Skip to main content

Verification of Epistemic Properties in Probabilistic Multi-Agent Systems

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5774))

Abstract

Over the past decade Multi-Agent Systems (MAS) have emerged as a successful approach to develop distributed applications. In recent years proposals have been made to extend MAS models with probabilistic behavior. Languages to reason about such systems were presented in order to deal with uncertainty that can be encountered in practical application domains. While in recent works model checking techniques have been successfully applied for verifying knowledge in classical MAS, no methods for verifying knowledge in probabilistic MAS yet exist. This paper proposes such a model checking approach for probabilistic MAS. The approach comprises a compositional modeling process, a modal logic with operators for the specification of epistemic and temporal properties, the corresponding model checking procedure, and an outline of how these techniques can be implemented into existing model checking tools. The advantages of the chosen design include the possibility to analyze the MAS both from the global perspective as well as from the perspective of the agents, and the polynomial complexity of the model checking algorithm.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arus, C., Celda, B., Dasmahaptra, S., Dupplaw, D., Gonzalez-Velez, H., Huffel, S.V., Lewis, P., Ariet, M.L.i., Mier, M., Peet, A., Robles, M.: On the design of a web-based decision support system for brain tumour diagnosis using distributed agents. In: Proc. IEEE/WIC/ACM Int. Conf. on Web Intelligence and Intelligent Agent Technology, pp. 208–211 (2006)

    Google Scholar 

  2. Duo, W., Yi, L., Wenhui, L., Qi, J., Rongqing, Y.: Intelligent multi-agent based information system of business process management. In: Pacific-Asia Workshop on Computational Intelligence and Industrial Application, pp. 469–473 (2008)

    Google Scholar 

  3. Gleizes, M.P., Link-Pezet, J., Glize, P.: An adaptive multi-agent tool for electronic commerce. In: IEEE Int. Workshops on Enabling Technologies, vol. 1, pp. 59–66 (2000)

    Google Scholar 

  4. Halpern, J.Y., Tuttle, M.R.: Knowledge, probability, and adversaries. J. ACM 40(4), 917–960 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  5. Wooldridge, M.J.: Introduction to Multiagent Systems. John Wiley & Sons, Inc., Chichester (2001)

    Google Scholar 

  6. Lehmann, D., Shelah, S.: Reasoning with time and chance. Information and Control 53, 165–198 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  7. Fagin, R., Halpern, J.Y., Moses, Y.: Reasoning about knowledge. MIT Press, Cambridge (1995)

    MATH  Google Scholar 

  8. der Hoek, W.V., Wooldridge, M.: Cooperation, knowledge and time: Alternating-time temporal epistemic logic and its applications. Studia Logica 75(1), 125–157 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. Halpern, J.Y.: Reasoning about Uncertainty. MIT Press, Cambridge (2003)

    MATH  Google Scholar 

  10. Grünwald, P., Halpern, J.Y.: A game-theoretic analysis of updating sets of probabilities. In: Proc. 24th Conf. in Uncertainty in Artificial Intelligence, pp. 240–247 (2008)

    Google Scholar 

  11. Fagin, R., Halpern, J.Y.: Reasoning about knowledge and probability. J. ACM 41(2), 340–367 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  12. de Carvalho Ferreira, N., Fisher, M., van der Hoek, W.: Specifying and reasoning about uncertain agents. International Journal of Approximate Reasoning 49(1), 35–51 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kooi, B.P.: Probabilistic dynamic epistemic logic. J. of Logic, Lang. and Inf. 12(4), 381–408 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  14. Lomuscio, A., Pecheur, C., Raimondi, F.: Automatic verification of knowledge and time with NuSMV. In: Proc. 20th IJCAI, pp. 1384–1389 (2007)

    Google Scholar 

  15. Lomuscio, A., Raimondi, F.: Model checking knowledge, strategies, and games in multi-agent systems. In: Proc. 5th Int. Joint Conf. on Autonomous Agents and Multiagent Systems, pp. 161–168. ACM Press, New York (2006)

