An Internal Semantics for Modal Logic: Preliminary Report
Ronald Fagin, Moshe Y. Vardi · 1985
Abstract: In Kripke semantics for modal logic, “pos-sible world^ " and the possibility relation are both primitive notions. This has both technical and con-ceptual shortcomings. From a technical point of view, the mathematics associated with Kripke. se-mantics is often quite complicated. From a concep-tual point of view, it is not clear how to use Kripke structures to model know!edge and belief, where one wants a clearer understanding of the notions that are primitive in Kripke semantics. We introduce modal structures as models for modal logic. We use the idea of possible worlds, but by directly describing the “internal semantics ” of each possible world. It is much easier to study the standard logical questions, such as completeness, decidability, and compactness, ushg modal structures. Furthermore, modal struc-tures offer a much more intuitive approach to mod-elling knowledge and belief. 1.