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Verifying Real-Time Temporal, Cooperation and Epistemic Properties for Uncertain Agents

  • Zining Cao
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4293)

Abstract

In this paper, we introduce a real-time temporal probabilistic knowledge logic, called RATPK, which can express not only real-time temporal and probabilistic epistemic properties but also cooperation properties. It is showed that temporal modalities such as “always in an interval”, “until in an interval”, and knowledge modalities such as “knowledge in an interval”, “common knowledge in an interval” and “probabilistic common knowledge” can be expressed in such a logic. The model checking algorithm is given and a case is studied.

Keywords

Model Check Multiagent System Epistemic Logic Boolean Expression Kripke Structure 
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., de Alfaro, L., Henzinger, T.A., Krishnan, S.C., Mang, F.Y.C., Qadeer, S., Rajamni, S.K., Tasiran, S.: MOCHA user manual, University of Berkeley Report (2000)Google Scholar
  2. 2.
    Alur, R., Henzinger, T.A.: Alternating-time temporal logic. Journal of the ACM 49(5), 672–713Google Scholar
  3. 3.
    Arnold, A., Niwinski, D.: Rudiments of μ-calculus. Studies in Logic, vol. 146. North-Holland, Amsterdam (2001)CrossRefGoogle Scholar
  4. 4.
    Bourahla, M., Benmohamed, M.: Model Checking Multi-Agent Systems. Informatica 29, 189–197 (2005)MATHGoogle Scholar
  5. 5.
    Bradfield, J., Stirling, C.: Modal Logics and mu-Calculi: An Introduction, ch. 4. In: Handbook of Process Algebra, Elsevier Science, Amsterdam (2001)Google Scholar
  6. 6.
    Clarke, E.M., Grumberg, J.O., Peled, D.A.: Model checking. MIT Press, Cambridge (1999)Google Scholar
  7. 7.
    Cao, Z., Shi, C.: Probabilistic Belief Logic and Its Probabilistic Aumann Semantics. J. Comput. Sci. Technol. 18(5), 571–579 (2003)MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    van Ditmarsch, H., van der Hoek, W., Kooi, B.P.: Dynamic Epistemic Logic with Assignment. In: AAMAS 2005, vol. 1, pp. 141–148. ACM, New York (2005)CrossRefGoogle Scholar
  9. 9.
    Emerson, E.A., Jutla, C.S., Sistla, A.P.: On model checking for fragments of the μ-calculus. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 385–396. Springer, Heidelberg (1993)Google Scholar
  10. 10.
    de, N., Ferreira, C., Fisher, M., van der Hoek, W.: Practical Reasoning for Uncertain Agents. In: Alferes, J.J., Leite, J.A. (eds.) JELIA 2004. LNCS (LNAI), vol. 3229, pp. 82–94. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    de, N., Ferreira, C., Fisher, M., van der Hoek, W.: Logical Implementation of Uncertain Agents. In: Bento, C., Cardoso, A., Dias, G. (eds.) EPIA 2005. LNCS (LNAI), vol. 3808, pp. 536–547. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  12. 12.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge. The MIT Press, Cambridge, Massachusetts (1995)MATHGoogle Scholar
  13. 13.
    Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Common knowledge revisited. Annals of Pure and Applied Logic 96, 89–105 (1999)MATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Halpern, J.Y., Moses, Y.: Knowledge and common knowledge in a distributed environment. J ACM 37(3), 549–587 (1990)MATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    van der Hoek, W.: Some considerations on the logic PFD: A logic combining modality and probability. J. Applied Non-Classical Logics 7(3), 287–307 (1997)Google Scholar
  16. 16.
    van der Hoek, W., Wooldridge, M.: Model Checking Knowledge, and Time. In: Bošnački, D., Leue, S. (eds.) SPIN 2002. LNCS, vol. 2318, pp. 95–111. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  17. 17.
    van der Hoek, W., Wooldridge, M.: Cooperation, Knowledge, and Time: Alternating-time Temporal Epistemic Logic and its Applications. Studia Logica 75, 125–157 (2003)MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    Jurdzinski, M.: Deciding the winner in parity games is in UP∩co-UP. Information Processing Letters 68, 119–134 (1998)CrossRefMathSciNetGoogle Scholar
  19. 19.
    Jurdzinski, M., Paterson, M., Zwick, U.: A Deterministic Subexponential Algorithm for Solving Parity Games. In: Proceedings of ACM-SIAM Symposium on Discrete Algorithms, SODA 2006 (January 2006)Google Scholar
  20. 20.
    Kacprzak, M., Lomuscio, A., Penczek, W.: Verification of multiagent systems via unbounded model checking. In: Proceedings of the 3rd International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2004) (2004)Google Scholar
  21. 21.
    Kooi, B.P.: Probabilistic Dynamic Epistemic Logic. Journal of Logic, Language and Information 12, 381–408 (2003)MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    McMillan, K.L.: Symbolic model checking: An Approach to the State Explosion Problem. Kluwer Academic, Dordrecht (1993)Google Scholar
  23. 23.
    Walukiewicz, I.: Completeness of Kozen’s axiomatisation of the propositional μ-calculus. Information and Computation 157, 142–182 (2000)MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Wooldridge, M., Fisher, M., Huget, M., Parsons, S.: Model checking multiagent systems with mable. In: Proceedings of the First International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2002) (2002)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Zining Cao
    • 1
  1. 1.Department of Computer Science and EngineeringNanjing University of Aero. & Astro.NanjingChina

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