Abstract
We continue the work initiated in Herzig and Lorini (J Logic Lang Inform, in press) whose aim is to provide a minimalistic logical framework combining the expressiveness of dynamic logic in which actions are first-class citizens in the object language, with the expressiveness of logics of agency such as STIT and logics of group capabilities such as CL and ATL. We present a logic called \({\mathcal{DDLA}}\) (Deterministic Dynamic logic of Agency) which supports reasoning about actions and joint actions of agents and coalitions, and agentive and coalitional capabilities. In \({\mathcal{DDLA}}\) it is supposed that, once all agents have selected a joint action, the effect of this joint action is deterministic. In order to assess \({\mathcal{DDLA}}\) we prove that it embeds Coalition Logic. We then extend \({\mathcal{DDLA}}\) with modal operators for agents’ preferences, and show that the resulting logic is sufficiently expressive to capture the game-theoretic concepts of best response and Nash equilibrium.
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References
Ågotnes T., Dunne P. E., van der Hoek W., Wooldridge M. (2007) Logics for coalitional games. In: Benthem J., Ju S., Veltman F. (eds) A meeting of the minds, volume 8 of texts in computer science. College Publications, London, pp 3–20
Alur R., Henzinger T., Kupferman O. (2002) Alternating-time temporal logic. Journal of the ACM 49: 672–713
Areces C., ten Cate B. (2006) Hybrid logics. In: Blackburn P., Benthem J., Wolter F. (eds) Handbook of modal logic (3). Elsevier, Amsterdam
Belnap N., Perloff M., Xu M. (2001) Facing the future: Agents and choices in our indeterminist world. Oxford University Press, New York
Blackburn P., de Rijke M., Venema Y. (2001) Modal logic. Cambridge University Press, Cambridge
Borgo, S. (2007). Coalitions in action logic. In Proceedings of the 20th international joint conference on artificial intelligence (IJCAI’07) (pp. 1822–1827). New York: AAAI Press.
Harel D., Kozen D., Tiuryn J. (2000) Dynamic logic. MIT Press, Cambridge
Harrenstein, P., van der Hoek, W., Ch. Meyer, J.-J., & Witteveen, C. (2002). On modal logic interpretations of games. In Proceedings of the 15th European conference on artificial intelligence (ECAI 2002), (pp. 28–32). New York: IOS Press.
Herzig, A., & Lorini, E. (2009). A dynamic logic of agency I: STIT, abilities and powers. Journal of Logic, Language and Information, (in press).
Horty J. F. (2001) Agency and deontic logic. Oxford University Press, Oxford
Lorini, E., Schwarzentruber, F., & Herzig, A. (2009). Epistemic games in modal logic: joint actions, knowledge and preferences all together. In Proceedings of the second international workshop on logic, rationality and interaction (LORI II), volume 5834 of LNAI, (pp. 212–226). Springer.
Osborne M. J., Rubinstein A. (1994) A course in game theory. MIT Press, Cambridge
Pauly, M. (2001). Logic for social software. PhD thesis. The Netherlands: University of Amsterdam
Pauly M. (2002) A modal logic for coalitional power in games. Journal of Logic and Computation 12(1): 149–166
Pauly, M., & Hansen, H. H. (2000). Axiomatising Nash-consistent coalition logic. In: Proceedings of the European conference on logics in AI (JELIA 2002), volume 2424 of LNAI (pp. 394–406) Springer.
Sahlqvist, H. (1975). Completeness and correspondence in the first and second order semantics for modal logics. In: S. Kanger (Ed.), Proceedings of the 3rd Scandinavian logic symposium, volume 82 of studies in logic, North-Holland.
Sauro, L., Gerbrandy, J., van der Hoek, W., & Wooldridge, M. (2006). Reasoning about action and cooperation. In: Proceedings of the fifth international joint conference on autonomous agents and multiagent systems (AAMAS 2006) (pp. 185–192) New York: ACM Press.
Troquard, N., van der Hoek, W., & Wooldridge, M. (2009). Model checking strategic equilibria. In D. A. Peled, M. J. Wooldridge (Eds.), Model checking and artificial intelligence, volume 5348 of LNAI (pp. 166–188).
van Benthem J. (2005) Open problems in logic and games. In: Artëmov S. N., Barringer H., d’Avila Garcez A. S., Lamb L. C., Woods J. (eds) We will show them! Essays in honour of Dov Gabbay volume 1. College Publications, London
van Benthem J. (2009) In praise of strategies. In: Eijck J., Verbrugge R. (eds) Discourses on social software, texts in logic and games. Amsterdam University Press, Amsterdam
van Benthem J., Girard P., Roy O. (2009) Everything else being equal: A modal logic for ceteris paribus preferences. Journal of Philosophical Logic 38(1): 83–125
van Benthem J., Liu F. (2007) Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17(2): 157–182
van der Hoek, W., Jamroga, W., & Wooldridge, M. (2005) A logic for strategic reasoning. In Proceedings of the fourth international joint conference on autonomous agens and multiagent systems (AAMAS 2005) (pp. 157–164) New York: ACM Press.
van der Hoek W., Pauly M. (2006) Modal logic for games and information. In: Blackburn P., Benthem J., Wolter F. (eds) Handbook of modal logic (3). Elsevier, Amsterdam
van der Hoek W., Wooldridge M. (2005) On the logic of cooperation and propositional control. Artificial Intelligence 64(1–2): 81–119
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Lorini, E. A Dynamic Logic of Agency II: Deterministic \({\mathcal{DLA}}\) , Coalition Logic, and Game Theory. J of Log Lang and Inf 19, 327–351 (2010). https://doi.org/10.1007/s10849-009-9104-y
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DOI: https://doi.org/10.1007/s10849-009-9104-y