Extended Fuzzy Constructive Logic

A logical system is introduced that is similar to the "fuzzy constructive logic" earlier developed by the author, but gives wider possibilities of establishing the truth of predicate formulas and logical deductions in the framework of this logic. The notions of strong and weak FCL* -validity of predicate formulas are defined. It is proved that every formula deducible in the constructive (intuitionistic) predicate calculus is strongly FCL* -valid. On the other hand, it is proved that some formulas not deducible in this calculus are not weakly FCL* -valid. A definition is given for the semantics of the traditional constructive logic on the base of the developed logical apparatus. Theorems are proved showing differences between the extended fuzzy constructive logic and the traditional constructive logic. Bibliography: 38 titles. © 2014 Springer Science+Business Media New York.