A complete many-valued logic with product-conjunction
type: Item
instance of: scholarly article
title: A complete many-valued logic with product-conjunction
zbMATH Open document ID: 0848.03005
DOI: 10.1007/BF01268618
author: Petr Hájek
author: Lluís Godo
author: Francesc Esteva
published in: Archive for Mathematical Logic
publication date: 1996-07-08T00:00:00Z
review text: Studies in the field of fuzzy sets related to triangular norms have shown that the infinitely many-valued logic over the real unit interval with 1 as the only designated truth degree and a product-based conjunction connective has not been discussed much till now, despite some representation theorems of \(t\)-norms which refer to the product as a kind of basic \(t\)-norm. Choosing the product conjunction, a corresponding implication connective via residuation (i.e., both of them as an adjoint pair), and defining negation formally from implication and the truth degree constant 0 like in intuitionistic logic, the authors constitute the system they investigate. The completeness proof is given via algebraic studies essentially like the corresponding proof for Łukasiewicz's infinite-valued logic, but now introducing and investigating product algebras for this product logic instead of the MV-algebras for the Łukasiewicz case.
reviewed by: Siegfried J. Gottwald
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 881130
zbMATH Keywords: axiomatizing product conjunction
zbMATH Keywords: infinite-valued logic
zbMATH Keywords: product algebras
zbMATH Keywords: product logic
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01268618
OpenAlex ID: W2024065710
description: scientific article; zbMATH DE number 881130