Tense Operators on Distributive Lattices with Implication

Studia Logica 111 (4):687-708 (2023)
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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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Time and modality.A. N. Prior - 1957 - Revue Philosophique de la France Et de l'Etranger 148:114-115.
Intuitionistic tense and modal logic.W. B. Ewald - 1986 - Journal of Symbolic Logic 51 (1):166-179.
Tense operators on De Morgan algebras.A. V. Figallo & G. Pelaitay - 2014 - Logic Journal of the IGPL 22 (2):255-267.
Modes of Adjointness.C. Smith & M. Menni - 2014 - Journal of Philosophical Logic 43 (2-3):365-391.

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