Theories Of Truth Degrees And Approximate Reasoning In A Class Of N - Valued Prepositional Logics

The classical two valued logical calculus lays a theoretical foundation for accurate logical reasonings. Many different approximate reasoning methods, however, have been provided owing to the inaccuracy of a great many of reasonings in our daily life. Professor Zadeh firstly introduced a theory of approximate reasoning based on fuzzy sets in 1973, it is different from the method in the field of Artifical Intelligence which stresses signal operations and attaches little importance to the numerical computation. In the kte of 1970s, Pavelka put forward an approximate reasoning system in his articles 《On fuzzy logic Ⅰ,Ⅱ,Ⅲ》 which imposed degrees on Axioms and reference rules, it is the forerunner of merging fuzzy sets into logical calculus.Actually, it is not the fact that approximate reasoning must keep in touch with fuzzy sets, the major part of approximate reasoning proposed by professor Wang Guo-jun in his monograph 《Nonclassical mathematical logic and approximate reasoning》 is independent of the theory of fuzzy sets. This dissertation develops an integrated framework of approximate reasoning for a class of n ?valued propositional logics which doesn't rely on fuzzy sets too, the main content is as follows:Base on the infinite product of evenly distributed probability spaces, the first section introduces the theory of truth degrees in n - valued propositional logics. Meanwhile, the distribution of the set of truth degrees in [0,1 ]and expressions of truth degrees are obtained,it is proved that the truth degrees set M of all formulas is dense in[0,1] and M = {t\ni|i=1,2,…;t=0,1 …t; ni}. Furthermore, general infernce rules with truth degrees are presented.In the second part, a pseudo - metric on the set of propositions is defined by?I ?means of the concept of truth degrees of propositions and a possible framework for approximate reasoning is proposed. Also, the continuity of logical operators " " " " " "and " " in the pseudo - metric space (F(S),p) is proved.Finally, the theory of approximate reasoning in the pseudo ?metric space (.F(S) , ) is discussed in detail and the inherent relation between two sorts of errors is given out.