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A topological duality for tense \(\theta \)-valued Łukasiewicz–Moisil algebras

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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.

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Notes

  1. Recall that W is an increasing subset of X iff \(x\in W\) and \(x\le y\) imply \(y\in W.\)

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Acknowledgements

The support of CONICET is gratefully acknowledged by Gustavo Pelaitay.

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Authors and Affiliations

  1. Instituto de Ciencias Básicas, Universidad Nacional de San Juan, 5400, San Juan, Argentina

    Aldo V. Figallo, Inés Pascual & Gustavo Pelaitay

  2. Departamento de Matemática, Universidad Nacional de San Juan, 5400, San Juan, Argentina

    Inés Pascual

Authors
  1. Aldo V. Figallo
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  2. Inés Pascual
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  3. Gustavo Pelaitay
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Correspondence to Gustavo Pelaitay.

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Communicated by A. Di Nola.

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Figallo, A.V., Pascual, I. & Pelaitay, G. A topological duality for tense \(\theta \)-valued Łukasiewicz–Moisil algebras. Soft Comput 23, 3979–3997 (2019). https://doi.org/10.1007/s00500-018-3360-1

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