In Praise of Strategies

  • Johan van Benthem
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7010)


This programmatic note high-lights a major theme in my lecture notes “Logic in Games”[37]: the need for explicit logics that define agents’ strategies, as the drivers of interaction in games. Our text outlines issues, recalls recent results, and raises new open problems. Results are mainly quoted, and the emphasis is on new notions and questions. For more details on the various topics discussed, see the relevant references.


Modal Logic Temporal Logic Belief Revision Imperfect Information Linear Logic 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Abramsky, S.: Semantics of interaction: An introduction to game semantics. In: Dybjer, P., Pitts, A. (eds.) Proceedings of the 1996 CLiCS Summer School, pp. 1–31. Cambridge University Press (1997)Google Scholar
  2. 2.
    Ågotnes, T., van Ditmarsch, H.: What will they say? Public announcement games. Synthese (Knowledge, Rationality and Action). Presented at: Logic, Game Theory and Social Choice, Tsukuba, Japan, vol. 6 (2009) (to appear)Google Scholar
  3. 3.
    Zvesper, J.A., Apt, K.R.: Proof-Theoretic Analysis of Rationality for Strategic Games with Arbitrary Strategy Sets. In: Dix, J., Leite, J., Governatori, G., Jamroga, W. (eds.) CLIMA XI. LNCS, vol. 6245, pp. 186–199. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  4. 4.
    Artemov, S.: Logic of proofs: A unified semantics for modality and lambda-terms. Tech. rep., Cornell University, Technical Report CFIS 98-06 (1998)Google Scholar
  5. 5.
    Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Proceedings of the 7th Conference on Theoretical Aspects of Rationality and Knowledge (TARK 1998), pp. 43–56. Morgan Kaufmann Publishers Inc., San Francisco (1998)Google Scholar
  6. 6.
    Baltag, A., Smets, S.: Group belief dynamics under iterated revision: Fixed points and cycles of joint upgrades. In: Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XII), pp. 41–50. ACM, New York (2009)CrossRefGoogle Scholar
  7. 7.
    Baltag, A., Smets, S., Zvesper, J.: Keep ‘hoping’ for rationality: A solution to the backward induction paradox. Synthese 169, 301–333 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Belnap, N., Perloff, M., Xu, M.: Facing the Future: Agents and Choices in Our Indeterminist World. Oxford University Press, Oxford (2001)Google Scholar
  9. 9.
    Bonanno, G.: Axiomatic characterization of the agm theory of belief revision in a temporal logic. Artificial Intelligence 171(2-3), 144–160 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Bradfield, J., Stirling, C.: Modal μ-calculi. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3, pp. 721–756. Elsevier (2007)Google Scholar
  11. 11.
    Brandenburger, A.: Tutorial on game theory. In: First Amsterdam-Lausanne-London Graduate Workshop, London School of Economics (2007)Google Scholar
  12. 12.
    Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy Logic. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 59–73. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    de Bruin, B.: Explaining Games, The Epistemic Program in Game Theory. PhD thesis, ILLC, University of Amsterdam (2004); DS-2004-03 (Extended version in Synthese Library, Springer, 2010)Google Scholar
  14. 14.
    Dégremont, C.: The Temporal Mind: Observations on Belief Change in Temporal Systems. PhD thesis, ILLC, University of Amsterdam, DS-2010-03 (2010)Google Scholar
  15. 15.
    Dégremont, C., Gierasimczuk, N.: Can Doxastic Agents Learn? On the Temporal Structure of Learning. In: He, X., Horty, J., Pacuit, E. (eds.) LORI 2009. LNCS, vol. 5834, pp. 90–104. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  16. 16.
    Dégremont, C., Roy, O.: Agreement theorems in dynamic-epistemic logic. In: Heifetz, A. (ed.) Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XII), pp. 91–98. ACM, New York (2009)CrossRefGoogle Scholar
  17. 17.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. The MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  18. 18.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Knowledge-based programs. Distributed Computing 10, 199–225 (1997)CrossRefGoogle Scholar
  19. 19.
    Fontaine, G.: Modal Fixpoint Logic: Some Model Theoretic Questions. PhD thesis, ILLC, University of Amsterdam (2010)Google Scholar
  20. 20.
    Gheerbrant, A.: Fixed-Point Logics on Trees. PhD thesis, ILLC, University of Amsterdam (2010)Google Scholar
  21. 21.
