Research On Quantification Of The First Order （?）ukasiewicz Calculus System

In this paper,a quantitative evaluation of first-order （?）ukasiewicz calculus system is carried out with the definition and properties of first-order axiomatic truth degree.Firstly,the formula with truth degree 1 and the formula with truth degree 0 are analyzed in the first-order logic,and their relation with theorems,generalized theorems and contradictions,generalized contradictions are given.The above work prepared for comparison of the truth degree of propositions in n-valued （?）ukasiewicz propositional logic system with axiomatic truth degree of formulas in first-order logic.Then,On the basis of introducing axiomatic truth degree into （?）ukasiewicz predicate calculus system,the axiomatic truth degree operation properties of content quantifiers and implication operators are analyzed,and a method of converting the truth degree of complex formulas into the truth degree of several simple formulas is given.The second,the operation properties of similarity and pseudo-distance between formulas are discussed in （?）ukasiewicz predicate calculus system,it is proved that the unary operation （?） and binary operation →and ∨ are continuous in pseudo metric space.Finally,the axiomatic truth degree in first-order logic is compared with the truth degree of propositions in （?） ukasiewicz propositional logic.The similarities and differences of truth degree properties between the axiomatic truth degree,the probability truth degree,the absolute truth degree,the random truth degree,the average truth degree of a theory in n-valued （?）ukasiewicz propositional logic system are given intuitively.