Research ArticleNo Access

Tense De Morgan $S 4$ $S 4$ -algebras

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

E-mail Address: ceciliasegura5@gmail.com

https://doi.org/10.1142/S1793557122500140Cited by:5 (Source: Crossref)

Abstract

In [Tense operators on De Morgan algebras, Log. J. IGPL22(2) (2014) 255–267], Figallo and Pelaitay introduced the notion of tense operators on De Morgan algebras. Also, other notions of tense operators on De Morgan algebras were given by Chajda and Paseka in [De Morgan algebras with tense operators, J. Mult.-Valued Logic Soft Comput.1 (2017) 29–45; The Poset-based logics for the De Morgan negation and set representation of partial dynamic De Morgan algebras, J. Mult.-Valued Logic Soft Comput.31(3) (2018) 213–237; Set representation of partial dynamic De Morgan algebras, in 2016 IEEE 46th Int. Symp. Multiple-Valued Logic (IEEE Computer Society, 2016), pp. 119–124]. In this paper, we introduce a new notion of tense operators on De Morgan algebras and define the class of tense De Morgan $S 4$ $S 4$ -algebras. The main purpose of this paper is to give a discrete duality for tense De Morgan $S 4$ $S 4$ -algebras. To do this, we will extend the discrete duality given in [W. Dzik, E. Orłowska and C. van Alten, Relational Representation Theorems for Lattices with Negations: A Survey, Lecture Notes in Computer Science (2006), pp. 245–266], for De Morgan algebras.

Communicated by V. A. Artamonov

Keywords:

AMSC: 06D30, 06D50

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