A Logic of Knowledge and Strategies with Imperfect Information

In this paper we put forward Epistemic Strategy Logic (ESL), a logic of knowledge and strategies in contexts of imperfect information. ESL extends Strategy Logic by adding modal operators for individual and collective knowledge. This enhanced framework allows us to represent explicitly and to reason about the knowledge agents have of their own and other agents’ strategies. We provide a semantics to ESL in terms of epistemic concurrent game models, then illustrate the expressive power of ESL as a specification language for games, both of perfect and imperfect information. Notably, we show that some fixed-point characterisations of operators for strategic abilities, which normally fail in contexts of imperfect information, can be recovered in a controlled way through the interplay of epistemic and strategy modalities.