propositional-logic skill

by parcadei·parcadei/Continuous-Claude-v3·3.9k stars·MIT

Problem-solving strategies for propositional logic in mathematical logic

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Install the propositional-logic skill

A skill is a folder. Copy it into your agent's skills folder and the agent loads it when the task matches its description.

git clone --depth 1 https://github.com/parcadei/Continuous-Claude-v3.git /tmp/Continuous-Claude-v3
mkdir -p ~/.claude/skills
cp -r /tmp/Continuous-Claude-v3/.claude/skills/math/mathematical-logic/propositional-logic ~/.claude/skills/propositional-logic

available in every project

In the Claude apps, zip the folder and upload it from the Skills settings. The folder on GitHub

The instructions your agent would load

SKILL.md as published, without the frontmatter. Read it on GitHub

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"

Z3ModusPonens

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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