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smithery/parcadei

propositional-logic

Problem-solving strategies for propositional logic in mathematical logic

Installation

$ npx skills add smithery/parcadei --skill propositional-logic
View on skills.sh ↗ Website ↗

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More details

Agent compatibility

Declared targets from SKILL.md / docs. Unmarked agents are not listed — the skill may still install via the CLI.

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Skill metadata

Parsed from SKILL.md frontmatter.

Allowed toolsBash, Read
Declared agents claude-code

Package contents

Files included with this skill beyond the listing page.

  • skill md SKILL.md 1,639 B
  • docs SUMMARY.md 99 B

History

  1. First recorded snapshot · 0 installs

SKILL.md

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

  1. 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

  1. 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)"

  1. 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.