Research On Axiomatic Truth Degree Of BL（?） Predicate Calculus System

First-order logic,as one of the standard formal logics of axiomatic systems,contains the research contents such as degree reasoning,which is a hot and difficult point.Based on the semantic theory of first-order logic calculus,this paper studies the axiomatic truth degree of first-order logic by using the satisfiability and completeness theorem.Firstly,the definition of the satisfiability of union and intersection operation is given.Then the relationship between two special formulas with logical effective formulas and theorems is explained.And the prenex normal form equivalent to formulas is obtained.The above results will prepare for the research of predicate logic degree.Then the equality and inequality properties of axiomatic truth degree in predicate logic system BL （?） are studied.In this paper,the truth degree properties of strongly equivalent operators are given,and the truth degree calculation methods and properties of several special closed formulas are discussed.Then,the inequality properties of operators and the truth degree of formulas with four kinds of operators＆ ∨、∧、 、→ are studied.Then,on the basis of axiomatic truth degree of first-order logic,starting from the similarity degree between formulas and combined with predicate logic system BL （?）.According to the properties of axiomatic truth degree,the operation methods of similarity are simplified,the truth degrees of several kinds of closed formulas are obtained,and the calculation methods and properties of similarity degree with four kinds of operators including ≡ 、→ ∨、＆、 and the calculation method of similarity between formulas including （?）、（?） are discussed.Finally,the pseudo-distance calculation method and its related properties of BL （?）predicate logic system are discussed.The pseudo distance inequality with ∨ ∧、 、→and other operators are studied,which provides a method for the subsequent research on approximate reasoning and other problems.