A new axiomatization for involutive monoidal t-norm-based logic
type: Item
instance of: scholarly article
title: A new axiomatization for involutive monoidal t-norm-based logic
zbMATH Open document ID: 0998.03024
DOI: 10.1016/S0165-0114(01)00100-2
author: Sándor Jenei
author: Siegfried J. Gottwald
published in: Fuzzy Sets and Systems
publication date: 2002-05-21T00:00:00Z
review text: The paper gives an alternative axiomatization for the monoidal t-norm-based residuated logic originally introduced by \textit{F. Esteva} and \textit{L. Godo} [Fuzzy Sets Syst. 124, 271-288 (2001; Zbl 0994.03017)]. The presented approach stresses the geometric understanding of Girard monoids, especially the rotation invariance \(T(x,y)\leq z\) iff \(T(y,N(z))\leq N(x)\), where \(T\) is a left-continuous triangular norm and \(N\) is a strong negation. The rotation invariance is transformed into axiom schemata for logical calculi, and then serves as a substitute for the standard adjointness condition linking conjunction and implication connectives in t-norm-based residuated logics. The proposed new (and equivalent) axiomatization may give new interesting results in the recently introduced residuated fuzzy logic based on left-continuous t-norms.
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 1743107
zbMATH Keywords: axiomatization
zbMATH Keywords: monoidal t-norm-based residuated logic
zbMATH Keywords: Girard monoids
zbMATH Keywords: rotation invariance
zbMATH Keywords: triangular norm
reviewed by: Radko Mesiar
MaRDI profile type: Publication
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cites work: Q4803010
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full work available at URL: s0165-0114(01)00100-2
OpenAlex ID: W2084613039
Wikidata QID: Q127481753
description: scientific article; zbMATH DE number 1743107