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An Algebraic Study of Tense Operators on Nelson Algebras

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Abstract

Ewald considered tense operators G, H, F and P on intuitionistic propositional calculus and constructed an intuitionistic tense logic system called IKt. In 2014, Figallo and Pelaitay introduced the variety IKt of IKt-algebras and proved that the IKt system has IKt-algebras as algebraic counterpart. In this paper, we introduce and study the variety of tense Nelson algebras. First, we give some examples and we prove some properties. Next, we associate an IKt-algebra to each tense Nelson algebras. This result allowed us to determine the congruence of the tense Nelson algebras and also to characterize the subdirectly irreducible tense Nelson algebras and particularly the simple tense Nelson algebras. Finally, we prove that there exists an equivalence between the category of IKt-algebras and the category of tense centered Nelson algebras.

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Acknowledgements

The authors acknowledge many helpful comments from the anonymous referee, which considerably improved the presentation of this paper. Jonathan Sarmiento want to thank the institutional support of Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET).

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Authors and Affiliations

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

    A. V. Figallo, G. Pelaitay & J. Sarmiento

  2. Departamento de Matemática, Universidad Nacional del Sur, 8000, Bahía Blanca, Buenos Aires, Argentina

    J. Sarmiento

Authors
  1. A. V. Figallo
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  2. G. Pelaitay
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  3. J. Sarmiento
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Correspondence to G. Pelaitay.

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Figallo, A.V., Pelaitay, G. & Sarmiento, J. An Algebraic Study of Tense Operators on Nelson Algebras. Stud Logica 109, 285–312 (2021). https://doi.org/10.1007/s11225-020-09907-0

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  • DOI: https://doi.org/10.1007/s11225-020-09907-0

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