Fuzzy constructive logic

We introduce a logical system in which the principles of fuzzy logic are interpreted from the point of view of the constructive approach The language of predicate formulas without functional symbols and symbols of constants is considered. The notion of identically trae predicate formula in the framework of the introduced logic is defined; two variants of this definition are given. Theorems concerning identically true predicate formulas are proved. Some connections between the introduced logic and the constructive (intuitionistic) predicate calculus are established. Bibliography: 40 titles. Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 358, 2008, pp. 130–152.