An alternating-time temporal logic with knowledge, perfect recall and past: axiomatisation and model-checking

We present a variant of ATL with incomplete information which includes the distributed knowledge operators corresponding to synchronous action and perfect recall. The cooperation modalities assume the use the distributed knowledge of coalitions and accordingly refer to perfect recall incomplete information strategies. We propose a model-checking algorithm for the logic. It is based on techniques for games with imperfect information and partially observable objectives, and involves deciding emptiness for automata on infinite trees. We also propose an axiomatic system and prove its completeness for a rather expressive subset. As for the constructs left outside this completely axiomatised subset, we present axioms by which they can be defined in the subset on the class of models in which every state has finitely many successors and give a complete axiomatisation for a “flat” subset of the logic with these constructs included.