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Reasoning about Joint Action and Coalitional Ability in Kn with Intersection

  • Thomas Ågotnes
  • Natasha Alechina
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6814)

Abstract

In this paper we point out that standard pdl-like logics with intersection are useful for reasoning about game structures. In particular, they can express coalitional ability operators known from coalition logic and atl. An advantage of standard, normal, modal logics is a well understood theoretical foundation and the availability of tools for automated verification and reasoning. We study a minimal variant, multi-modal K with intersection of modalities, interpreted over models corresponding to game structures. There is a restriction: we consider only game structures that are injective. We give a complete axiomatisation of the corresponding models, as well as a characterisation of key complexity problems. We also prove a representation theorem identifying the effectivity functions corresponding to injective games.

Keywords

Model Check Modal Logic Joint Action Multiagent System Effectivity Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Ågotnes, T., Goranko, V., Jamroga, W.: Alternating-time temporal logics with irrevocable strategies. In: Samet, D. (ed.) Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XI), June 2007, pp. 15–24. Presses Universitaires de Louvain, Brussels, Belgium (2007)CrossRefGoogle Scholar
  2. 2.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49, 672–713 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Belnap, N., Perloff, M.: Seeing to it that: a canonical form for agentives. Theoria 54, 175–199 (1988)CrossRefGoogle Scholar
  4. 4.
    Broersen, J., Herzig, A., Troquard, N.: A normal simulation of coalition logic and an epistemic extension. In: Samet, D. (ed.) Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK-2007), Brussels, Belgium, June 25-27, pp. 92–101 (2007)Google Scholar
  5. 5.
    Danecki, S.: Nondeterministic propositional dynamic logic with intersection is decidable. In: Skowron, A. (ed.) SCT 1984. LNCS, vol. 208, pp. 34–53. Springer, Heidelberg (1985)CrossRefGoogle Scholar
  6. 6.
    Gargov, G., Passy, S.: A note on boolean modal logic. In: Proc. of The Summer School and Conf. on Mathematical Logic ”Heyting 1988”, pp. 311–321. Plenum Press, New York (1988)Google Scholar
  7. 7.
    Goranko, V.: Coalition games and alternating temporal logics. In: Proceeding of the Eighth Conference on Theoretical Aspects of Rationality and Knowledge (TARK VIII), pp. 259–272. Morgan Kaufmann, San Francisco (2001)Google Scholar
  8. 8.
    Goranko, V., Jamroga, W., Turrini, P.: Strategic games and truly playable effectivity functions. In: Tumer, Yolum, Sonenberg, Stone (eds.) Proceedings of the 10th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2011), Taipei, Taiwan, pp. 727–734 (2011)Google Scholar
  9. 9.
    Harel, D.: Dynamic logic. In: Gabbay, D., Guenthner, F. (eds.) Handbook of Philosophical Logic, Volume II: Extensions of Classical Logic. Synthese Library, vol. 165, pp. 497–604. D. Reidel Publishing Co., Dordrecht (1984)CrossRefGoogle Scholar
  10. 10.
    Lange, M.: Model checking propositional dynamic logic with all extras. J. Applied Logic 4(1), 39–49 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Lorini, E.: A dynamic logic of agency II: Deterministic DLA, coalition logic, and game theory. Journal of Logic, Language and Information 19, 327–351 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Lutz, C., Sattler, U.: The complexity of reasoning with boolean modal logics. In: Wolter, F., Wansing, H., de Rijke, M., Zakharyaschev, M. (eds.) Advances in Modal Logic, vol. 3, pp. 329–348. World Scientific, Singapore (2002)CrossRefGoogle Scholar
  13. 13.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  14. 14.
    Pauly, M.: A modal logic for coalitional power in games. Journal of Logic and Computation 12(1), 149–166 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    van Benthem, J.: Games in dynamic-epistemic logic. Bulletin of Economic Research 53(4), 219–248 (2001)Google Scholar
  16. 16.
    van Benthem, J.: Extensive games as process models. J. of Logic, Lang. and Inf. 11, 289–313 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    van der Hoek, W., Pauly, M.: Modal logic for games and information. In: van Benthem, J., Blackburn, P., Wolter, F. (eds.) The Handbook of Modal Logic, pp. 1152–1180. Elsevier, Amsterdam (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Thomas Ågotnes
    • 1
  • Natasha Alechina
    • 2
  1. 1.Department of Information Science and Media StudiesUniversity of BergenNorway
  2. 2.School of Computer ScienceUniversity of NottinghamUK

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