Combined Logics of Knowledge, Time, and Actions for Reasoning about Multi-agent Systems

  • Nikolay V. Shilov
  • Natalia O. Garanina
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6581)

Abstract

We present a summary of our studies (in period 2002-2007) of the model checking problem for finitely-generated synchronous/asynchronous environments with/without perfect recall for combinations of propositional logics of (common) knowledge, (branching) time, and actions.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Abdulla, P.A., Ĉerâns, K., Jonsson, B., Tsay, Y.-K.: Algorithmic analysis of programs with well quasi-ordered domains. Information and Computation 160(1-2), 109–127 (2000)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Arnold, A., Niwinski, D.: Rudiments of μ-calculus. North Holland, Amsterdam (2001)MATHGoogle Scholar
  3. 3.
    Bull, R., Segerberg, K.: Basic Modal Logic. In: Gabbay, D., Cuenthner, F. (eds.) Handbook of Philosophical Logic, vol. 3. Kluwer Academic Publishers, Dordrecht (2001)Google Scholar
  4. 4.
    Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)Google Scholar
  5. 5.
    Dixon, C., Fernandez Gago, M.-C., Fisher, M., van der Hoek, W.: Using Temporal Logics of Knowledge in the Formal Verification of Security Protocols. In: Proceedings of TIME 2004, Tatihou, Normandie, France, July 1-3. IEEE, Los Alamitos (2004)Google Scholar
  6. 6.
    Dixon, C., Nalon, C., Fisher, M.: Tableau for Logics of Time and Knowledge with Interactions Relating to Synchrony. Journal of Applied Non-Classical Logics 14(4), 397–445 (2004)CrossRefMATHGoogle Scholar
  7. 7.
    Emerson, E.A.: Temporal and Modal Logic. In: van Leeuwen, J., Meyer, A.R., Nivat, M., Paterson, M., Perrin, D. (eds.) Handbook of Theoretical Computer Science (B). Elsevier, The MIT Press (1990)Google Scholar
  8. 8.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (1995)MATHGoogle Scholar
  9. 9.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comp. Sci. 256(1-2), 63–92 (2001)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Gammie, P., van der Meyden, R.: MCK: Model checking the logic of knowledge. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 479–483. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Garanina, N.O., Kalinina, N.A., Shilov, N.V.: Model checking knowledge, actions and fixpoints. In: Proc. of Concurrency, Specification and Programming Workshop CS&P 2004, Germany, Humboldt Universitat, Berlin, Informatik-Bericht, vol. 2(170), pp. 351–357 (2004)Google Scholar
  12. 12.
    Garanina, N.O., Shilov, N.V.: Model Checking Knowledge of acting Agents with log-files. In: Meetings of Minds: Proc. of Int. Workshop Logic, Rationality and Interaction, China (2007)Google Scholar
  13. 13.
    Halpern, J.Y., Vardi, M.Y.: The complexity of Reasoning About Knowledge and Time. In: Proc. of Symp. Theor. of Computing (STOC), pp. 304–315 (1986)Google Scholar
  14. 14.
    Halpern, J.Y., van der Meyden, R., Vardi, M.Y.: Complete Axiomatizations for Reasoning about Knowledge and Time. SIAM Journal on Computing 33(3), 674–703 (2004)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)MATHGoogle Scholar
  16. 16.
    Hintikka, J.: Knowledge and Belief. Cornell University Press, Ithica (1962)Google Scholar
  17. 17.
    van der Hoek, W., Wooldridge, M.J.: Model Checking Knowledge and Time. In: Bošnački, D., Leue, S. (eds.) SPIN 2002. LNCS, vol. 2318, pp. 95–111. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Kacprzak, M., Lomuscio, A., Penczek, W.: Unbounded Model Checking for Knowledge and Time. In: Proceedings of the CS&P 2003 Workshop, Warsaw University, vol. 1, pp. 251–264 (2003)Google Scholar
