Categorical study for Algebras of lattice-valued logic and lattice-valued modal logic

TL;DR

This paper investigates the categorical relationships and dualities between lattice-valued relational systems and algebras of lattice-valued modal logic, providing a foundational framework for understanding their interconnections.

Contribution

It introduces dualities for algebras of lattice-valued logic and modal logic using categorical and functorial approaches, expanding the theoretical understanding of these structures.

Findings

Established a duality for lattice-valued logic algebras

Developed a duality for lattice-valued modal logic algebras

Analyzed co-adjointness and adjointness of functors in this context

Abstract

The paper explores categorical interconnections between lattice-valued Relational systems and algebras of Fitting's lattice-valued modal logic. We define lattice-valued boolean systems, and then we study co-adjointness, adjointness of functors. As a result, we get a duality for algebras of lattice-valued logic. Following this duality results, we establish a duality for algebras of lattice-valued modal logic