Łukasiewicz Logic

The family of Łukasiewicz logics originated with the three-valued propositional logic introduced by Jan Łukasiewicz (1920). Its intermediate truth value represented modal possibility. More generally, for an integer , the -valued system has truth-value set . Its negation and implication operations are

			(1)
			(2)

A formula is a tautology when it has value 1 under every assignment of values in to its variables.

The infinite-valued Łukasiewicz logic uses the full interval with the same operations. The case agrees with classical propositional calculus.