Quantitative Research On Mtl Calculus System

Since the concept of truth degree was put forward,the quantification of propositional logic and predicate logic is a research hotspot.In this dissertation,two logic systems formed by the expansion of MTL propositional logic system(i.e.MTL ? predicate calculus system and NM nilpotent minimum logic system),are carried out quantitative research respectively.Firstly,based on the predicate calculus system MTL ? of left continuous triangle norm,the concept of axiomatic truth degree of formulas are introduced by the axiomatic method,the MP rule,HS rule and meet inference rules of this truth degree are proved,the computational transformation methods of axiomatic truth degree and the value rang-e of axiomatic truth degree of specific form formulas are given.Secondly,the concept of similarity degree and pseudo-distances of first order clos-ed logic formulas in MTL ? predicate logic system are introduced,some good propert-ies about similarity degree are proved as well as the continuity problem of logic-al operators about this pesudo-distance are discussed.Finally,in the NM system of nilpotent minimum logic,the concept of the integral truth degree of the formulas are proposed by formula induced integral function method,and the MP rule,the HS rule of the integral truth degree are proved by means of the integral invariance.The integral similarity degree and integral pseudo-distance are introduced on the whole set of formulas,and some good properties about the similarity degree and pseudo-distance are proved.At the same time in terms of the concept of divergence degrees and diameter,a new membership function for reflecting the consistency degrees of theories in NM propositional fuzzy logic is proposed,which is proved that of inconsistent theories are equal to 0 and that of completely consistent theories are equal to 1.