Theory of Generalized Tautology in Lukasiewicz Logic System

Theory of generalized tautology in logic system-W, WandWkis generalized and applied to Lukasiewicz logic system. The main resultsare asfollows: congruence about onset of logic formulasF(S)hasbeenobtained in thesystem; it is proved that in this system, for any irrational numberα, there does not exist accessibleα-tautology; and for any real numberα, there does not exist accessibleα+-tautology; and the relation theorems have been given between categories of generalized contradictions and between categories of generalized tautologies respectively.