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Discrete Duality for Nelson Algebras with Tense Operators

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Abstract

In this paper, we continue with the study of tense operators on Nelson algebras (Figallo et al. in Studia Logica 109(2):285–312, 2021, Studia Logica 110(1):241–263, 2022). We define the variety of algebras, which we call tense Nelson D-algebras, as a natural extension of tense De Morgan algebras (Figallo and Pelaitay in Logic J IGPL 22(2):255–267, 2014). In particular, we give a discrete duality for these algebras. To do this, we will extend the representation theorems for Nelson algebras given in Sendlewski (Studia Logica 43(3):257–280, 1984) to the tense case.

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Acknowledgements

Jonathan Sarmiento and Gustavo Pelaitay 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, Av. Ignacio de la Roza 230 (O), Capital, J5402DCP, San Juan, Argentina

    Aldo V. Figallo, Gustavo Pelaitay & Jonathan Sarmiento

  2. Departamento de Matemática, Universidad Nacional del Sur, Av. Leandro N. Alem 1253, B8000CPB, Bahía Blanca, Buenos Aires, Argentina

    Jonathan Sarmiento

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  1. Aldo V. Figallo
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  2. Gustavo Pelaitay
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  3. Jonathan Sarmiento
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Correspondence to Jonathan Sarmiento.

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Figallo, A.V., Pelaitay, G. & Sarmiento, J. Discrete Duality for Nelson Algebras with Tense Operators. Stud Logica 111, 1–19 (2023). https://doi.org/10.1007/s11225-022-10013-6

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