propositional-logic
Solves propositional logic problems using Z3 solvers, truth tables, and natural deduction rules.
Install
mkdir -p .claude/skills/propositional-logic && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/2320" && unzip -o skill.zip -d .claude/skills/propositional-logic && rm skill.zipInstalls to .claude/skills/propositional-logic
Activation
This is the description your AI agent reads to decide when to run this skill — the better it matches your request, the more reliably it fires.
Problem-solving strategies for propositional logic in mathematical logicKey capabilities
- →Classify logical formulas as tautologies or contradictions
- →Generate truth tables for formulas
- →Perform satisfiability checking
- →Apply natural deduction inference rules
- →Verify logical arguments using semantic tableaux
How it works
The skill utilizes Z3 and SymPy to programmatically evaluate logical expressions, providing automated verification for propositional logic problems.
Inputs & outputs
When to use propositional-logic
- →Prove logical equivalence
- →Solve satisfiability problems
- →Generate truth tables
- →Verify inference rules
About this skill
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.
When not to use it
- →When working with non-propositional logic systems
- →When manual proof generation is strictly required
Prerequisites
Limitations
- →Limited to propositional logic
- →Truth table method is restricted to formulas with 4 or fewer variables
How it compares
It replaces manual truth table construction and proof derivation with automated computational solvers.
Compared to similar skills
propositional-logic side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| propositional-logic (this skill) | 2 | 7mo | Review | Intermediate |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| annas-archive-ebooks | 22 | 7mo | Review | Beginner |
Try saying
Example prompts that trigger this skill in your AI assistant.
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