Bitopological Duality for Algebras of Fittings logic and Natural Duality extension

TL;DR

This paper develops a bitopological duality framework for algebras related to Fitting's multi-valued logic and extends natural duality theory to a broader class of finite algebras with bounded distributive lattices.

Contribution

It introduces a novel bitopological duality for Fitting's multi-valued logic algebras and extends natural duality theory to encompass a wider class of finite algebras.

Findings

Established a duality for algebras of Fitting's logic

Extended natural duality to $ ext{ISP}( ext{L})$ for finite bounded distributive lattices

Provides a foundation for further algebraic and logical analysis

Abstract

In this paper, we investigate a bitopological duality for algebras of Fitting's multi-valued logic. We also extend the natural duality theory for $\mathbb{ISP_I}(\mathcal{L})$ by developing a duality for $\mathbb{ISP}(\mathcal{L})$, where $\mathcal{L}$ is a finite algebra in which underlying lattice is bounded distributive.