BOOLEAN ALGEBRAS
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. The propositional core is complete for the two-element Boolean algebra; its quantificational extensions add cylindric and polyadic structure over the same Boolean base. It spans that core, its fragments and extensions, and the historical term and syllogistic traditions that codify classical validity.
Entries are organized by expressive strength. Propositional and Boolean systems form the base; first-order, higher-order, and second-order logics add quantification; fragments (guarded, two-variable, fluted, monadic) trade expressiveness for decidability. Ontological extensions—mereology, plural logic, free logic, definite descriptions—adjust the domain and reference of quantification while remaining Boolean at the propositional level. Historical entries (Aristotelian syllogistic, Stoic propositional logic, Mohist and School of Names dialectics, the Arabic logicians) present classical validity in their own idioms.