    Ghosh, S.: Strategies made explicit in dynamic game logic. In: van Benthem, J., Pacuit, E. (eds.) Proceedings of the Workshop on Logic and Intelligent Interaction, ESSLLI 2008, pp. 74–81 (2008)Google Scholar
  22. 22.
    Gierasimczuk, N.: Knowing One’s Limits: Logical Analysis of Inductive Inference. PhD thesis, ILLC, University of Amsterdam (2010)Google Scholar
  23. 23.
    Girard, P.: Modal Logic for Belief and Preference Change. PhD thesis, ILLC, University of Amsterdam, DS-2008-04 (2008)Google Scholar
  24. 24.
    Gochet, P.: La formalisation du savoir-faire. Colloquium IPHRST Paris, Philosophical Institute, Université de Liège (2006)Google Scholar
  25. 25.
    Harrenstein, P.: Logic in Conflict. PhD thesis, Department of Computer Science, Utrecht University (2004)Google Scholar
  26. 26.
    Hollenberg, M.: Logic and Bisimulation. PhD thesis, Zeno Institute for Philosophy, University of Utrecht (1996)Google Scholar
  27. 27.
    Hoshi, T.: Epistemic Dynamics and Protocol Information. PhD thesis, Department of Philosophy, Stanford University, DS-2009-08 (2009)Google Scholar
  28. 28.
    Liu, F.: Changing for the Better: Preference Dynamics and Agent Diversity. PhD thesis, ILLC, University of Amsterdam, DS-2008-02 (2008); extended version appeared as Reasoning About Preference Dynamics. Synthese Library. Springer, Heidelberg (2011) Google Scholar
  29. 29.
    Osborne, M.J., Rubinstein, A.: A Course in Game Theory. The MIT Press, Cambridge (1994)zbMATHGoogle Scholar
  30. 30.
    Pacuit, E., Simon, S.: Reasoning with protocols under imperfect information. The Review of Symbolic Logic 4, 412–444 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Parikh, R., Pauly, M.: Game logic - An overview. Studia Logica 75, 165–182 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  32. 32.
    Pauly, M.: Logic for Social Software. PhD thesis, ILLC, University of Amsterdam, DS-2001-10 (2001)Google Scholar
  33. 33.
    Ramanujam, R., Simon, S.: A logical structure for strategies. In: Proceedings Logic and the Foundations of Game and Decision Theory (LOFT 7). Texts in Logic and Games, vol. 3, pp. 183–208. Amsterdam University Press (2008)Google Scholar
  34. 34.
    Ramanujam, R., Simon, S.: Dynamic logic of tree composition. In: Perspectives in Concurrency Theory, pp. 408–430. CRC Press (2009)Google Scholar
  35. 35.
    Renne, B.: Propositional games with explicit strategies. In: Mints, G., de Queiroz, R. (eds.) Proceedings of the 13th Workshop on Logic, Language, Information and Computation (WoLLIC 2006). Electronic Notes in Theoretical Computer Science, vol. 165, pp. 133–144 (2006)Google Scholar
  36. 36.
    Rodenhauser, B.: Updating epistemic uncertainty. Master’s thesis, ILLC, University of Amsterdam, MoL-2001-07 (2001)Google Scholar
  37. 37.
    van Benthem, J.: Logic in Games. ILLC, Lecture Notes & Book Pre-Version. University of Amsterdam (1999-2003)Google Scholar
  38. 38.
    van Benthem, J.: Games in dynamic epistemic logic. Bulletin of Economic Research 53, 219–248 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    van Benthem, J.: Extensive games as process models. Journal of Logic, Language and Information 11(3), 289–313 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  40. 40.
    van Benthem, J.: 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, vol. 1, pp. 229–264. King’s College Publications, London (2005)Google Scholar
  41. 41.
    van Benthem, J.: Dynamic logic of belief revision. Journal of Applied Non-Classical Logics 17, 129–155 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  42. 42.
    van Benthem, J.: Five questions on games. In: Hendricks, V., Hansen, P.G. (eds.) Game Theory: Five Questions, pp. 9–19. Automatic Press, Copenhagen (2007), InterviewGoogle Scholar
  43. 43.
    van Benthem, J.: Logic games: From tools to models of interaction. In: Gupta, A., Parikh, R., van Benthem, J. (eds.) Logic at the Crossroads, pp. 283–317. Allied Publishers, Mumbai (2007)Google Scholar
  44. 44.
    van Benthem, J.: Rational dynamics and epistemic logic in games. International Game Theory Review 9(1), 13–45 (2007); Erratum reprint 9(2), 377–409 MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    van Benthem, J.: Logic and Games. Texts in Logic and Games. FoLLI Series. Springer, Heidelberg (to appear)Google Scholar
  46. 46.
