Predicate Logic
- 1 installs
- 3.9k repo stars
- Updated January 26, 2026
- parcadei/continuous-claude-v3
Guides Claude through predicate-logic problems by analyzing quantifiers and free/bound variables and proving with z3.
About
A decision-tree skill for predicate logic, analyzing quantifier scope and free/bound variables. A developer uses it when they want Claude to prove first-order statements with z3.
- Quantifier and variable-scope analysis
- z3 proofs for universal instantiation
Predicate Logic by the numbers
- 1 all-time installs (skills.sh)
- Ranked #1,803 of 2,064 Data Science & ML skills by installs in the Skillselion catalog
- Data as of Aug 5, 2026 (Skillselion catalog sync)
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| Installs | 1 |
|---|---|
| repo stars | ★ 3.9k |
| Last updated | January 26, 2026 |
| Repository | parcadei/continuous-claude-v3 ↗ |
What it does
Guides Claude through predicate-logic problems by analyzing quantifiers and free/bound variables and proving with z3.
Files
Predicate Logic
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.
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