predicate-logic skill
Problem-solving strategies for predicate logic in mathematical logic
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Install the predicate-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/predicate-logic ~/.claude/skills/predicate-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
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
- z3solve.py prove "resolutionvalid"
- 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))))"Z3UniversalInstantiation
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.
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