Strategic and Epistemic Reasoning for the Game Description Language GDL-II

The game description language GDL has been developed as a logic-based formalism for representing the rules of arbitrary games in general game playing. A recent language extension called GDL-II allows to describe nondeterministic games with any number of players who may have incomplete, asymmetric information. In this paper, we show how the well-known Alternating-time Temporal Epistemic Logic (ATEL) can be adapted for strategic and epistemic reasoning about general games described in GDL-II. We provide a semantic characterisation of GDL-II descriptions in terms of ATEL models. We also provide a syntactic translation of GDL-II descriptions into ATEL formulas, and we prove that these two characterisations are equivalent. We show that model checking in this setting is decidable by giving an algorithm, and we demonstrate how our results can be used to verify strategic and epistemic properties of games described in GDL-II.