Abstract
We study the logic of strategic ability of coalitions of agents with bounded memory by introducing Alternating-time Temporal Logic with Bounded Memory (ATLBM), a variant of Alternating-time Temporal Logic (ATL). ATLBM accounts for two main consequences of the assumption that agents have bounded memory. First, an agent can only remember a strategy that specifies actions in a bounded number of different circumstances. While the ATL-formula \({\langle\!\langle{C}\rangle\!\rangle\square\varphi}\) means that coalition C has a joint strategy which will make φ true forever, the ATLBM-formula \({\langle\!\langle{C}\rangle\!\rangle^n\square\varphi}\) means that C has a joint strategy which for each agent in C specifies what to do in no more than n different circumstances and which will make φ true forever. Second, an agent has bounded recall—a strategy can only take the last m states of the system into account. We use the logic to study the interaction between strategic ability, bounded number of decisions, bounded recall and incomplete information. We discuss the logical properties and expressiveness of ATLBM, and its relationship to ATL. We show that ATLBM can express properties of strategic ability under bounded memory which cannot be expressed in ATL.
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References
Ågotnes, T. (2004). A logic of finite syntactic epistemic states. Ph.D. thesis, Department of Informatics, University of Bergen.
Ågotnes T., Goranko V., Jamroga W. (2007) Alternating-time temporal logics with irrevocable strategies. In: Samet D.(eds) Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XI). Belgium, Brussels, pp 15–24
Alur R., Henzinger T.A., Kupferman O. (2002) Alternating-time temporal logic. Journal of the ACM 49(5): 672–713
Belnap N., Perloff M. (1990) Seeing to it that: A canonical form for agentives. In: Kyburg H.E., Loui R.P., Carlson G.N.(eds) Knowledge representation and defeasible reasoning. Kluwer, Boston, pp 167–190
Belnap N.D., Perloff M., Xu M. (2001) Facing the future: Agents and choices in our indeterminist world. Oxford University Press, USA
Emerson E.A. (1990) Temporal and modal logic. In: van Leeuwen J.(eds) Handbook of theoretical computer science Volume B: Formal models and semantics. Elsevier Science Publishers B.V., Amsterdam, The Netherlands, pp 996–1072
Goranko V., van Drimmelen G. (2006) Complete axiomatization and decidability of alternating-time temporal logic. Theoretical Computer Science 353(1–3): 93–117
Herzig, A., & Troquard, N. (2006). Knowing how to play: Uniform choices in logics of agency. In G. Weiss & P. Stone (Eds.), AAMAS’06: 5th International Joint Conference on Autonomous Agents and Multi Agent Systems (pp. 209–216). Hakodate, Japan, May 8–12, 2006.
Jamroga W., Ågotnes T. (2007) Constructive knowledge: What agents can achieve under imperfect information. Journal of Applied Non-Classical Logics 17(4): 423–475
Jamroga W., van der Hoek W. (2004) Agents that know how to play. Fundamenta Informaticae 63(2–3): 185–219
Jonker, G. (2003). Feasible strategies in alternating-time temporal epistemic logic. Master’s thesis, University of Utrech, The Netherlands.
Pauly M. (2002) A modal logic for coalitional power in games. Journal of Logic and Computation 12(1): 149–166
Schobbens P.-Y. (2004) Alternating-time logic with imperfect recall. Electronic Notes in Theoretical Computer Science 85(2): 82–93
van der Hoek W., Wooldridge M. (2003) Cooperation, knowledge and time: Alternating-time temporal epistemic logic and its applications. Studia Logica 75: 125–157
Wooldridge, M., & van der Hoek, W. (2002). Time, knowledge, and cooperation: Alternating-time temporal epistemic logic and its applications. In Proceedings of the 5th International Conference on Coordination Models and Languages (p. 4).
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Ågotnes, T., Walther, D. A Logic of Strategic Ability Under Bounded Memory. J of Log Lang and Inf 18, 55–77 (2009). https://doi.org/10.1007/s10849-008-9075-4
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DOI: https://doi.org/10.1007/s10849-008-9075-4