A logic that acknowledges more than the two classical truth-values of truth and falsity. Intermediate values may be motivated by the demands of vagueness, of avoiding the logical paradoxes, and of avoiding the view that future contingent propositions are determinately true or false, this being thought to lead to fatalism. The original three-valued system in modern logic is due to the Polish logician Łukaziewicz. See also fuzzy logic, sea-battle.