INCLUSION CRITERIA

An entry belongs in this subdivision if and only if it is complete for a matrix of more than two truth values—a set of values with designated elements and truth-functional connectives—generating one of the many-valued varieties (MV, BL, MTL, De Morgan, Kleene, bilattice).

Required: At least one of the following:
- A truth-value set of three or more values, or a continuum of degrees, with designated values
- Truth-functional connectives interpreted over that set (a t-norm, a De Morgan lattice, a bilattice)
- Completeness for an MV, BL, MTL, or related many-valued variety

Not sufficient: Two-valued semantics (Boolean). Completeness for a Heyting variety (Heyting). Failure of distribution alone (Orthomodular). A supertruth predicate defined by quantifying over classical precisifications, whose connectives are not truth-functional and which therefore has no matrix—that is a modal construction over a bivalent base and belongs in Modal. A degree read as probability rather than as truth (Applications/Probabilistic).

Boundary: Connexive logics are placed by their semantics: McCall's CC1 and its relatives have a many-valued matrix and belong here; Wansing-style connexive systems built on a constructive base with strong negation are cross-listed with Heyting. Fuzzy description logics and probabilistic logics that deploy degrees for an application belong in Applications; the pure many-valued calculi belong here. A count of named positions or standpoints is not a set of truth values: without a designated subset and a matrix it does not belong here. Logics complete for a residuated-lattice variety but individuated by dropping a structural rule rather than by their truth degrees are cross-listed with Structural.