Embedding Coalition Logic in the Minimal Normal Multimodal Logic with Intersection

Abstract

We present a satisfiability-preserving embedding of coalition logic into a normal modal logic. An advantage of standard, normal, and modal logics is a well-understood theoretical foundation and the availability of tools for automated verification and reasoning. The target logic is multimodal K with intersection of modalities, interpreted over standard Kripke models corresponding to game structures. There is a restriction: we consider only game structures that are injective. We argue that this is a minor limitation, e.g., because coalition logic cannot discern between injective and non-injective game structures. We give a complete axiomatization of the corresponding models, as well as a characterization of key complexity problems. We also prove a representation theorem identifying the effectivity functions corresponding to injective games.