Fuzzy Logic in Broader Sense: Its Current State and Future?

The so called Fuzzy Logic in Narrow Sense (FLn) is the basic constituent of mathematical fuzzy logic. Its development has been initiated by the paper of J. A Goguen [7] and the first, highly sophisticated paper is that of J. Pavelka [24]. His work has been continued by the author of this paper in [14] and especially in the book [13]. Fuzzy logic has been established as a generalization of classical mathematical logic with clearly distinguished syntax and semantics. The syntax consists of precise definitions of the formula, proof, formal theory, model, provability, etc. and the semantics is formed by a special residuated lattice. The latter in the above mentioned works is an MV-algebra and, namely, the standard Łukasiewicz algebra since Pavelka proved that completeness of the syntax w.r.t. semantics can be kept providing that the corresponding algebra fulfils the following four equations: ∨