Tense SHn--algebras

TL;DR

This paper introduces tense SHn-algebras, extending symmetrical Heyting algebras with tense operators, and develops their duality theory based on existing dualities for related algebraic structures.

Contribution

It defines and studies tense SHn-algebras, generalizing tense Lukasiewicz-Moisil algebras, and establishes their duality theory using Esakia and Goldblatt dualities.

Findings

Defined tense SHn-algebras with two tense operators

Established duality theory for tense SHn-algebras

Generalized tense Lukasiewicz-Moisil algebras

Abstract

In 1982, L. Iturrioz introduced symmetrical Heyting algebras of order n (or SHn-algebras). In this paper, we define and study tense SHn-algebras namely, SHn-algebras endowed with two tense operators. These algebras constitute a generalization of tense Lukasiewicz-Moisil algebras. Our main interest is the duality theory for tense SHn- algebras. In order to do this, we requiere Esakia's duality for Heyting algebras and Goldblatt's duality for bounded distributive lattices with operations.