Predicate Logic

SkillAI & models

Lets your agent solve formal logic problems step by step using structured reasoning strategies.

Available today. Use it from your connected AI after setup.

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

  1. 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)"
  2. Prenex Normal Form

    • Move all quantifiers to front
    • Standardize variables to avoid capture
    • sympy_compute.py simplify "prenex(formula)"
  3. 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
  4. Resolution Proof

    • Convert to CNF, negate conclusion
    • Apply resolution rule until empty clause or saturation
    • z3_solve.py prove "resolution_valid"
  5. 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