# Mathematical Logic

> Formal logic and proof systems

- Skill: `ffsshhttiikk/mathematical-logic` (Agent Skill)
- Install (CLI): `npx skillmds@latest add ffsshhttiikk/mathematical-logic`
- Raw SKILL.md: https://api.skillmd.com/api/skills/ffsshhttiikk/mathematical-logic/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- License: MIT
- Author: ffsshhttiikk (https://skillmd.com/u/ffsshhttiikk)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/ffsshhttiikk/mathematical-logic

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## What I do
- Apply propositional and predicate calculus
- Construct mathematical proofs
- Analyze logical equivalence and validity
- Work with formal proof systems
- Apply Boolean algebra and logic circuits
- Study model theory and computability

## When to use me
When proving theorems, designing logic circuits, or studying formal systems.

## Key Concepts
- **Propositional Logic**: Variables p,q,r with operators ∧,∨,¬,→,↔
- **Predicate Logic**: Quantifiers ∀,∃ with predicates
- **Truth Tables**: Evaluate compound propositions
- **Modus Ponens**: From p and p→q, infer q
- **Proof by Contradiction**: Assume ¬P, derive contradiction, conclude P
- **Boolean Algebra**: Identities like De Morgan's laws ¬(p∧q) = ¬p∨¬q