Wiebe van der Hoek Michael Wooldridge Cooperation , Knowledge , and Time : Alternating - time Temporal Epistemic Logic and its Applications

Branching-time temporal logics have proved to be an extraordinarily successful tool in the formal specification and verification of distributed systems. Much of their success stems from the tractability of the model checking problem for the branching time logic ctl, which has made it possible to implement tools that allow designers to automatically verify that systems satisfy requirements expressed in ctl. Recently, ctl was generalised by Alur, Henzinger, and Kupferman in a logic known as “Alternating-time Temporal Logic” (atl). The key insight in atl is that the path quantifiers of ctl could be replaced by “cooperation modalities”, of the form 〈〈Γ〉〉, where Γ is a set of agents. The intended interpretation of an atl formula 〈〈Γ〉〉φ is that the agents Γ can cooperate to ensure that φ holds (equivalently, that Γ have a winning strategy for φ). In this paper, we extend atl with knowledge modalities, of the kind made popular in the work of Fagin, Halpern, Moses, Vardi and colleagues. Combining these knowledge modalities with atl, it becomes possible to express such properties as “group Γ can cooperate to bring about φ iff it is common knowledge in Γ that ψ”. The resulting logic — Alternating-time Temporal Epistemic Logic (atel) — shares the tractability of model checking with its atl parent, and is a succinct and expressive language for reasoning about game-like multiagent systems.