Abstract
The aim of this paper, is to provide a logical framework for reasoning about actions, agency, and powers of agents and coalitions in game-like multi-agent systems. First we define our basic Dynamic Logic of Agency (\({\mathcal{DLA}}\)). Differently from other logics of individual and coalitional capability such as Alternating-time Temporal Logic (ATL) and Coalition Logic, in \({\mathcal{DLA}}\) cooperation modalities for expressing powers of agents and coalitions are not primitive, but are defined from more basic dynamic logic operators of action and (historic) necessity. We show that STIT logic can be reconstructed in \({\mathcal{DLA}}\). We then extend \({\mathcal{DLA}}\) with epistemic operators, which allows us to distinguish capability and power. We finally characterize the conditions under which agents are aware of their capabilities and powers.
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Ågotnes T. (2006) Action and knowledge in alternating-time temporal logic. Synthese 149(2): 377–409
Alur R., Henzinger T., Kupferman O. (2002) Alternating-time temporal logic. Journal of the ACM 49: 672–713
Ågotnes T., van der Hoek W., & Wooldridge M. (2007). Quantified coalition logic. In Proceedings of the Twentieth International Joint Conference on Artificial Intelligence (IJCAI’07) (pp. 1181–1186). New York: AAAI Press.
Balbiani P., Herzig A., Troquard N. (2008) Alternative axiomatics and complexity of deliberative STIT theories. Journal of Philosophical Logic 37(4): 387–406
Barnes B. (1988) The nature of power. Polity Press, Cambridge
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.
Broersen J., Herzig A., Troquard N. (2006) Embedding alternating-time temporal logic in strategic STIT logic of agency. Journal of Logic and Computation 16(5): 559–578
Broersen, J., Herzig, A., & Troquard, N. (2007). Normal coalition logic and its conformant extension. In Proceedings of the Eleventh Conference on Theoretical Aspects of Rationality and Knowledge (TARK 2007) (pp. 92–101).
Broersen, J. (2008). A logical analysis of the interaction between ‘obligation-to-do’ and ‘knowingly doing’. In Proceedings of the Ninth International Conference on Deontic Logic in Computer Science (DEON’08) (Vol. 5076 of LNCS pp. 140–154). Berlin: Springer-Verlag.
Castelfranchi, C. (2003). The micro–macro constitution of power. ProtoSociology, 18–19.
Harel D., Kozen D., Tiuryn J. (2000) Dynamic logic. MIT Press, Cambridge
Herzig, A., & Schwarzentruber, F. (2008). Properties of logics of individual and group agency. In C. Areces & R. Goldblatt (Eds.) Proceedings of Advances in Modal Logic (pp. 133–149). College Publications.
Herzig, A., & Troquard, N. (2006). Knowing how to play: Uniform choices in logics of agency. In Proceedings of the Fifth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2006) (pp. 209–216). New York: ACM Press.
Horty J. F. (2001) Agency and deontic logic. Oxford University Press, Oxford
Horty J. F., Belnap N. (1995) The deliberative STIT: A study of action, omission, and obligation. Journal of Philosophical Logic 24(6): 583–644
Jamroga W., Ågotnes T. (2007) Constructive knowledge: What agents can achieve under imperfect information. Journal of Applied Non-Classical Logics 17(4): 423–425
Jamroga W., van der Hoek W. (2004) Agents that know how to play. Fundamenta Informaticae 63(2-3): 185–219
Lorini, E. A dynamic logic of agency II: Deterministic DLA coalition logic, and game theory. Journal of Logic, Language and Information (in press).
Lorini E., Herzig A. (2008) A logic of intention and attempt. Synthese 163(1): 45–77
Pauly, M. (2001). Logic for social software. PhD thesis, University of Amsterdam, The Netherlands.
Pauly M. (2002) A modal logic for coalitional power in games. Journal of Logic and Computation 12(1): 149–166
Parikh R., Pacuit E., Cogan E. (2006) The logic of knowledge based obligation. Synthese 149(2): 311–341
Reiter R. (2001) Knowledge in action: Logical foundations for specifying and implementing dynamical systems. MIT Press, Cambridge
Sahlqvist, H. (1975). Completeness and correspondence in the first and second order semantics for modal logics. In S. Kanger (Eds.) Proceedings of the 3rd Scandinavian Logic Symposium Volume 82 of Studies in Logic North-Holland.
Schobbens, P. Y. (2004). Alternating-time logic with imperfect recall. In Electronic Notes in Theoretical Computer Science 85(2). Amsterdam: Elsevier.
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). A logic of games and propositional control. In Proceedings of the Eight International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2009) (pp. 961–968). New York: ACM Press.
van Benthem J. (2009) In praise of strategies. In: Eijck J., Verbrugge R. (eds) Discourses on social software texts in logic and games. University Press, Amsterdam
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., Wooldridge M. (2005) On the logic of cooperation and propositional control. Artificial Intelligence 64(1-2): 81–119
van der Hoek W., Wooldridge M. (2003) Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications. Studia Logica 75: 125–157
Weber M. (1947) The theory of social and economic organization. Oxford University Press, New York
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Herzig, A., Lorini, E. A Dynamic Logic of Agency I: STIT, Capabilities and Powers. J of Log Lang and Inf 19, 89–121 (2010). https://doi.org/10.1007/s10849-009-9105-x
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DOI: https://doi.org/10.1007/s10849-009-9105-x