Title: Agents that Know How to Play.
Authors: Wojciech Jamroga, Parlevink Group, University of Twente, and Institute of Mathematics, University of Gdansk;
   Wiebe van der Hoek, Department of Computer Science, University of Liverpool

We look at ways to enrich Alternating-time Temporal Logic (ATL) - a formalism for specification and verification of multi-agent systems - with a notion of knowledge. Starting point of our study is a recent proposal for a system called Alternating-time Temporal Epistemic Logic (ATEL). We show that, assuming that agents act under uncertainty in some states of the system, the notion of allowable strategy should be defined with some caution. Moreover, we demonstrate a subtle difference between an agent knowing that he has a suitable strategy and knowing the strategy itself. We also point out that the agents should be assumed similar epistemic capabilities in the semantics of both strategic and epistemic operators.

Trying to implement these ideas, we propose two different modifications of ATEL. The first one, dubbed Alternating-time Temporal Observational Logic (ATOL), is a logic for agents with bounded recall of the past. With the second, ATEL-R*, we present a framework to reason about both perfect and imperfect recall, in which we also incorporate operators for reasoning about the past. We identify some feasible subsystems of this expressive system.

Keywords: multiagent systems, branching-time temporal logic, epistemic logic, knowledge, transition systems, games with incomplete information.

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