Mechanised Modal Model Theory

In this paper, we discuss the mechanisation of some fundamental propositional modal model theory. The focus on models is novel: previous work in mechanisations of modal logic have centered on proof systems and applications in model-checking. We have mechanised a number of fundamental results from the first two chapters of a standard textbook (Blackburn et al. [1]). Among others, one important result, the Van Benthem characterisation theorem, characterises the connection between modal logic and first order logic. This latter captures the desired saturation property of ultraproduct models on countably incomplete ultrafilters.