AgentSkillsCN

propositional-logic

数学逻辑命题逻辑问题的解题策略

SKILL.md
--- frontmatter
name: propositional-logic
description: "Problem-solving strategies for propositional logic in mathematical logic"
allowed-tools: [Bash, Read]

Propositional Logic

When to Use

Use this skill when working on propositional-logic problems in mathematical logic.

Decision Tree

  1. •

    Identify Formula Structure

    • •Classify: tautology, contradiction, or contingent?
    • •Main connective: AND, OR, IMPLIES, NOT, IFF?
    • •z3_solve.py sat "formula" to check satisfiability
  2. •

    Truth Table Method

    • •For small formulas (<=4 variables): enumerate all valuations
    • •sympy_compute.py truthtable "p & (p -> q) -> q"
    • •Tautology = all T, Contradiction = all F
  3. •

    Natural Deduction

    • •Apply inference rules: Modus Ponens, Modus Tollens
    • •Conditional proof: assume antecedent, derive consequent
    • •z3_solve.py prove "Implies(And(p, Implies(p,q)), q)"
  4. •

    Semantic Tableaux

    • •Build tree by decomposing formula
    • •Closed branches = contradictions
    • •All branches closed = valid argument

Tool Commands

Z3_Sat

bash
uv run python -m runtime.harness scripts/z3_solve.py sat "And(p, Implies(p, q), Not(q))"

Z3_Tautology

bash
uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(And(p, Implies(p, q)), q)"

Sympy_Truthtable

bash
uv run python -m runtime.harness scripts/sympy_compute.py truthtable "p & (p >> q) >> q"

Z3_Modus_Ponens

bash
uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(And(p, Implies(p,q)), q)"

Cognitive Tools Reference

See .claude/skills/math-mode/SKILL.md for full tool documentation.