A topological duality for tense θ -valued Łukasiewicz–Moisil algebras

Abstract

In 2011, tense θ-valued Łukasiewicz–Moisil algebras (or tense LM θ -algebras) were introduced by Chiriţă as an algebraic counterpart of the tense θ-valued Moisil propositional logic. In this paper we develop a topological duality for these algebras. In order to achieve this we extend the topological duality given in Figallo et al. (J Mult Valued Logic Soft Comput 16(3–5):303–322, 2010), for θ-valued Łukasiewicz–Moisil algebras. This new topological duality enables us to describe the tense LM θ -congruences and the tense θLM θ -congruences on a tense LM θ -algebra and also to determine some properties of these algebras.