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.
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© 1998 Springer Science+Business Media Dordrecht
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Hájek, P. (1998). Miscellanea. In: Metamathematics of Fuzzy Logic. Trends in Logic, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5300-3_9
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DOI: https://doi.org/10.1007/978-94-011-5300-3_9
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-0370-7
Online ISBN: 978-94-011-5300-3
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