The Priestley duality for Wajsberg algebras
type: Item
instance of: scholarly article
title: The Priestley duality for Wajsberg algebras
zbMATH Open document ID: 0717.03026
DOI: 10.1007/BF00401552
published in: Studia Logica
publication date: 1990-01-01T00:00:00Z
review text: Wajsberg algebras are the algebraic counterpart of Łukasiewicz logic that is defined with axioms which characterize implication and negation and with Modus Ponens as a rule [\textit{A. J. Rodriguez}, Un estudio algebraico de los cálculos proposicionales de Łukasiewicz. Ph. D. Thesis, Univ. Barcelona (1980)]. In this paper, Wajsberg algebras are considered as Kleene algebras and bounded distributive lattices. The aim of this paper is to develop a duality theory for Wajsberg algebras, extending the duality between Kleene algebras and some ordered topological spaces that is considered by \textit{W. Cornish} and \textit{P. Fowler} [J. Austral. Math. Soc., Ser. A 27, 209-220 (1978; Zbl 0403.06010)]. A Wajsberg space is characterized as Kleene space over a family of partial functions satisfying a number of algebraic and topological properties.
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 06F30
zbMATH DE Number: 4181328
zbMATH Keywords: infinite-valued propositional calculi
zbMATH Keywords: Wajsberg algebras
zbMATH Keywords: Łukasiewicz logic
zbMATH Keywords: Kleene algebras
zbMATH Keywords: duality
zbMATH Keywords: Wajsberg space
zbMATH Keywords: Kleene space
author: Néstor G. Martínez
reviewed by: Georgiy E. Tseytlin
MaRDI profile type: Publication
cites work: Proper n-valued Lukasiewicz algebras as S-algebras of Lukasiewicz n- valued propositional calculi
cites work: Coproducts of De Morgan algebras
cites work: Q4187871
cites work: Algebraic Analysis of Many Valued Logics
cites work: A New Proof of the Completeness of the Lukasiewicz Axioms
cites work: Q4156761
cites work: Super-Łukasiewicz implicational logics
cites work: Super-Łukasiewicz propositional logics
cites work: Interpretation of AF \(C^*\)-algebras in Łukasiewicz sentential calculus
cites work: Representation of Distributive Lattices by means of ordered Stone Spaces
cites work: Ordered Topological Spaces and the Representation of Distributive Lattices
cites work: W-algebras which are Boolean products of members of SR[1] and CW- algebras
cites work: Q3855183
description: scientific article; zbMATH DE number 4181328