• README ⤓ .txt 2026-07-17T121634.146 000000000000560
  Formal logical systems: consequence relations, proof systems, and model-theoretic semantics that define what follows from what. A logical system specifies a language, a notion of well-formed formula, and either a derivability relation (⊢) via inference rules or a satisfaction relation (⊨) via models—or both, with soundness and completeness connecting them.
• Algebraic
  Logics individuated by the variety of algebras—the class of logical matrices—with respect to which they are complete.
• Applications
  Logics developed for, or specialized to, a particular domain of application.
• Hyperintensional
  Logics in which necessarily equivalent formulas are not interchangeable.
• Metatheory
  Formal systems studied as objects, rather than reasoning conducted within any one of them.
• Modal
  Logics that extend a propositional or predicate base with intensional operators evaluated over relational structures.
• Structural
  Logics individuated by their treatment of the structural rules of the sequent calculus—weakening, contraction, exchange, and associativity.
• Team
  Logics whose semantics evaluates a formula not at a single assignment but at a set of them—a team.
• Theories
  First-order and higher-order theories: systems individuated by a non-logical signature and the axioms governing it, with the consequence relation inherited from a base logic rather than defined.
• Type
  Type systems and typed lambda calculi understood as logics through the propositions-as-types correspondence, in which types are propositions, terms are proofs, and reduction is proof normalization.
• CRITERIA ⤓ .txt 2026-07-16T005510.000 000000000009408
  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.