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

Abstract

In 2011, tense $$\theta $$ -valued Łukasiewicz–Moisil algebras (or tense $$LM_\theta $$ -algebras) were introduced by Chiriţa as an algebraic counterpart of the tense $$\theta $$ -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 $$\theta $$ -valued Łukasiewicz–Moisil algebras. This new topological duality enables us to describe the tense $$LM_\theta $$ -congruences and the tense $$\theta LM_\theta $$ -congruences on a tense $$LM_\theta $$ -algebra and also to determine some properties of these algebras.