Lean Knowledge Formalization

Lean 4 Knowledge Systems & Reasoning Formalization

Guide to formalizing knowledge representation, reasoning systems, and domain-specific logic in Lean 4.

Routing

• USE FOR: Knowledge representation, ontology engineering, symbolic AI, commonsense reasoning, causal reasoning, legal reasoning, and abductive inference in Lean 4. Use when formalizing knowledge structures, reasoning systems, argumentation frameworks, deontic logic, defeasible reasoning, or any domain where structured knowledge and inference must be formally verified. Core skill for knowledge-lifecycle and provenance architectures.
• DO NOT USE FOR: KRR methodology not in Lean (use @ai-symbolic-neuro); commonsense reasoning methodology (use @ai-commonsense-reasoning); causal/deontic methodology (use @ai-causal-deontic).
• TRIGGERS: knowledge formalisation, ontology in Lean, symbolic AI Lean, abductive inference Lean, legal reasoning Lean.

Workflow

1. Classify the knowledge object: ontology, taxonomy, causal model, deontic norm, or abductive rule.
2. Pick the matching encoding pattern from the body (description-logic encoding, SCM encoding, etc.).
3. Produce the Lean encoding; check Mathlib primitives at the current pin.
4. Hand off: to @lean-causal-reasoning if causal-DAG-specific, to @lean-proof-review for review, to @lean-zettelkasten.

Recovery & STOP

• STOP if the question is methodological (not Lean) — delegate to @ai-symbolic-neuro / @ai-commonsense-reasoning / @ai-causal-deontic.
• STOP if Mathlib lacks the needed structure — escalate to @lean-research.
• STOP if the encoding requires graph-theoretic foundations not in the body — delegate to @lean-math-discrete or @math-graph-knowledge.

Handoffs

• Predecessors: agent:gateway, skill:lean-research.
• Successors: skill:lean-proof-review, skill:lean-causal-reasoning, skill:lean-zettelkasten.

Detailed reference

Full content for lean-knowledge-formalization lives in references/lean-knowledge-formalization-handbook.md. Load that file when the skill is convened; the SKILL.md only carries the dispatch contract and the parts index.

See also

• ../../references/lean-knowledge-formalization-handbook.md — Full handbook (extracted from this skill)
• ../lean-proof-review/SKILL.md — Successor
• ../lean-causal-reasoning/SKILL.md — Successor
• ../lean-zettelkasten/SKILL.md — Successor