/propositional-logic
Problem-solving strategies for propositional logic in mathematical logic
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/propositional-logic
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Problem-solving strategies for propositional logic in mathematical logic
SKILL.md
propositional-logic.SKILL.mdname: 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
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.
Read more
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
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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