INCLUSION CRITERIA
An entry belongs in this division if and only if its semantics distinguishes necessarily equivalent formulas, because the semantic value of a formula is not a set of possible worlds.
Required: At least one of the following:
- A state-based semantics with exact verification and a parthood or fusion structure on states (truthmaker semantics and its logics)
- Points of evaluation that are not possible worlds—impossible worlds, situations, or partial states—at which logical laws may fail or hold only partially
- A content, subject-matter, or variable-inclusion condition on consequence, imposed in addition to truth preservation
Not sufficient: Being non-truth-functional, since every intensional operator is that (Modal). A modal operator over a Kripke frame, however fine the accessibility conditions—a frame still identifies a proposition with a set of worlds, and necessary equivalents stay interchangeable (Modal). A third truth value or a degree (Algebraic). Failing a classical law for any reason other than the fineness of the semantic value.
Boundary: Variable sharing enforced by a substructural proof theory belongs in Structural/Relevant, where dropping weakening is what does the work; variable inclusion imposed as a content condition, with no substructural calculus, belongs here—this is the seam Structural's own criteria flags as borderline and defers to the presence of a calculus. Truthmaker semantics as a technique for characterizing content is cross-listed with Metatheory/Model-Theory; the logics built on it live here. Situation semantics with a linguistic target is cross-listed with Applications/Semantics. Impossible-worlds constructions presented as an extension of a Kripke frame are cross-listed with Modal.