Note on tense SHn-algebras

Abstract

In this article, we continue the study of tense SH-algebras. These algebras constitute a generalization of tense Lukasiewicz-Moisil algebras. In particular, we describe a discrete duality for tense SHn-algebras bearing in mind the results indicated by Orlowska and Rewitzky for SHn--algebras. In addition, we introduce a propositional calculus and prove this calculus has tense SHn-algebras as algebraic counterpart. Finally, the duality mentioned above allowed us to show the completeness theorem for this calculus.