Categorical study for algebras of Fitting's lattice-valued logic and lattice-valued modal logic - Ray, Kumar Sankar; Das, Litan Kumar (Annals of mathematics and artificial intelligence, 2021)
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 adjointness and co-adjointness of functors defined on them. As a result, we get a duality for algebras of lattice-valued logic. Following this duality result, we establish a duality for algebras of lattice-valued modal logic. Keywords Lattice-valued Boolean systems * Lattice-valued relational systems * Algebras of Fitting's lattice-valued modal logic * Adjoint * Co-adjoint * Duality Mathematics Subject Classification (2010) 03B50 * 06D22 * 06D50 * 18B99