propositional-logic
Problem-solving strategies for propositional logic in mathematical logic
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技能内容
Propositional Logic
When to Use
Use this skill when working on propositional-logic problems in mathematical logic.
Decision Tree
- Identify Formula Structure
- Classify: tautology, contradiction, or contingent?
- Main connective: AND, OR, IMPLIES, NOT, IFF?
z3_solve.py sat "formula"to check satisfiability
- 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
- 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)"
- 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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原文件路径
.claude/skills/math/mathematical-logic/propositional-logic/SKILL.md