Axiomatic truth degrees of formula in MTL∀predicate logic system

The quantification of propositional logic and predicate logic is a research hotspot. Based on left continuous triangle norm,the concept of truth degree of formulas in MTL∀ is introduced by the axiomatic method.The MP rule,HS rule and meet inference rules of this truth degree are proved. Meantime,the concept of similarity degree and pseudo-distances of first order closed logic formulas in MTL?predicate logic system are introduced,some good properties about similarity degree are proved. Furthermore, the continuity problem of logical operators about this pesudo distance is discussed.