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Erschienen in:
03.07.2018 | Foundations
A topological duality for tense \(\theta \)-valued Łukasiewicz–Moisil algebras
Erschienen in: Soft Computing | Ausgabe 12/2019
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Abstract
In 2011, tense \(\theta \)-valued Łukasiewicz–Moisil algebras (or tense \(LM_\theta \)-algebras) were introduced by Chiriţă as an algebraic counterpart of the tense \(\theta \)-valued Moisil propositional logic. In this paper we develop a topological duality for these algebras. In order to achieve this we extend the topological duality given in Figallo et al. (J Mult Valued Logic Soft Comput 16(3–5):303–322, 2010), for \(\theta \)-valued Łukasiewicz–Moisil algebras. This new topological duality enables us to describe the tense \(LM_\theta \)-congruences and the tense \(\theta LM_\theta \)-congruences on a tense \(LM_\theta \)-algebra and also to determine some properties of these algebras.