• README ⤓ .txt 2026-07-17T121634.146 000000000000664
  Logics individuated by the variety of algebras—the class of logical matrices—with respect to which they are complete. Where a modal logic is individuated by its accessibility relation, a substructural logic by which structural rules it drops, and a typed calculus by its judgments, an entry here is individuated by its algebra of truth values together with the designated set that fixes its consequence relation. Having an algebraic semantics is not what places a logic here—every logic in the collection has one—but having its individuation exhausted by that algebra, with no intensional operator, structural restriction, or term calculus doing the work instead.
• Boolean
  The logics complete for Boolean algebras: the bivalent classical systems in which excluded middle, non-contradiction, and bivalence hold and consequence is truth preservation over two-valued models.
• Heyting
  The logics complete for Heyting algebras: intuitionistic logic, which identifies truth with construction and drops unrestricted excluded middle, and the systems bounded below by it.
• Many-Valued
  The logics complete not for a single variety but for a family of them: the matrices with more than two truth values, where consequence is preservation of designated values.
• Orthomodular
  The logics complete for orthomodular lattices, in which the distributive law fails while the weaker orthomodular law survives.
• CRITERIA ⤓ .txt 2026-07-17T121634.146 000000000000680
  Not sufficient: Having an algebraic semantics, since every logic in the collection has one. This division is for logics whose individuation is the variety, with no accessibility relation, no structural-rule restriction, and no term calculus doing the work instead. An intensional operator over a truth base belongs in Modal; controlling structural rules belongs in Structural; a typed-term formalism belongs in Type; the study of algebraizability itself belongs in Metatheory.