Triangle algebras: A formal logic approach to interval-valued residuated lattices
type: Item
instance of: scholarly article
title: Triangle algebras: A formal logic approach to interval-valued residuated lattices
zbMATH Open document ID: 1174.03028
published in: Fuzzy Sets and Systems
publication date: 2009-08-28T00:00:00Z
review text: To obtain a triangle algebra, the authors extend the definition of a residuated lattice with a new constant \(u\) (uncertainty) and two new unary connectives \(v\) (necessity) and \(\mu \) (possibility). The authors show that triangle algebras serve as an equational representation of interval-valued residuated lattices (IVRLs). Also, they present triangle logic, a system of many-valued logic capturing the tautologies of IVRLs. Triangle algebras are used to cast the essence of using closed intervals of bounded lattices \(L\) as truth values into a set of appropriate logical axioms.
reviewed by: Dana Piciu
Mathematics Subject Classification ID: 03G10
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 06F05
zbMATH DE Number: 5599383
zbMATH Keywords: interval-valued residuated lattices
zbMATH Keywords: triangle algebras
zbMATH Keywords: triangle logic
zbMATH Keywords: many-valued logic
author: B. Van Gasse
author: C. Cornelis
author: G. Deschrijver
author: E. E. Kerre
MaRDI profile type: Publication
full work available at URL: j.fss.2007.09.003
OpenAlex ID: W2103602076
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DOI: 10.1016/J.FSS.2007.09.003
description: scientific article; zbMATH DE number 5599383