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propositional-logic

Analyze propositional formulas and arguments using truth tables, deduction rules, and branching proof trees. Classify formulas as always true, always false, or dependent on their inputs, and check whether an argument follows from its premises.

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原文查看原文说明

Problem-solving strategies for propositional logic in mathematical logic

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适用场景

  • Classifying formulas with truth tables
  • Checking whether a formula can be true
  • Verifying arguments with deduction rules
  • Testing arguments with branching proof trees

包含的文件(1)

  • SKILL.md1.6 KB

SKILL.md(原文)

安装前可以查看交给 AI 代理的指令内容。

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

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

Z3_Tautology

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

Sympy_Truthtable

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

Z3_Modus_Ponens

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.

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