INCLUSION CRITERIA
A system belongs here if and only if it defines a consequence relation or validity notion with explicit formal machinery.
Required: At least one of the following:
- Axioms and inference rules defining a derivability relation ⊢
- A model-theoretic semantics defining a satisfaction relation ⊨
- Truth tables, matrices, or algebraic semantics
- Sequent calculus, natural deduction, or other proof system
- Type judgments with formation, introduction, and elimination rules
- Kripke frames, neighborhood semantics, or other relational semantics
Not sufficient: Having "logic" in the name. Having "calculus" in the name — the word means a system of calculation as readily as a system of inference, and functional, matrix, umbral, and vector calculus are notations for analysis and algebra with no consequence relation between them. Using logical vocabulary informally. Philosophical positions about logic unless tied to a specific formal system.
Not required: Western origin. Modern notation. Completeness proofs. The system may be ancient, may use non-standard notation, and may lack metatheoretic results—but it must have the formal apparatus.