Miscellanea

Abstract

This chapter is devoted to three mutually unrelated topics showing three directions of further development of fuzzy logic. (Needless to say, several other directions are possible.) In Section 1 we present a rather strong fuzzy logic, based on the work of Takeuti and Titani, and containing Łukasiewicz, Gödel and product predicate logics Ł∀, G∀, Π∀ as its sublogics. We show completeness with respect to a non-finitary notion of provability. In Section 2 we show how to develop fuzzy logic that is not necessarily truth-functional. This section is based on work by Pavelka. Section 3 is based on recent work by Hájek, Paris and Shepherdson and discusses the Liar paradox in the frame of fuzzy logic. The final Section 4 contains some conclusions.