Abstract
The Game Description Language (GDL) has been introduced as an official language for specifying games in the AAAI General Game Playing Competition since 2005. It was originally designed as a declarative language for representing rules of arbitrary games with perfect information. More recently, an epistemic extension of GDL, called EGDL, has been proposed for representing and reasoning about imperfect information games. In this paper, we develop an axiomatic system for a variant of EGDL and prove its soundness and completeness with respect to the semantics based on the epistemic state transition model. With a combination of action symbols, temporal modalities and epistemic operators, the completeness proof requires novel combinations of techniques used for completeness of propositional dynamic logic and epistemic temporal logic. We demonstrate how to use the proof theory for inferring game properties from game rules.
Most of the work was done while the first author was a postdoc at IRIT, University of Toulouse.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
van Benthem, J.: Games in dynamic-epistemic logic. Bull. Econ. Res. 53(4), 219–248 (2001)
van Benthem, J.: Logic in Games. MIT Press, Cambridge (2014)
Blackburn, P., De Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2002)
van Ditmarsch, H., Knight, S.: Partial information and uniform strategies. In: Bulling, N., Torre, L., Villata, S., Jamroga, W., Vasconcelos, W. (eds.) CLIMA 2014. LNCS (LNAI), vol. 8624, pp. 183–198. Springer, Cham (2014). doi:10.1007/978-3-319-09764-0_12
Fagin, R., Moses, Y., Halpern, J.Y., Vardi, M.Y.: Reasoning About Knowledge. MIT press, Cambridge (2003)
Genesereth, M., Love, N., Pell, B.: General game playing: overview of the AAAI competition. AI Mag. 26(2), 62–72 (2005)
Halpern, J.Y., van Der Meyden, R., Vardi, M.Y.: Complete axiomatizations for reasoning about knowledge and time. SIAM J. Comput. 33(3), 674–703 (2004)
Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artif. Intell. 54(3), 319–379 (1992)
Hintikka, J.: Knowledge and Belief: An Introduction to the Logic of the Two Notions. Cornell University Press, Ithaca (1962)
van der Hoek, W., Pauly, M.: Modal logic for games and information. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic, vol. 3, pp. 1077–1148. Elsevier, Amsterdam (2006)
van der Hoek, W., Wooldridge, M.: Cooperation, knowledge, and time: alternating-time temporal epistemic logic and its applications. Stud. Log. 75(1), 125–157 (2003)
Huang, X., van der Meyden, R.: An epistemic strategy logic. In: SR 2014, pp. 35–41 (2014)
Jamroga, W., van der Hoek, W.: Agents that know how to play. Fundam. Inform. 63(2), 185–219 (2004)
Jiang, G., Zhang, D., Perrussel, L., Zhang, H.: Epistemic GDL: a logic for representing and reasoning about imperfect information games. In: IJCAI 2016, pp. 1138–1144 (2016)
Kozen, D., Parikh, R.: An elementary proof of the completeness of PDL. Theor. Comput. Sci. 14(1), 113–118 (1981)
Love, N., Hinrichs, T., Haley, D., Schkufza, E., Genesereth, M.: General game playing: Game description language specification. Stanford Logic Group (2006). http://logic.stanford.edu/reports/LG-2006-01.pdf
Pritchard, D.B.: The Encyclopedia of Chess Variants. Games & Puzzles, UK (1994)
Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM J. Res. Dev. 3(2), 114–125 (1959)
Schiffel, S., Thielscher, M.: Reasoning about general games described in GDL-II. In: AAAI 2011, pp. 846–851 (2011)
Schobbens, P.Y.: Alternating-time logic with imperfect recall. Electron. Notes Theor. Comput. Sci. 85(2), 82–93 (2004)
Sistla, A.P., Clarke, E.M.: The complexity of propositional linear temporal logics. J. ACM 32(3), 733–749 (1985)
Thielscher, M.: A general game description language for incomplete information games. In: AAAI 2010, pp. 994–999 (2010)
Thielscher, M.: GDL-III: a proposal to extend the game description language to general epistemic games. In: ECAI 2016, pp. 1630–1631 (2016)
Zhang, D., Thielscher, M.: A logic for reasoning about game strategies. In: AAAI 2015, pp. 1671–1677 (2015)
Zhang, D., Thielscher, M.: Representing and reasoning about game strategies. J. Philos. Log. 44(2), 203–236 (2015)
Acknowledgments
We are grateful to Prof. Thomas Ã…gotnes and A/Prof. Yi Wang for their valuable suggestions, and special thanks are due to two anonymous referees for their insightful comments.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer-Verlag GmbH Germany
About this paper
Cite this paper
Jiang, G., Perrussel, L., Zhang, D. (2017). On Axiomatization of Epistemic GDL. In: Baltag, A., Seligman, J., Yamada, T. (eds) Logic, Rationality, and Interaction. LORI 2017. Lecture Notes in Computer Science(), vol 10455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-55665-8_41
Download citation
DOI: https://doi.org/10.1007/978-3-662-55665-8_41
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-55664-1
Online ISBN: 978-3-662-55665-8
eBook Packages: Computer ScienceComputer Science (R0)