  19. 19.
    Kacprzak, M., Penczek, W.: Model Checking for Alternating-Time mu-Calculus via Translation to SAT. In: Proc. of Concurrency, Specification and Programming Workshop CS&P 2004, Germany, Humboldt Universitat, Berlin, Informatik-Bericht, vol. 2(170) (2004)Google Scholar
  20. 20.
    Kozen, D.: Results on the Propositional Mu-Calculus. Theoretical Computer Science 27(3), 333–354 (1983)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Kouzmin, E.V., Shilov, N.V., Sokolov, V.A.: Model Checking μ-Calculau in Well-Structured Transition Systems. In: Proceedings of 11th International Symposium on Temporal Representation and Reasoning (TIME 2004), France, pp. 152–155. IEEE Press, Los Alamitos (2004)Google Scholar
  22. 22.
    Kozen, D., Tiuryn, J.: Logics of Programs. In: Handbook of Theoretical Computer Science, vol. B, pp. 789–840. Elsevier, MIT Press (1990)Google Scholar
  23. 23.
    Lomuscio, A., Penczek, W.: Verifying Epistemic Properties of Multi-agent Systems via Bounded Model Checking. Fundamenta Informaticae 55(2), 167–185 (2003)MathSciNetMATHGoogle Scholar
  24. 24.
    van der Meyden, R.: Common Knowledge and Update in Finite Environments. Information and Computation 140(2), 115–157 (1998)MathSciNetCrossRefMATHGoogle Scholar
  25. 25.
    van der Meyden, R., Shilov, N.V.: Model checking knowledge and time in systems with perfect recall. In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 432–445. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  26. 26.
    van der Meyden, R., Wong, K.: Complete Axiomatizations for Reasoning about Knowledge and Branching Time. Studia Logica 75(1), 93–123 (2003)MathSciNetCrossRefMATHGoogle Scholar
  27. 27.
    Rescher, N.: Epistemic Logic. Survey of the Logic of Knowledge. University of Pittsburgh Press, Pittsburgh (2005)Google Scholar
  28. 28.
    Shilov, N.V., Yi, K.: How to find a coin: propositional program logics made easy. In: Current Trends in Theoretical Computer Science, vol. 2, pp. 181–213. World Scientific, Singapore (2004)CrossRefGoogle Scholar
  29. 29.
    Shilov, N.V., Garanina, N.O.: Combining Knowledge and Fixpoints. Preprint n. 98 of A.P. Ershov Institute of Informatics Systems, Novosibirsk (2002)Google Scholar
  30. 30.
    Shilov, N.V., Garanina, N.O.: Model Checking Knowledge And Fixpoints. In: Proc. 4th Int. Workshop on Fixed Points on Computer Science, Copenhagen, Denmark, pp. 25–39 (2002)Google Scholar
  31. 31.
    Shilov, N.V., Garanina, N.O., Choe, K.-M.: 2.7. Update and Abstraction in Model Checking of Knowledge and Branching Time. Fundameta Informaticae 72(1-3), 347–361 (2006)MathSciNetMATHGoogle Scholar
  32. 32.
    Shilov, N.V., Garanina, N.O.: Well-Structured Model Checking of Multiagent Systems. In: Virbitskaite, I., Voronkov, A. (eds.) PSI 2006. LNCS, vol. 4378, pp. 363–376. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  33. 33.
    Wooldridge, M.: Practical reasoning with procedural knowledge: A logic of BDI agents with know-how. In: Gabbay, D.M., Ohlbach, H.J. (eds.) FAPR 1996. LNCS, vol. 1085, pp. 663–678. Springer, Heidelberg (1996)CrossRefGoogle Scholar
  34. 34.
    Wooldridge, M.: An Introduction to Multiagent Systems. John Wiley & Sons Ltd., Chichester (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Nikolay V. Shilov
    • 1
  • Natalia O. Garanina
    • 1
  1. 1.Institute of Informatics SystemsRussian Academy of SciencesNovosibirskRussia

Personalised recommendations