Algebras for Galois-style connections and their discrete duality
type: Item
instance of: scholarly article
title: Algebras for Galois-style connections and their discrete duality
zbMATH Open document ID: 1195.03059
author: Ingrid Rewitzky
author: Ewa Orłowska
published in: Fuzzy Sets and Systems
publication date: 2010-05-07T00:00:00Z
review text: Discrete duality is a duality between a class of algebras and an associated class of relational systems without a topology. In the paper such a duality is established for classes of bounded distributive lattices with Galois-style pairs of modal operators and for MTL algebras which are the semantic structures for the monoidal t-norm logic MTL.
reviewed by: Wiesław A. Dudek
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 03B52
Mathematics Subject Classification ID: 06A15
Mathematics Subject Classification ID: 06D50
zbMATH DE Number: 5705403
zbMATH Keywords: Galois connection
zbMATH Keywords: residuation
zbMATH Keywords: modal operator
zbMATH Keywords: frame
zbMATH Keywords: discrete duality
zbMATH Keywords: bounded distributive lattices
zbMATH Keywords: MTL algebras
zbMATH Keywords: monoidal t-norm logic MTL
MaRDI profile type: Publication
full work available at URL: j.fss.2009.12.013
OpenAlex ID: W2063947486
cites work: Q4056047
cites work: Priestley dualities for some lattice-ordered algebraic structures, including MTL, IMTL and MV-algebras
cites work: Incomplete information: Structure, inference, complexity
cites work: Relational Representation Theorems for General Lattices with Negations
cites work: Relational Representation Theorems for Lattices with Negations: A Survey
cites work: Algebraic methods in philosophical logic
cites work: Q4329277
cites work: Boolean algebras arising from information systems
cites work: Q4316881
cites work: Q3313943
cites work: Monoidal t-norm based logic: Towards a logic for left-continuous t-norms
cites work: Q4230685
cites work: Q3425583
cites work: Boolean Algebras with Operators
cites work: Dual tableaux. Foundations, methodology, case studies
cites work: Duality via Truth: Semantic frameworks for lattice-based logics
cites work: Q5445172
cites work: Context Algebras, Context Frames, and Their Discrete Duality
cites work: Relational Methods in Computer Science
cites work: Q5483303
cites work: Representation of Distributive Lattices by means of ordered Stone Spaces
cites work: Characterisation of main classes of fuzzy relations using fuzzy modal operators
cites work: Fuzzy modal-like approximation operators based on double residuated lattices
cites work: Fuzzy Information Relations and Operators: An Algebraic Approach Based on Residuated Lattices
cites work: Topological representations of distributive lattices and Brouwerian logics
cites work: Duality for algebras of relevant logics
cites work: Q3952147
cites work: Fuzzy logics with modalities
DOI: 10.1016/J.FSS.2009.12.013
description: scientific article; zbMATH DE number 5705403