Classical logic
Classical logic (or standard logic)[1][2] or Frege–Russell logic[3] is the intensively studied and most widely used class of deductive logic.[4] Classical logic has had much influence on analytic philosophy.
Generalized semantics[edit]
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; "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 algebra, which has no intermediate elements.