On Heyting algebras with negative tense operators

TL;DR

This paper introduces tense H-algebras, extending Heyting algebras with negative tense operators, and demonstrates their role as algebraic semantics for a logic with Galois negations, also establishing a duality theory.

Contribution

It defines tense H-algebras, proves their connection to intuitionistic logic with Galois negations, and develops a Priestley-style duality for these algebras.

Findings

Tense H-algebras serve as algebraic semantics for intuitionistic logic with Galois negations.

A Priestley-style duality for H-algebras is established.

The study extends the algebraic understanding of tense operators in intuitionistic logic.

Abstract

In this paper, we will study Heyting algebras endowed with tense negative operators, which we call tense H-algebras and we proof that these algebras are the algebraic semantics of the Intuitionistic Propositional Logic with Galois Negations. Finally, we will develop a Priestley-style duality for H-algebras.