Graph Games and Logic Design

  • Johan van Benthem
  • Fenrong LiuEmail author
Conference paper
Part of the Logic in Asia: Studia Logica Library book series (LIAA)


Graph games are interactive scenarios with a wide range of applications. This position paper discusses old and new graph games in tandem with matching logics and identifies general questions behind this match. Throughout, we pursue two strands: logic as a way of analyzing existing graph games, and logic as an inspiration for designing new graph games. Our aim is modest: we propose a perspective that complements existing game-theoretic and computational ones, we raise questions, make observations, and suggest research directions—technical results are left to future work. But frankly, our main aim with this survey paper is to show that graph games are concrete, fun, easy to grasp, and yet challenging to study.



This research is supported by Tsinghua University Initiative Scientific Research Program (2017THZWYX08).


  1. Ågotnes, T., and H. van Ditmarsch. 2011. What will they say? Public announcement games. Synthese KRA 179 (1): 57–85.CrossRefGoogle Scholar
  2. Aigner, M., and M. Fromme. 1984. A game of cops and robbers. Discrete Applied Mathematics 8 (1): 1–12.CrossRefGoogle Scholar
  3. Areces, C., F. Carreiro, S. Figueira, and S. Mera. 2011. Expressive power, and decidability for memory logics. In Proceedings WoLLIC, 2008. Lecture notes in computer science, vol. 6642, 20–34. Berlin: Springer.Google Scholar
  4. Areces, C., R. Fervari, and G. Hoffmann. 2015. Relation-changing modal operators. Logic Journal of the IGPL 23: 601–627.CrossRefGoogle Scholar
  5. Areces, C., D. Figueira, S. Figueira, and S. Mera. 2008. Basic model theory, and for memory logics. In Proceedings WoLLIC, 2011. Lecture notes in computer science, vol. 5110, 56–68. Berlin: Springer.Google Scholar
  6. Areces, C., K. Mierzewski, and F. Zaffora Blando. 2018 (in this volume). Poison logics and memory logics. Manuscript, Department of Philosophy, Stanford University.Google Scholar
  7. Aucher, G., J. van Benthem, and D. Grossi. 2017. Modal logics of sabotage revisited. Logic and Computation 28 (2): 269–303.CrossRefGoogle Scholar
  8. van Benthem, J. 2011. Logical dynamics of information and interaction. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  9. van Benthem, J. 2014. Logic in games. Cambridge: The MIT Press.CrossRefGoogle Scholar
  10. van Benthem, J., K. Mierzewski, and F. Zaffora Blando. 2019. The modal logic of stepwise removal. To appear in Reports on Symbolic Logic.Google Scholar
  11. van Benthem, J., B. ten Cate, and J. Väanänen. 2009. Lindström theorems for fragments of first-order logic. Logical Methods in Computer Science 5 (3): 1–27.Google Scholar
  12. van Benthem, J., J. Gerbrandy, T. Hoshi, and E. Pacuit. 2009. Merging frameworks for interaction. Journal of Philosophical Logic 38 (5): 491–526.CrossRefGoogle Scholar
  13. van Benthem, J., and D. Klein. 2019. Logics for analyzing games. Stanford on-line encyclopedia of philosophy.Google Scholar
  14. Chen, Y. 2018. Model theory for modal logics of definable point deletion. Department of Philosophy, Tsinghua University.Google Scholar
  15. Diestel, R. 1997. Graph theory. Heidelberg: Springer.Google Scholar
  16. Duchet, P., and H. Meyniel. 1993. Kernels in directed graphs: A poison game. Discrete Mathematics 115: 273–276.CrossRefGoogle Scholar
  17. Gabbay, D., and V. Shethman. 1998. Products of modal logics. Logic Journal of the IGPL 6: 73–146.CrossRefGoogle Scholar
  18. Ghosh, S. 2018. Strategizing: a meeting of methods. Chennai: Indian Institute of Statistics. Under submission.Google Scholar
  19. Girard, P., F. Liu, and J. Seligman. 2014. Logical dynamics of belief change in the community. Synthese 191: 2403–2431.CrossRefGoogle Scholar
