| 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
-
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.