15 Combining modal logics

Abstract

Publisher Summary This chapter surveys two key combination methods––namely, fusions and products. It also examines some other combination methods. The properties of combined logics depend on those of their components plus the particular method of combination. The idea of combining modal logics is natural for many applications. The chapter explores the way in which modal logics can be combined and highlights the consequences of combining them. The formation of fusions is the simplest and the most natural way of combining modal logics. The formation of Cartesian products of various structures—vector and topological spaces, algebras—is a standard mathematical way of capturing the multidimensional character of the world. In modal logic, products of Kripke frames are natural constructions allowing it to reflect interactions between modal operators representing time, space, knowledge, or actions. The product construction as a combination method on modal logics is introduced and is used in applications in computer science and artificial intelligence.