Theory of truth degrees of formulas in Lukasiewicz n-valued propositional logic and a limit theorem

摘要

The concept of truth degrees of formulas in Lukasiewicz n-valued propositional logic L_n is proposed. A limit theorem is obtained, which says that the truth function T_n induced by truth degrees converges to the integrated truth function tau when n converges to infinite. Hence this limit theorem builds a bridge between the discrete valued Lukasiewicz logic and the continuous valued Lukasiewicz logic. Moreover, the results obtained in the present paper is a natural generalization of the correspondingresults obtained in two-valued propositional logic.