  20. Glendenning, L. 2005. Mastering quoridor. D.Sc. Thesis, University of New Mexico, Albuquerque.Google Scholar
  21. Goranko, V. 2018. A characterization of observer-fugitive games. Philosophical Institute, University of Stockholm.Google Scholar
  22. Grädel, E., W. Thomas, and T. Wilke (eds.). 2002. Automata, logics, and infinite games: A guide to current research. Lecture notes in computer science, vol. 2500. Berlin: Springer.Google Scholar
  23. Grossi, D. 2013. Abstract argument games via modal logic. Synthese 190 (5): 5–29.CrossRefGoogle Scholar
  24. Grossi, D., and P. Turrini. 2012. Short sight in extensive games. In Proceedings AAMAS 12, Valencia, 805–812.Google Scholar
  25. Grossi, D., and S. Rey. 2019. Credulous acceptability, poison games, and modal logic. In Proceedings AAMAS 2019, Montreal.Google Scholar
  26. Gurevich, Y., and S. Shelah. 1986. Fixed-point extensions of first-order logic. Annals of Pure and Applied Logic, 32.Google Scholar
  27. Li, D. 2018. Losing Connections: Modal logics of definable link deletion. Department of Philosophy, Tsinghua University. Presented at LOFT 13, Milano.Google Scholar
  28. Liu, F. 2011. Reasoning about preference dynamics. Dordrecht: Springer Science Publishers.CrossRefGoogle Scholar
  29. Liu, F. 2017. Choice points for graph games. Seminar Note. Department of Philosophy, Tsinghua University.Google Scholar
  30. Liu, C., F. Liu, and K. Su. 2015. A dynamic-logical characterization of solutions in sight-limited extensive games. In Proceedings PRIMA, 467–480.Google Scholar
  31. Löding, C. and Ph. Rohde. 2003. Model checking and satisfiability for sabotage modal logic. In Proceedings FSTTCS 2003, Springer lecture notes in computer science, 302–313.Google Scholar
  32. Mann, A., G. Sandu, and M. Sevenster. 2011. Independence-friendly logic: A game- theoretic approach. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  33. Marx, M., and Y. Venema. 1998. Multi-dimensional modal logic. Dordrecht: Springer Science Publishers.Google Scholar
  34. Mierzewski, K. 2018. Sabotage in the random graph. Department of Philosophy, Stanford University.Google Scholar
  35. Mierzewski, K., and F. Zaffora Blando. 2016 (in this volume). The modal logic(s) of poison games. Department of Philosophy, Stanford University. New version with co-author Carlos Areces to appear in Proceedings Fourth Asian Workshop on Philosophical Logic, Beijing. 2018.Google Scholar
  36. Mostowski, A. 1991. Games with forbidden positions. Technical Report 78, University of Danzig, Institute of Mathematics and Informatics.Google Scholar
  37. Nowakowski, R., and P. Winkler. 1983. Vertex-to-vertex pursuit in a graph. Discrete Mathematics 43: 235–239.CrossRefGoogle Scholar
  38. Osborne, M., and A. Rubinstein. 1994. A course in game theory. Cambridge: The MIT Press.Google Scholar
  39. Parsons, T. 1976. Pursuit-evasion in a graph. Theory and applications of graphs. Springer lecture notes in mathematics, vol. 642, 426–441.Google Scholar
  40. Segerberg, K. 1973. Two-dimensional modal logic. Journal of Philosophical Logic 2 (1): 77–96.CrossRefGoogle Scholar
  41. Seligman, J., and D. Thompson. 2015. Boolean network games and iterated boolean games. In Proceedings LORI Taiwan. Springer lecture notes in computer science, vol. 9394, 353–365.Google Scholar
  42. Thompson, D. 2018. A modal logic of local graph change. Department of Philosophy, Stanford University. To appear in Proceedings fourth Asian workshop on philosophical logic, Beijing. 2018.Google Scholar
  43. Zhang, T. 2018 (in this volume). Localized sabotage algorithm. Manuscript: Tsinghua University.Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Stanford UniversityStanfordUSA
  2. 2.Tsinghua UniversityBeijingChina

Personalised recommendations