Predicate Logic
SkillAI & modelsLets your agent solve formal logic problems step by step using structured reasoning strategies.
Available today. Use it from your connected AI after setup.
No other account needed.
Connect ahel once, and every AI you use reads what you have installed.
Then ask your AI: use the Predicate Logic skill
About this capability
Problem-solving strategies for predicate logic in mathematical logic
What this skill tells your AI
The instructions your AI receives, as published by parcadei/continuous-claude-v3 in .claude/skills/math/mathematical-logic/predicate-logic/SKILL.md and read by ahel’s review.
When to Use
Use this skill when working on predicate-logic problems in mathematical logic.
Decision Tree
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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)"
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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"
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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.
Signals
- GitHub stars
- 4k
- Forks
- 300
- Last commit
- Jan 2026
Advanced
- Catalog kind
- skill
- Gateway key
predicate-logic- Source
- github.com/parcadei/continuous-claude-v3