Formal Theories in Fuzzy Logic

Abstract

In this paper, we deal with syntactical aspects of two kinds of fuzzy logic, namely of fuzzy logic in narrow (FLn) and of broader sense (FLb). Fuzzy logic in narrow sense is now quite well established though the work is far from being finished. The goal of this logic is to develop means for modeling of the vagueness phenomenon. One of its partial goals, besides vagueness, is to formulate analogues of most theorems of the classical logic. This makes us possible to clarify the relation of fuzzy logic to the classical one and also, to gain a more profound understanding to both logics.