“Fuzzification” of binary and finite multivalued logical calculi

Abstract

It is shown that fuzzification of binary logics results in multivalued logics with an infinite or finite number of values. Canonic formulae in fuzzified binary logics are discussed using some previous results of the author. The case of “hybrid” logics where either the variables or the functions run through different sets of values is discussed briefly. It is shown that the generalized connectives suggested by the author are suitable for forming functionally complete systems in these hybrid logics. Further fuzzification of finite multivalued calculi is discussed briefly. It is shown that a “fuzzified” multiple-valued logical function turns into an n-tuple of functions. A few simple illustrative examples are given.