INCLUSION CRITERIA
An entry belongs in this subdivision if and only if it is complete for Boolean algebras—a bivalent logic validating excluded middle, non-contradiction, and bivalence, with consequence defined as truth preservation over two-valued models.
Required: At least one of the following:
- A two-valued truth-functional or model-theoretic semantics
- A proof system deductively equivalent to classical propositional, first-order, or higher-order logic
- A classical fragment or ontological extension (quantifier, identity, description, plural) whose propositional base is Boolean
Not sufficient: A first-order theory whose novelty is its non-logical signature and axioms rather than its logic—arithmetic, set theory, mereology (those belong in Theories). Completeness for Heyting algebras or a proper subvariety (Heyting). Admitting a third value or degrees (Many-Valued). Failure of distribution (Orthomodular). Adding a modal, temporal, or other intensional operator (Modal).
Boundary: Intuitionistic fragments belong in Heyting. Free and plural logics stay here—they alter the quantifier and its domain, which is logical apparatus. Mereology alters neither: it adds a relation and axioms for it, and belongs in Theories with arithmetic and set theory. Historical syllogistic and term logics belong here as classical validity systems; their debate practice belongs in Argumentation and Rhetoric. Aristotle's modal syllogistic stays beside its assertoric companion: its necessity and contingency are term-modifiers inside the syllogistic apparatus, not operators over a relational semantics, and the entry is placed by the apparatus they modify — a system individuated by intensional operators over frames goes to Modal, as Avicenna's temporal-modal syllogistic does.