Effectible residuated lattices and \(n\)-th roots
type: Item
instance of: scholarly article
title: Effectible residuated lattices and \(n\)-th roots
zbMATH Open document ID: 1209.03055
author: Remigijus Petras Gylys
published in: Fuzzy Sets and Systems
publication date: 2010-07-28T00:00:00Z
review text: The author introduces ``effectible residuated lattices'' and ``effectible Girard algebras'' as generalizations of various structures considered by Höhle and others, which, in turn, are generalizations of many structures arising as the algebras of many-valued logics as well as the order-theoretic counterparts of classes of bounded linear operators in Hilbert space. The present paper gives sufficient conditions for a Girard algebra to be an effect algebra. Similar conditions are given for residuated lattices to coincide with a suitable generalization of effect algebras.
reviewed by: Daniele Mundici
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 5762244
zbMATH Keywords: residuated lattice
zbMATH Keywords: Girard algebra
zbMATH Keywords: MV-algebra
zbMATH Keywords: Höhle monoid
zbMATH Keywords: effect algebra
MaRDI profile type: Publication
full work available at URL: j.fss.2009.12.009
OpenAlex ID: W2047159468
cites work: An elementary proof of Chang's completeness theorem for the infinite-valued calculus of Łukasiewicz
cites work: Algebraic foundations of many-valued reasoning
cites work: Q4836216
cites work: Q2762622
cites work: Probabilistic averaging in bounded commutative residuated \(\ell\)-monoids
cites work: Q4650586
cites work: Q4836218
cites work: MV-ALGEBRA VALUED FILTER THEORY
cites work: Q4369814
cites work: Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
cites work: Q4828845
cites work: Divisible effect algebras
DOI: 10.1016/J.FSS.2009.12.009
description: scientific article; zbMATH DE number 5762244