## Mathematical fuzzy logic – state of art 2001.(English)Zbl 1078.03508

Summary: The aim of this paper is to survey the present state of development of mathematical fuzzy logic (or fuzzy logic in the narrow sense) based on the logical systems BL and BL$$\forall$$ (basic fuzzy propositional and predicate logic) as introduced in my monograph [Metamathematics of fuzzy logic. Dordrecht: Kluwer (1998; Zbl 0937.03030)]. Note that there was another survey [the author, Logic colloquium ’98, Lect. Notes Log. 13, 197–205 (2000; Zbl 0949.03023)] written in 1998. The present paper is based on my lectures held on WOLLIC’2001 in July 2001 in Brasília, Brazil, and on Reason Park in August/September 2001 in Foligno, Italy. The paper cannot be any self-contained exposition; it should be understood as a guide for studying the book [loc. cit.] and later results. (Needless to say, only a selection of results is presented.) The reader should also be informed about four recent monographs dealing with many-valued (fuzzy) logic, each from its specific point of view: R. L. O. Cignoli, I. M. L. D’Ottaviano and D. Mundici, Algebraic foundations of many-valued reasoning [Dordrecht: Kluwer (2000; Zbl 0937.06009)], S. Gottwald, A treatise on many-valued logics [Baldock: Research Studies Press (2001; Zbl 1048.03002)], V. Novák, I. Perfilieva and J. Močkoř, Mathematical principles of fuzzy logic [Dordrecht: Kluwer (1999; Zbl 0940.03028)], and E. Turunen, Mathematics behind fuzzy logic [Heidelberg: Physica-Verlag (1999; Zbl 0940.03029)].

### MSC:

 03B52 Fuzzy logic; logic of vagueness 03-02 Research exposition (monographs, survey articles) pertaining to mathematical logic and foundations