Finite-valued logic

In logic, a finite-valued logic (also finitely many-valued logic) is a propositional calculus in which truth values are discrete. Traditionally, in Aristotle's logic, the bivalent logic, also known as binary logic was the norm, as the law of the excluded middle precluded more than two possible values (i.e., "true" and "false") for any proposition.^[1] Modern three-valued logic (ternary logic) allows for an additional possible truth value (i.e. "undecided").^[2]

The term finitely many-valued logic is typically used to describe many-valued logic having three or more, but not infinite, truth values. The term finite-valued logic encompasses both finitely many-valued logic and bivalent logic.^[3][4] Fuzzy logics, which allow for degrees of values between "true" and "false", are typically not considered forms of finite-valued logic.^[5] However, finite-valued logic can be applied in Boolean-valued modeling,^[6][7] description logics,^[8] and defuzzification^[9][10] of fuzzy logic. A finite-valued logic is decidable (sure to determine outcomes of the logic when it is applied to propositions) if and only if it has a computational semantics.^[11]