Theory of truth degrees of propositions in the logic system L_n~*

Approximate reasoning based on the idea of fuzzy sets was firstly proposed by Zadeh1] in 1973, which differs from the one advocated in Artificial Intelligence. Indeed, Artificial Intelligence emphasizes symbolic manipulation and roots itself in logic, em…

Theory of truth degrees of propositions in the logic system L*n

By means of infinite product of uniformly distributed probability spaces of cardinal n the concept of truth degrees of propositions in the n-valued generalized Lu- kasiewicz propositional logic system L*n is introduced in the present paper. It is proved that the set consisting of truth degrees of all formulas is dense in 0,1], and a general expres- sion of truth degrees of formulas as well as a deduction rule of truth degrees is then ob- tained. Moreover, similarity degrees among formulas are proposed and a pseudo-metric is defined therefrom on the set of formulas, and hence a possible framework suitable for developing approximate reasoning theory in n-valued generalized Lukasiewicz proposi- tional logic is established.