Editing Classical logic (section)

==Generalized semantics==

With the advent of [[algebraic logic]], it became apparent that classical [[propositional calculus]] admits other [[semantics]]. In [[Boolean-valued semantics]] (for classical [[propositional logic]]), the truth values are the elements of an arbitrary [[Boolean algebra (structure)|Boolean algebra]]; "true" corresponds to the maximal element of the algebra, and "false" corresponds to the minimal element. Intermediate elements of the algebra correspond to truth values other than "true" and "false". The principle of bivalence holds only when the Boolean algebra is taken to be the [[two-element Boolean algebra|two-element algebra]], which has no intermediate elements.