    Google Scholar 

  16. Wu, L., Su, K., Chen, Q.: Model checking temporal logics of knowledge and its application in security verification. In: Hao, Y., Liu, J., Wang, Y.-P., Cheung, Y.-m., Yin, H., Jiao, L., Ma, J., Jiao, Y.-C. (eds.) CIS 2005. LNCS (LNAI), vol. 3801, pp. 349–354. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. 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)

    Chapter  Google Scholar 

  18. Kacprzak, M., Lomuscio, A., Penczek, W.: Verification of multiagent systems via unbounded model checking. In: Proc. 3rd Int. Joint Conf. on Autonomous Agents and Multiagent Systems, pp. 638–645. ACM Press, New York (2004)

    Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Hinton, A., Kwiatkowska, M.Z., Norman, G., Parker, D.: PRISM: A tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  21. van der Meyden, R., Shilov, N.V.: Model checking knowledge and time in systems with perfect recall (extended abstract). In: Pandu Rangan, C., Raman, V., Sarukkai, S. (eds.) FST TCS 1999. LNCS, vol. 1738, pp. 432–445. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  22. Su, K., Sattar, A., Luo, X.: Model checking temporal logics of knowledge via OBDDs. The Computer Journal 50(4), 403–420 (2007)

    Article  Google Scholar 

  23. Cimatti, A., Clarke, E., Giunchiglia, E., Giunchiglia, F., Pistore, M., Roveri, M., Sebastiani, R., Tacchella, A.: NuSMV 2: An opensource tool for symbolic model checking. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, p. 359. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  24. Dekhtyar, M.I., Dikovsky, A.J., Valiev, M.K.: Temporal verification of probabilistic multi-agent systems. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Pillars of Computer Science. LNCS, vol. 4800, pp. 256–265. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  25. Rutten, J., Kwiatkowska, M.Z., Norman, G., Parker, D.: Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems. CRM Monograph Series, vol. 23. American Mathematical Society, Providence (2004)

    Google Scholar 

  26. Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. Springer, Heidelberg (2002)

    Book  MATH  Google Scholar 

  27. Katoen, J.P., Kwiatkowska, M.Z., Norman, G., Parker, D.: Faster and symbolic CTMC model checking. In: de Luca, L., Gilmore, S. (eds.) PROBMIV 2001, PAPM-PROBMIV 2001, and PAPM 2001. LNCS, vol. 2165, pp. 23–38. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  28. Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(5), 512–535 (1994)

    Article  MATH  Google Scholar 

  29. Aziz, A., Singhal, V., Balarin, F.: It usually works: The temporal logic of stochastic systems. In: Wolper, P. (ed.) CAV 1995. LNCS, vol. 939, pp. 155–165. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  30. Emerson, E.A., Mok, A.K., Sistla, A.P., Srinivasan, J.: Quantitative temporal reasoning. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 136–145. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  31. Ben-Ari, M., Manna, Z., Pnueli, A.: The temporal logic of branching time. In: Proc. 8th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 164–176. ACM Press, New York (1981)

    Google Scholar 

  32. Peled, D.A., Clarke, E.M., Grumberg, O.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  33. Ciesinski, F., Größer, M.: On probabilistic computation tree logic. In: Baier, C., Haverkort, B.R., Hermanns, H., Katoen, J.-P., Siegle, M. (eds.) Validation of Stochastic Systems. LNCS, vol. 2925, pp. 147–188. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  34. Vardi, M.Y.: Automatic verification of probabilistic concurrent finite state programs. In: Proc. 26th Annual Symposium on Foundations of Computer Science, pp. 327–338. IEEE, Los Alamitos (1985)

    Google Scholar 

  35. Delgado, C.: Modelagem e verificação de propriedades epistêmicas em sistemas multi-agentes. PhD thesis, Universidade Federal do Rio de Janeiro - UFRJ (2007)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Delgado, C., Benevides, M. (2009). Verification of Epistemic Properties in Probabilistic Multi-Agent Systems. In: Braubach, L., van der Hoek, W., Petta, P., Pokahr, A. (eds) Multiagent System Technologies. MATES 2009. Lecture Notes in Computer Science(), vol 5774. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04143-3_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04143-3_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04142-6

  • Online ISBN: 978-3-642-04143-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics