GDL Meets ATL: A Logic for Game Description and Strategic Reasoning

  • Guifei Jiang
  • Dongmo Zhang
  • Laurent Perrussel
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8862)


This paper presents a logical framework that extends the Game Description Language with coalition operators from Alternating-time Temporal Logic and prioritised strategy connectives. Our semantics is built upon the standard state transition model. The new framework allows us to formalise van Benthem’s game-oriented principles in multi-player games, and formally derive Weak Determinacy and Zermelo’s Theorem for two-player games. We demonstrate with a real-world game how to use our language to specify a game and design a strategy, and how to use our framework to verify a winning/no-losing strategy. Finally, we show that the model-checking problem of our logic is in 2EXPTIME with respect to the size of game structure and the length of formula, which is no worse than the model-checking problem in ATL ⋆ .


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Alur, R., Henzinger, T.A., Kupferman, O.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713 (2002)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Chatterjee, K., Henzinger, T.A., Piterman, N.: Strategy logic. Information and Computation 208(6), 677–693 (2010)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    van der Hoek, W., Jamroga, W., Wooldridge, M.: A logic for strategic reasoning. In: Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems, pp. 157–164. ACM (2005)Google Scholar
  4. 4.
    Kaneko, M., Nagashima, T.: Game logic and its applications. Studia Logica 57(2/3), 325–354 (1996)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Parikh, R.: The logic of games and its applications. In: Karplnski, M., van Leeuwen, J. (eds.) Topics in the Theory of Computation Selected Papers of the International Conference on ‘Foundations of Computation Theory’, FCT 1983. North-Holland Mathematics Studies, vol. 102, pp. 111–139. North-Holland (1985)Google Scholar
  6. 6.
    Pauly, M., Parikh, R.: Game logic-an overview. Studia Logica 75(2), 165–182 (2003)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    van Benthem, J.: Reasoning about strategies. In: Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky, pp. 336–347. Springer (2013)Google Scholar
  8. 8.
    Pauly, M.: A modal logic for coalitional power in games. Journal of Logic and Computation 12(1), 149–166 (2002)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Genesereth, M., Love, N., Pell, B.: General game playing: Overview of the AAAI competition. AI Magazine 26(2), 62–72 (2005)Google Scholar
  10. 10.
    Mogavero, F., Murano, A., Vardi, M.Y.: Reasoning about strategies. In: IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, pp. 133–144. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2010)Google Scholar
  11. 11.
    Ramanujam, R., Simon, S.E.: Dynamic logic on games with structured strategies. In: Proceedings of the Eleventh International Conference on Principles of Knowledge Representation and Reasoning (KR 2008), pp. 49–58 (2008)Google Scholar
  12. 12.
    Zhang, D., Thielscher, M.: Representing and reasoning about game strategies. To Appear in J. Philosophical Logic (2014)Google Scholar
  13. 13.
    van Benthem, J.: In praise of strategies. In: Eijck, J.V., Verbrugge, R. (eds.) Games, Actions, and Social Software. ILLC scientific publications, Institute for Logic, Language and Computation (ILLC), University of Amsterdam (2008)Google Scholar
  14. 14.
    Herzig, A., Lorini, E., Walther, D.: Reasoning about actions meets strategic logics. In: Grossi, D., Roy, O., Huang, H. (eds.) LORI 2013. LNCS, vol. 8196, pp. 162–175. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Walther, D., van der Hoek, W., Wooldridge, M.: Alternating-time temporal logic with explicit strategies. In: Proceedings of the 11th Conference on Theoretical Aspects of Rationality and Knowledge, pp. 269–278. ACM (2007)Google Scholar
  16. 16.
    Van den Herik, H.J., Uiterwijk, J.W., Van Rijswijck, J.: Games solved: Now and in the future. Artificial Intelligence 134(1), 277–311 (2002)CrossRefMATHGoogle Scholar
  17. 17.
    Polak, B.: Backward induction: Chess, strategies, and credible threats (2007),
  18. 18.
    Allis, L.V., van den Herik, H.J., Huntjens, M.P.H.: Go-moku solved by new search techniques. Computational Intelligence 12, 7–23 (1996)CrossRefGoogle Scholar
  19. 19.
    Allis, L., van der Meulen, M., van den Herik, H.: Proof-number search. Artificial Intelligence 66(1), 91–124 (1994)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Allis, L.V.: A knowledge-based approach of connect-four. Vrije Universiteit, Subfaculteit Wiskunde en Informatica (1988)Google Scholar
  21. 21.
    Allis, L.V.: Searching for solutions in games and artificial intelligence. Ph.D. thesis, University of Limburg, The Netherlands (1994)Google Scholar
  22. 22.
    Wágner, J., Virág, I.: Solving renju. ICGA Journal 24(1), 30–35 (2001)Google Scholar
  23. 23.
    Ruan, J., Van Der Hoek, W., Wooldridge, M.: Verification of games in the game description language. Journal of Logic and Computation 19(6), 1127–1156 (2009)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Guifei Jiang
    • 1
    • 2
  • Dongmo Zhang
    • 1
  • Laurent Perrussel
    • 2
  1. 1.AIRGUniversity of Western SydneyAustralia
  2. 2.IRITUniversity of Toulouse 1France

Personalised recommendations