    van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)CrossRefzbMATHGoogle Scholar
  47. 47.
    van Benthem, J., Blackburn, P.: Modal logic, a semantic perspective. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3, pp. 1–84. Elsevier Science Publishers, Amsterdam (2007)CrossRefGoogle Scholar
  48. 48.
    van Benthem, J., Gerbrandy, J., Hoshi, T., Pacuit, E.: Merging frameworks for interaction. Journal of Philosophical Logic 38, 491–526 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    van Benthem, J., Gheerbrant, A.: Game solution, epistemic dynamics and fixed-point logics. Fundamenta Informaticae 100(1-4), 19–41 (2010)MathSciNetzbMATHGoogle Scholar
  50. 50.
    van Benthem, J., Ghosh, S., Liu, F.: Modelling simultaneous games with dynamic logic. Knowledge, Rationality and Action 165, 247–268 (2008)MathSciNetzbMATHGoogle Scholar
  51. 51.
    van Benthem, J., Girard, P., Roy, O.: Everything else being equal. a modal logic approach to ceteris paribus preferences. Journal of Philosophical Logic 38, 83–125 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    van Benthem, J., Ikegami, D.: Modal Fixed-Point Logic and Changing Models. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 146–165. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  53. 53.
    van Benthem, J., Liu, F.: Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics 17, 157–182 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  54. 54.
    van Benthem, J., Pacuit, E.: Modeling protocols and transforming temporal models. ManuscriptGoogle Scholar
  55. 55.
    van Benthem, J., Pacuit, E.: The tree of knowledge in action: Towards a common perspective. In: Governatori, G., Hodkinson, I., Venema, Y. (eds.) Proceedings of Advances in Modal Logic (AiML IV), pp. 87–106. King’s College Press (2006)Google Scholar
  56. 56.
    van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204(11), 1620–1662 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  57. 57.
    van Benthem, J., van Otterloo, S., Roy, O.: Preference logic, conditionals, and solution concepts in games. In: Lagerlund, H., Lindström, S., Sliwinski, R. (eds.) Modality Matters, pp. 61–76 (2006)Google Scholar
  58. 58.
    van der Hoek, W.: Extended modal logic for social software. Invited Lecture, LORI Workshop, Beijing (2007)Google Scholar
  59. 59.
    van der Hoek, W., Walther, D., Wooldridge, M.: Alternating-time temporal logic with explicit strategies. In: Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XI), pp. 269–278. ACM, New York (2007)Google Scholar
  60. 60.
    van der Hoek, W., Wooldridge, M., Jamroga, W.: A logic for strategic reasoning. In: Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems (AAMAS 2005), pp. 157–164. ACM, New York (2005)CrossRefGoogle Scholar
  61. 61.
    van der Meyden, R.: The dynamic logic of permission. Journal of Logic and Computation 6(3), 465–479 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  62. 62.
    van Eijck, J., Kuppusamy, L., Wang, Y.: Verifying epistemic protocols under common knowledge. In: Heifetz, A. (ed.) Proceedings of the 12th Conference on Theoretical Aspects of Rationality and Knowledge (TARK XII), pp. 257–266. ACM, New York (2009)Google Scholar
  63. 63.
    van Eijck, J., Sietsma, F., Wang, Y.: Logic of information flow on communication channels. In: Grossi, D., Kurzen, L., Velazquez Quesada, F. (eds.) Logic and Interactive Rationality Yearbook 2009, ILLC, University of Amsterdam, pp. 283–308 (2010)Google Scholar
  64. 64.
    van Otterloo, S.: A Security Analysis of Multi-Agent Protocols. PhD thesis, ILLC, University of Amsterdam, and Department of Computing, University of Liverpool, DS-2005-05 (2005)Google Scholar
  65. 65.
    Wang, Y.: Epistemic Modelling and Protocol Dynamics. PhD thesis, ILLC, University of Amsterdam, DS-2010-06 (2010)Google Scholar
  66. 66.
    Xu, M.: Combinations of Stit and actions. Journal of Logic, Language and Information 19, 485–503 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  67. 67.
    Zvesper, J.: Playing with Information. PhD thesis, ILLC, University of Amsterdam, DS-2010-02 (2010)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Johan van Benthem
    • 1
  1. 1.ILLCAmsterdam and Stanford UniversityUSA

Personalised recommendations