Monadic fuzzy predicate logics
type: Item
instance of: scholarly article
title: Monadic fuzzy predicate logics
zbMATH Open document ID: 1006.03023
DOI: 10.1023/A:1016544704961
author: Petr Hájek
published in: Studia Logica
publication date: 2002-08-26T00:00:00Z
review text: The paper is a contribution to the development of fuzzy logic, namely to the arithmetic properties of the monadic fuzzy predicate logic. The author first recalls basic results in classical monadic predicate logic, which is complete and decidable, and then shows that in fuzzy logic this problem is much more complicated and interesting. He first focuses on Łukasiewicz logic and shows that the set TAUT (tautologies w.r.t. standard semantics) as well as the set fTAUT (tautologies on all finite models) are \(\Pi_1\) and the set SAT (satisfiable formulas w.r.t. standard semantics) is \(\Pi_1\)-complete and fSAT is \(\Sigma_1\). For monadic Gödel logic, TAUT is \(\Sigma_1\), fTAUT and SAT are \(\Pi_1\) and fSAT is recursive. For monadic product logic, the properties of TAUT and SAT are (up to now) unknown and fTAUT is \(\Pi_1\) and fSAT is recursive. Finally, for monadic BL-fuzzy logic, the properties of TAUT and SAT are unknown, fTAUT is \(\Pi_1\) and fSAT is \(\Sigma_1\). Some further results concerning arithmetical properties are added. The paper also points to open questions in this field.
reviewed by: Vilém Novák
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03B50
zbMATH DE Number: 1788480
zbMATH Keywords: fuzzy logic
zbMATH Keywords: monadic logic
zbMATH Keywords: arithmetical hierarchy
zbMATH Keywords: Łukasiewicz logic
zbMATH Keywords: tautologies
zbMATH Keywords: satisfiable formulas
zbMATH Keywords: Gödel logic
zbMATH Keywords: product logic
MaRDI profile type: Publication
full work available at URL: a:1016544704961
OpenAlex ID: W1522382480
description: scientific article; zbMATH DE number 1788480