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

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