Vibecosystem propositional-logic

Problem-solving strategies for propositional logic in mathematical logic

install

source · Clone the upstream repo

git clone https://github.com/vibeeval/vibecosystem

Claude Code · Install into ~/.claude/skills/

T=$(mktemp -d) && git clone --depth=1 https://github.com/vibeeval/vibecosystem "$T" && mkdir -p ~/.claude/skills && cp -r "$T/skills/math/mathematical-logic/propositional-logic" ~/.claude/skills/vibeeval-vibecosystem-propositional-logic && rm -rf "$T"

manifest: skills/math/mathematical-logic/propositional-logic/SKILL.md

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.