Ten questions and one problem on fuzzy logic
The paper is a philosophical discussion concerning vagueness and the role of fuzzy logic for it. The author summarizes his point of view in the form of answers to ten questions originally raised by the well-known logician R. Parikh, namely: ``In which contexts do we use vague predicates'', ``What properties of vague predicates are important'', ``How are truth functions related to connectives'', ``What are the limitations'', ``What is true'', ``What are we enabled to say'', ``How do we communicate'', ``Is fuzzy logic helpful with the Sorites paradox'', ``How do we make decisions'' and ``What do we gain by accepting fuzzy logic''? The second part of the paper is a very brief overview of the problem of undefinability of truth, namely the dequotation schema \[ \varphi \equiv Tr(\overline{\varphi}). \] The latter has been fully answered in another paper [\textit{P. Hájek, J. B. Paris} and \textit{J. C. Shepherdson}, ``The liar paradox and fuzzy logic'', J. Symb. Log. (to appear)]. The author underlines especially the comparative character of truth values and (correctly) advocates fuzzy logic as a well-developed nontrivial mathematical theory, which may, besides its nice applications, bring some new light to classical logical problems. Most of the ideas of this paper are mathematically well established in the author's recent book [\textit{P. Hájek}, Metamathematics of fuzzy logic (Kluwer, Dordrecht) (1998)].
scientific article; zbMATH DE number 1308109