Fuzzy logic and arithmetical hierarchy
type: Item
instance of: scholarly article
title: Fuzzy logic and arithmetical hierarchy
zbMATH Open document ID: 0857.03011
DOI: 10.1016/0165-0114(94)00299-M
author: Petr Hájek
published in: Fuzzy Sets and Systems
publication date: 1997-03-11T00:00:00Z
review text: For fuzzy logic in the sense of \textit{J. Pavelka} [Z. Math. Logik Grundlagen Math. 25, 45-52, 119-134, 447-464 (1979; Zbl 0435.03020, Zbl 0446.03015, and Zbl 0446.03016)], i.e. for an extension of Łukasiewicz's \([0,1]\)-valued propositional logic with graded notions of proof and of entailment and with truth degree constants for all truth degrees, the author gives a considerably simplified axiomatization. He also proves completeness for the restricted case that only truth degree constants for the rational truth degrees are accepted and that the fuzzy sets of premisses have only rational membership degrees. Finally he proves \(\Pi_2\)-completeness for the notion of provability for this logic.
reviewed by: Siegfried J. Gottwald
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03F20
Mathematics Subject Classification ID: 03B25
zbMATH DE Number: 919400
zbMATH Keywords: rational Pavelka logic
zbMATH Keywords: undecidability of provability
zbMATH Keywords: fuzzy logic
zbMATH Keywords: axiomatization
zbMATH Keywords: rational truth degrees
zbMATH Keywords: fuzzy sets of premisses
zbMATH Keywords: rational membership degrees
MaRDI profile type: Publication
Wikidata QID: Q56083681
cites work: Q3484813
cites work: Q4836227
cites work: On Fuzzy Logic III. Semantical completeness of some many‐valued propositional calculi
cites work: Q5573961
cites work: Fragments of Many-Valued Statement Calculi
full work available at URL: 0165-0114(94)00299-m
OpenAlex ID: W2025952124
description: scientific article; zbMATH DE number 919400