Symbolic Model Checking for Dynamic Epistemic Logic

  • Johan van Benthem
  • Jan van Eijck
  • Malvin Gattinger
  • Kaile Su
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9394)


Dynamic Epistemic Logic (DEL) can model complex information scenarios in a way that appeals to logicians. However, existing DEL implementations are ad-hoc, so we do not know how the framework really performs. For this purpose, we want to hook up with the best available model-checking and SAT techniques in computational logic. We do this by first providing a bridge: a new faithful representation of DEL models as so-called knowledge structures that allow for symbolic model checking. Next, we show that we can now solve well-known benchmark problems in epistemic scenarios much faster than with existing DEL methods. Finally, we show that our method is not just a matter of implementation, but that it raises significant issues about logical representation and update.


Model Check Multiagent System Knowledge Structure Kripke Model Symbolic Model 
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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  1. 1.
    Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements, common knowledge, and private suspicions. In: Bilboa, I. (ed.) TARK 1998, pp. 43–56 (1998)Google Scholar
  2. 2.
    van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204(11), 1620–1662 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    van Benthem, J., Gerbrandy, J., Hoshi, T., Pacuit, E.: Merging frameworks for interaction. Journal of Philosophical Logic 38(5), 491–526 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. In: Cambridge Tracts in Theoretical Computer Science, no. 53. CUP, Cambridge (2001)Google Scholar
  5. 5.
    Bryant, R.E.: Graph-Based Algorithms for Boolean Function Manipulation. IEEE Transaction on Computers C-35(8), 677–691 (1986)Google Scholar
  6. 6.
    Charrier, T., Schwarzentruber, F.: Arbitrary public announcement logic with mental programs. In: Proceedings of the 2015 International Conference on Autonomous Agents and Multiagent Systems, pp. 1471–1479. IFAAMAS (2015)Google Scholar
  7. 7.
    Chaum, D.: The dining cryptographers problem: Unconditional sender and recipient untraceability. Journal of Cryptology 1(1), 65–75 (1988)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Clarke, E.M., Grumberg, O., Long, D.E.: Model checking and abstraction. ACM Transactions on Programming Languages and Systems 16(5), 1512–1542 (1994)CrossRefGoogle Scholar
  9. 9.
    Cordón-Franco, A., van Ditmarsch, H., Fernández-Duque, D., Soler-Toscano, F.: A geometric protocol for cryptography with cards. Designs, Codes and Cryptography 74(1), 113–125 (2015), MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    van Ditmarsch, H.: The russian cards problem. Studia Logica 75(1), 31–62 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic epistemic logic, vol. 1. Springer, Heidelberg (2007)CrossRefzbMATHGoogle Scholar
  12. 12.
    van Ditmarsch, H., van der Hoek, W., van der Meyden, R., Ruan, J.: Model Checking Russian Cards. Electr. Notes Theor. Comput. Sci. 149(2), 105–123 (2006)CrossRefzbMATHGoogle Scholar
  13. 13.
    van Ditmarsch, H., van der Hoek, W., Ruan, J.: Connecting dynamic epistemic and temporal epistemic logics. Logic Journal of IGPL 21(3), 380–403 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Duque, D.F., Goranko, V.: Secure aggregation of distributed information. CoRR abs/1407.7582 (2014),
  15. 15.
    van Eijck, J.: DEMO-S5. Tech. rep., CWI (2014)Google Scholar
  16. 16.
    van Eijck, J., Ruan, J., Sadzik, T.: Action emulation. Synthese 185(1), 131–151 (2012)CrossRefzbMATHGoogle Scholar
  17. 17.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge, vol. 4. MIT Press, Cambridge (1995)zbMATHGoogle Scholar
  18. 18.
    Gammie, P.: hBDD. (2011, updated 2014)
  19. 19.
    Gattinger, M.: HasCacBDD (2015),
  20. 20.
    Gierasimczuk, N., Szymanik, J.: A note on a generalization of the Muddy Children puzzle. In: Apt, K.R. (ed.) TARK 2011, pp. 257–264. ACM (2011)Google Scholar
  21. 21.
    Gorogiannis, N., Ryan, M.D.: Implementation of Belief Change Operators Using BDDs. Studia Logica 70(1), 131–156 (2002)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Knuth, D.E.: The Art of Computer Programming. Combinatorial Algorithms, Part 1, vol. 4A. Addison-Wesley Professional (2011)Google Scholar
  23. 23.
    Littlewood, J.: A Mathematician’s Miscellany. Methuen, London (1953)zbMATHGoogle Scholar
  24. 24.
    Lomuscio, A., Qu, H., Raimondi, F.: MCMAS: an open-source model checker for the verification of multi-agent systems. International Journal on Software Tools for Technology Transfer, 1–22 (2015)Google Scholar
  25. 25.
    Lomuscio, A.R., van der Meyden, R., Ryan, M.: Knowledge in Multiagent Systems: Initial Configurations and Broadcast. ACM Trans. Comp. L. 1(2), 247–284 (2000)MathSciNetCrossRefGoogle Scholar
  26. 26.
    Luo, X., Su, K., Sattar, A., Chen, Y.: Solving Sum and Product Riddle via BDD-Based Model Checking. In: Web Intel./IAT Workshops, pp. 630–633. IEEE (2008)Google Scholar
  27. 27.
    Lv, G., Su, K., Xu, Y.: CacBDD: A BDD Package with Dynamic Cache Management. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 229–234. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  28. 28.
    van der Meyden, R., Su, K.: Symbolic Model Checking the Knowledge of the Dining Cryptographers. In: CSFW, pp. 280–291. IEEE Computer Society (2004)Google Scholar
  29. 29.
    Somenzi, F.: CUDD: CU Decision Diagram Package Release 2.5.0 (2012)Google Scholar
  30. 30.
    Su, K., Sattar, A., Luo, X.: Model Checking Temporal Logics of Knowledge Via OBDDs. The Computer Journal 50(4), 403–420 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Johan van Benthem
    • 1
    • 2
  • Jan van Eijck
    • 1
    • 3
  • Malvin Gattinger
    • 1
  • Kaile Su
    • 4
    • 5
  1. 1.Institute for Logic, Language & Computation (ILLC)University of AmsterdamAmsterdamThe Netherlands
  2. 2.Department of PhilosophyStanford UniversityStanfordUSA
  3. 3.Centrum Wiskunde & InformaticaAmsterdamThe Netherlands
  4. 4.Institute for Integrated and Intelligent SystemsGriffith UniversityNathanAustralia
  5. 5.Department of Computer ScienceJinan UniversityGuangzhouChina

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