Tense operators on De Morgan algebras

The purpose of this article is to investigate the variety of algebras, which we call tense De Morgan algebras, as a natural generalization of tense algebras developed in Burges (1984, Handbook of Philosophical Logic, vol. II, pp. 89–139) (see also, Kowalski (1998, Rep. Math. Logic, 32, 53–95)). It is worth mentioning that the latter is a proper subvariety of the first one, as it is shown in a simple example. Our main interest is the representation theory for these classes of algebras.