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propositional-logic

Problem-solving strategies for propositional logic in mathematical logic

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This page reorganizes the original catalog entry around fit, installability, and workflow context first. The original raw source lives below.

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3,611

Hot score

Updated

March 20, 2026

Overall rating

C5.0

Composite score

5.0

Best-practice grade

B84.0

Install command

npx @skill-hub/cli install parcadei-continuous-claude-v3-propositional-logic

Repository

parcadei/Continuous-Claude-v3

Skill path: .claude/skills/math/mathematical-logic/propositional-logic

Problem-solving strategies for propositional logic in mathematical logic

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Primary workflow: Ship Full Stack.

Technical facets: Full Stack.

Target audience: everyone.

License: Unknown.

Original source

Catalog source: SkillHub Club.

Repository owner: parcadei.

This is still a mirrored public skill entry. Review the repository before installing into production workflows.

What it helps with

Install propositional-logic into Claude Code, Codex CLI, Gemini CLI, or OpenCode workflows
Review https://github.com/parcadei/Continuous-Claude-v3 before adding propositional-logic to shared team environments
Use propositional-logic for development workflows

Works across

Claude CodeCodex CLIGemini CLIOpenCode

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Original source / Raw SKILL.md

---
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
```bash
uv run python -m runtime.harness scripts/z3_solve.py sat "And(p, Implies(p, q), Not(q))"
```

### Z3_Tautology
```bash
uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(And(p, Implies(p, q)), q)"
```

### Sympy_Truthtable
```bash
uv run python -m runtime.harness scripts/sympy_compute.py truthtable "p & (p >> q) >> q"
```

### Z3_Modus_Ponens
```bash
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.