propositional-logic
The logic of sentential connectives -- and, or, not, if-then, if-and-only-if -- as a formal system. Covers syntax (well-formed formulas), semantics (truth tables), satisfiability, validity, logical equivalence, normal forms (CNF, DNF), natural-deduction rules, and common translation pitfalls. Use when formalizing arguments with propositional structure, checking validity mechanically, or teaching the foundations of formal reasoning.
Profile →npx skills add majiayu000/claude-skill-registry --skill propositional-logic-tibsfox-gsd-skill-creator --agent claude-code
Same command for any agent — swap --agent for codex, cursor, copilot.
Weekly change comes from our own snapshots, not the repository page — it measures attention, not adoption.
# Propositional Logic Propositional logic (also called sentential logic or zeroth-order logic) is the formal study of how truth values combine under sentential connectives. It is the entry point to formal logic and the foundation of every downstream system: predicate logic extends it with quantifiers, modal logic extends it with possibility and necessity, and computer science uses it everywhere from circuit design to SAT solvers. This skill covers the syntax, semantics, proof theory, and translation discipline of propositional logic as taught in introductory logic courses. **Agent affinity:** boole (algebraic treatment), frege (axiomatic framing), russell (translation from natural language) **Concept IDs:** log-propositional-logic, log-truth-tables, log-if-then-relationships, log-argument-structure ## Syntax: Well-Formed Formulas The alphabet of propositional logic consists of: - **Atomic propositions** (propositional variables): p, q, r, s, ..., usually lowercase letters, standing for indivisible declarative sentences - **Connectives**: negation (not, symbolized as ¬ or ~), conjunction (and, ∧), disjunction (or, ∨), conditional (if...then, →), biconditional (if and only if, ↔) - *
- Syntax: Well-Formed Formulas
- Semantics: Truth Tables
- Satisfiability, Validity, Equivalence
- Key Equivalences (Memorize)
- Normal Forms
- Conjunctive Normal Form (CNF)
- Disjunctive Normal Form (DNF)
- Natural Deduction Rules
- Introduction rules
- Elimination rules
- Translation from Natural Language
- "If...then" is NOT causation
- "Unless" is the inclusive or
- "Only if" is the converse of "if"
What does the propositional-logic skill do?
The logic of sentential connectives -- and, or, not, if-then, if-and-only-if -- as a formal system. Covers syntax (well-formed formulas), semantics (truth tables), satisfiability, validity, logical equivalence, normal forms (CNF, DNF), natural-deduction rules, and common translation pitfalls. Use when formalizing arguments with propositional structure, checking validity mechanically, or teaching the foundations of formal reasoning.
How do I install it?
Run `npx skills add majiayu000/claude-skill-registry --skill propositional-logic-tibsfox-gsd-skill-creator --agent claude-code` — it drops the skill into your project so the agent can pick it up. Swap the --agent value for codex, cursor or copilot if you use one of those.
Where does this skill come from?
From majiayu000/claude-skill-registry, a repository with 534 stars. We read it straight from the repository tree rather than a submitted listing, so what you see here is what is actually published.
Is a popular skill a good skill?
Not necessarily. Stars measure attention, not adoption — a repository can trend for a week and be abandoned. That is why we show the weekly change from our own snapshots next to the total, instead of a single flattering number.