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Tense Operators on Distributive Lattices with Implication

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Abstract

Inspired by the definition of tense operators on distributive lattices presented by Chajda and Paseka in 2015, in this paper, we introduce and study the variety of tense distributive lattices with implication and we prove that these are categorically equivalent to a full subcategory of the category of tense centered Kleene algebras with implication. Moreover, we apply such an equivalence to describe the congruences of the algebras of each variety by means of tense 1-filters and tense centered deductive systems, respectively.

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Acknowledgements

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

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Authors and Affiliations

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

    Gustavo Pelaitay

  2. CONICET and Departamento de Matemática Facultad de Ciencias Exactas, Universidad Nacional del Centro, Tandil, Argentina

    William Zuluaga

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  1. Gustavo Pelaitay
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  2. William Zuluaga
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Correspondence to Gustavo Pelaitay.

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Pelaitay, G., Zuluaga, W. Tense Operators on Distributive Lattices with Implication. Stud Logica 111, 687–708 (2023). https://doi.org/10.1007/s11225-023-10047-4

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