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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)

Abstract

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 ⋆ .

Keywords

Reachable State Logical Framework Game Strategy Strategic Reasoning Strategy Rule 
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.
    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), http://oyc.yale.edu/economics/econ-159/lecture-15
  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

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