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propositional-logic

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Problem-solving strategies for propositional logic in mathematical logic

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How to use this skill

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Source SKILL.md: https://github.com/foryourhealth111-pixel/Vibe-Skills/blob/HEAD/bundled/skills/propositional-logic/SKILL.md

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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.