Ten questions and one problem on fuzzy logic
type: Item
instance of: scholarly article
title: Ten questions and one problem on fuzzy logic
zbMATH Open document ID: 0930.03024
DOI: 10.1016/S0168-0072(98)00037-2
author: Petr Hájek
published in: Annals of Pure and Applied Logic
publication date: 2000-02-08T00:00:00Z
review text: 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)].
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03A05
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 1308109
zbMATH Keywords: fuzzy logic
zbMATH Keywords: vagueness
zbMATH Keywords: many-valued logic
zbMATH Keywords: philosophical discussion
zbMATH Keywords: undefinability of truth
zbMATH Keywords: dequotation schema
reviewed by: Vilém Novák
MaRDI profile type: Publication
cites work: An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
cites work: Metamathematics of fuzzy logic
cites work: Existence, Negation, and Abstraction in the Neoplatonic Hierarchy1
cites work: On the structure of semi-groups on a compact manifold with boundary
cites work: Bemerkungen zum Komprehensionsaxiom. Dem Andenken an Heinrich Scholz gewidmet
cites work: Q3964561
cites work: Q4888136
cites work: Q3997786
full work available at URL: s0168-0072(98)00037-2
OpenAlex ID: W2060306799
description: scientific article; zbMATH DE number 1308109