Module checking of strategic ability

Module checking is a decision problem proposed in late 1990s to formalize verification of open systems, i.e., systems that must adapt their behavior to the input they receive from the environment. It was recently shown that module checking offers a distinctly different perspective from the better-known problem of model checking. So far, specifications in temporal logic CTL have been used for module checking. In this paper, we extend module checking to handle specifications in alternating-time temporal logic (ATL). We define the semantics of ATL module checking, and show that its expressivity strictly extends that of CTL module checking, as well as that of ATL itself. At the same time, we show that ATL module checking enjoys the same computational complexity as CTL module checking. We also investigate a variant of ATL module checking where the environment acts under uncertainty. Finally, we revisit the semantics of ability in the module checking problem, and propose a variant where strategies of agents in the module depend only on what the agents are able to observe.