INCLUSION CRITERIA
An entry belongs in this division if and only if it is individuated by the class of algebras, or of logical matrices, with respect to which it is complete—its algebra of truth values together with the designated set that defines its consequence relation.
Required: At least one of the following:
- A completeness theorem with respect to a variety of algebras (Boolean, Heyting, MV, BL, MTL, orthomodular, De Morgan, bilattice)
- A matrix semantics: a set of truth values with designated elements and truth functions for the connectives
- A consequence relation defined as preservation of designated values
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.
Boundary: Accounts of truth-value assignment—model constructions, proof-conditional and realizability interpretations—are metatheory, not logics, and belong in Metatheory. A logic whose connectives are not truth-functional, such as supervaluation with its supertruth predicate, has no matrix and belongs where its apparatus does. Subdivisions may overlap by subvariety inclusion (Gödel logic is both Heyting and BL); such entries are cross-listed rather than duplicated.