predicate-logic
This skill performs logic tasks including quantifier analysis and resolution proofs using Z3.
Install
mkdir -p .claude/skills/predicate-logic && curl -L -o skill.zip "https://agentskills.codes/api/skills/download/2325" && unzip -o skill.zip -d .claude/skills/predicate-logic && rm skill.zipInstalls to .claude/skills/predicate-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 predicate logic in mathematical logicKey capabilities
- →Perform quantifier analysis for universal and existential logic
- →Convert formulas to prenex normal form
- →Execute Skolemization for resolution proofs
- →Construct countermodels for invalid arguments
How it works
It uses Z3 and SymPy scripts to automate logical operations, including quantifier manipulation and resolution-based proof generation.
Inputs & outputs
When to use predicate-logic
- →Prove a logical implication using Z3
- →Convert a formula to prenex normal form
- →Find a countermodel for a formula
About this skill
Predicate Logic
When to Use
Use this skill when working on predicate-logic problems in mathematical logic.
Decision Tree
-
Quantifier Analysis
- Identify: ForAll (universal), Exists (existential)
- Scope of quantifiers and free/bound variables
z3_solve.py prove "ForAll([x], P(x)) implies P(a)"
-
Prenex Normal Form
- Move all quantifiers to front
- Standardize variables to avoid capture
sympy_compute.py simplify "prenex(formula)"
-
Skolemization (for Exists)
- Replace existential quantifiers with Skolem functions
- Exists x. P(x) -> P(c) or P(f(y)) depending on scope
- Needed for resolution-based proofs
-
Resolution Proof
- Convert to CNF, negate conclusion
- Apply resolution rule until empty clause or saturation
z3_solve.py prove "resolution_valid"
-
Model Theory
- Construct countermodel to refute invalid argument
- Finite model for finite domain
z3_solve.py model "Exists([x], P(x) & Not(Q(x)))"
Tool Commands
Z3_Forall
uv run python -m runtime.harness scripts/z3_solve.py prove "ForAll([x], Implies(P(x), Q(x)))"
Z3_Exists
uv run python -m runtime.harness scripts/z3_solve.py sat "Exists([x], And(P(x), Not(Q(x))))"
Z3_Universal_Instantiation
uv run python -m runtime.harness scripts/z3_solve.py prove "Implies(ForAll([x], P(x)), P(a))"
Z3_Model
uv run python -m runtime.harness scripts/z3_solve.py model "Exists([x], P(x))"
Cognitive Tools Reference
See .claude/skills/math-mode/SKILL.md for full tool documentation.
When not to use it
- →For non-mathematical logic problems
Prerequisites
Limitations
- →Limited to predicate logic scope
- →Requires specific script invocation patterns
How it compares
It automates complex logical derivations and model checking that would otherwise require manual truth table or natural deduction construction.
Compared to similar skills
predicate-logic side by side with the closest alternatives in the catalog.
| Skill | Installs | Updated | Safety | Difficulty |
|---|---|---|---|---|
| predicate-logic (this skill) | 2 | 7mo | Review | Advanced |
| literature-review | 559 | 2mo | Review | Advanced |
| openalex-database | 48 | 7mo | Review | Intermediate |
| scientific-critical-thinking | 18 | 7mo | Review | Advanced |
Try saying
Example prompts that trigger this skill in your AI assistant.
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