Multiple-Valued Logic

Multiple-valued logic is a propositional logic having more than the two classical truth values true and false. A finite-valued logic chooses a set of truth values with , interprets each -ary connective as a function , and specifies which values are designated as logically acceptable.

For example, the -valued Łukasiewicz logic uses and operations

			(1)
			(2)

Different choices of truth values, connectives, and designated values produce different multiple-valued logics. Infinite-valued systems are also possible. Fuzzy logic commonly uses the full interval , although its interpretation and applications are not identical to those of every multiple-valued logic.

Łukasiewicz (1920) introduced a three-valued logic, and Post (1921) developed a general theory of finite-valued propositional systems.