Modal Bilattice Logic and its Extensions

Abstract

We consider the lattices of extensions of three logics: (1) modal bilattice logic; (2) full Belnap–Dunn bimodal logic; (3) classical bimodal logic. It is proved that these lattices are isomorphic to each other. Furthermore, the isomorphisms constructed preserve various nice properties, such as tabularity, pretabularity, decidability or Craig’s interpolation property.