Abstract
In this article, we propose a Dynamic Logic of Propositional Control DL-PC in which the concept of ‘seeing to it that’ (abbreviated stit) as studied by Belnap, Horty and others can be expressed; more precisely, we capture the concept of the so-called Chellas stit theory and the deliberatibe stit theory, as opposed to Belnap’s original achievement stit. In this logic, the sentence ‘group G sees to it that φ’ is defined in terms of dynamic operators: it is paraphrased as ‘group G is going to execute an action now such that whatever actions the agents outside G can execute at the same time, φ is true afterwards’. We also prove that the satisfiability problem is decidable. In the second part of the article we extend DL-PC with operators modeling normative concepts, resulting in a logic DL-PCLeg. In particular, we define the concepts of ‘legally seeing to it that’ and ‘illegally seeing to it that’. We prove that the decidability result for DL-PC transfers to DL-PCLeg.
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References
Ågotnes, T.: Action and knowledge in alternating-time temporal logic. Synthese 149(2), 377–409 (2006)
Ågotnes, T., van der Hoek, W., Wooldridge, M.: Robust normative systems and a logic of norm compliance. Logic Journal of IGPL 18(1), 4–30 (2009)
Alur, R., de Alfaro, L., Henzinger, T.A., Krishnan, S.C., Mang, F.Y.C., Qadeer, S., Rajamani, S.K., Taşiran, S.: Mocha user manual. University of Berkeley Report (2000)
Alur, R., Henzinger, T.A.: Reactive modules. Formal Methods in System Design 15(1), 7–48 (1999)
Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. J. of the ACM 49(5), 672–713 (2002)
Balbiani, P., Gasquet, O., Herzig, A., Schwarzentruber, F., Troquard, N.: Coalition games over Kripke semantics. In: Dégremont, C., Keiff, L., Rückert, H. (eds.) Dialogues, Logics and Other Strange Things – Essays in Honour of Shahid Rahman, pp. 11–32. College Publications (2008), http://www.collegepublications.co.uk/tributes/?00007
Balbiani, P., Herzig, A., Troquard, N.: Alternative axiomatics and complexity of deliberative stit theories. J. of Philosophical Logic 37(4), 387–406 (2008)
Belnap, N., Perloff, M., Xu, M.: Facing the Future: Agents and Choices in Our Indeterminist World. Oxford University Press (2001)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science. University Press (2001)
Broersen, J.: Modeling attempt and action failure in probabilistic stit logic. In: Walsh, T. (ed.) IJCAI, pp. 792–797. IJCAI/AAAI (2011)
Cohen, P.R., Levesque, H.J.: Intention is choice with commitment. Artificial Intelligence 42(2–3), 213–261 (1990)
Herzig, A., Lorini, E.: A dynamic logic of agency I: STIT, abilities and powers. Journal of Logic, Language and Information 19, 89–121 (2010)
Herzig, A., Lorini, E., Moisan, F., Troquard, N.: A dynamic logic of normative systems. In: Walsh, T. (ed.) International Joint Conference on Artificial Intelligence, IJCAI, Barcelona. Morgan Kaufmann Publishers (2011)
Herzig, A., Schwarzentruber, F.: Properties of logics of individual and group agency. In: Areces, C., Goldblatt, R. (eds.) Advances in Modal Logic, AiML, Nancy, pp. 133–149. College Publications (2008)
Herzig, A., Schwarzentruber, F.: Properties of logics of individual and group agency. In: Areces, C., Goldblatt, R. (eds.) AiML 2008, Nancy, pp. 133–149. College Publications (2008)
van der Hoek, W., Walther, D., Wooldridge, M.: On the logic of cooperation and the transfer of control. JAIR 37, 437–477 (2010)
van der Hoek, W., Wooldridge, M.: On the dynamics of delegation, cooperation and control: a logical account. In: Proc. AAMAS 2005 (2005)
van der Hoek, W., Wooldridge, M.: On the logic of cooperation and propositional control. Artificial Intelligence 164(1-2), 81–119 (2005)
Horty, J.: Agency and deontic logic. Oxford University Press (2001)
Jamroga, W., van der Hoek, W.: Agents that know how to play. Fundamenta Informaticae 63(2-3), 185–219 (2004)
Lomuscio, A., Raimondi, F.: mcmas: A Model Checker for Multi-agent Systems. In: Hermanns, H. (ed.) TACAS 2006. LNCS, vol. 3920, pp. 450–454. Springer, Heidelberg (2006)
Miller, J.S., Moss, L.S.: The undecidability of iterated modal relativization. Studia Logica 79(3), 373–407 (2005)
Sergot, M.J., Craven, R.: The Deontic Component of Action Language \(n{\mathcal{C}}+\). In: Goble, L., Meyer, J.-J.C. (eds.) DEON 2006. LNCS (LNAI), vol. 4048, pp. 222–237. Springer, Heidelberg (2006)
Shoham, Y., Tennenholtz, M.: On social laws for artificial agent societies: Off-line design. In: Agre, P.E., Rosenschein, S.J. (eds.) Computational Theories of Interaction and Agency, pp. 597–618. MIT Press, Cambridge (1996)
Tiomkin, M.L., Makowsky, J.A.: Propositional dynamic logic with local assignments. Theor. Comput. Sci. 36, 71–87 (1985)
van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204(11), 1620–1662 (2006)
van der Hoek, W., Lomuscio, A., Wooldridge, M.: On the complexity of practical ATL model checking. In: Proc. AAMAS 2006 (2005)
van der Hoek, W., Wooldridge, M.: Cooperation, knowledge, and time: Alternating-time temporal epistemic logic and its applications. Studia Logica 75, 125–157 (2003)
van Ditmarsch, H., Herzig, A., de Lima, T.: From situation calculus to dynamic logic. J. of Logic and Computation 21(2), 179–204 (2011)
van Ditmarsch, H.P., van der Hoek, W., Kooi, B.P.: Dynamic epistemic logic with assignment. In: Dignum, F., Dignum, V., Koenig, S., Kraus, S., Singh, M.P., Wooldridge, M. (eds.) Proc. of AAMAS 2005, pp. 141–148. ACM (2005)
van Ditmarsch, H.P., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Kluwer Academic Publishers (2007)
van Eijck, J.: Making things happen. Studia Logica 66(1), 41–58 (2000)
Wilm, A.: Determinism and non-determinism in PDL. Theor. Comput. Sci. 87(1), 189–202 (1991)
Wooldridge, M.: Computationally grounded theories of agency. In: 4th International Conference on Multi-Agent Systems, ICMAS 2000, pp. 13–22. IEEE Computer Society (2000)
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Herzig, A., de Lima, T., Lorini, E., Troquard, N. (2012). A Computationally Grounded Dynamic Logic of Agency, with an Application to Legal Actions. In: Ågotnes, T., Broersen, J., Elgesem, D. (eds) Deontic Logic in Computer Science. DEON 2012. Lecture Notes in Computer Science(), vol 7393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31570-1_12
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