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Abstract

Multi-agent systems are composed by many independent agents where the task of some of them may depend on the task of others. In this work we present a generic Stochastic Petri Net model for agents and illustrate the usage of a sound, complete and decidable logic system to verify properties in multi-agent systems modelled as Stochastic Petri Nets: the \(\mathcal{DS}_3\) logic. This logic takes advantage of the intuitive graphical interpretation of Petri Nets, allowing the user to model the behaviour of agents and their interactions by means of nets (i.e. seen Petri Nets as graphs). Our approach leads not only to a usual place-transition connection provided by Petri-nets underlying graphs modelling, such as the verification of properties and validation of agents, but also regards the verification of properties concerning their behaviour inside an environment.

The authors thank CAPES, CNPq and FAPERJ for the partial support of this research.

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References

  1. Wooldridge, M.: An Introduction to MultiAgent Systems. John Wiley & Sons (2002)

    Google Scholar 

  2. Khosravifar, S.: Modeling multi agent communication activities with Petri Nets. International Journal of Information and Education Technology 3(3), 310–314 (2013)

    Article  Google Scholar 

  3. Van Belle, W., Nose, K.: Agent mobility and reification of computational state: An experiment in migration. In: Wagner, T.A., Rana, O.F. (eds.) AA-WS 2000. LNCS (LNAI), vol. 1887, pp. 166–173. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  4. Ganty, P., Majumdar, R.: Algorithmic verification of asynchronous programs. ACM Transactions on Programming Languages and Systems 34(1), 1–48 (2012)

    Article  Google Scholar 

  5. Marsan, M.A.: Stochastic Petri Nets: An elementary introduction. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 1–29. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  6. Everdij, M.H.C., Klompstra, M.B., Blom, H.A.P., Klein Obbink, B.: Compositional specification of a multi-agent system by stochastically and dynamically coloured petri nets. In: Blom, H., Lygeros, J. (eds.) Stochastic Hybrid Systems. Lecture Notes in Control and Information Science, vol. 337, pp. 325–350. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Holvoet, T.: Agents and petri nets. Petri Net Newsletter 49 (1995)

    Google Scholar 

  8. Perše, M., Kristan, M., Perš, J., Kovacic, S.: Recognition of multi-agent activities with Petri Nets. In: 17th International Electrotechnical and Computer Science Conference, pp. 217–220 (2008)

    Google Scholar 

  9. Rongier, P., Liégeois, A.: Analysis and prediction of the behavior of one class of multiple foraging robots with the help of stochastic petri nets. In: Proceedings of 1999 IEEE International Conference on Systems, Man, and Cybernetics, EEE SMC 1999, vol. 5, pp. 143–148 (1999)

    Google Scholar 

  10. Haas, P.J.: Stochastic Petri nets: modelling, stability, simulation. Springer (2002)

    Google Scholar 

  11. Lyon, D.: Using stochastic petri nets for real-time nth-order stochastic composition. Computer Music Journal 19(4), 13–22 (1995)

    Article  Google Scholar 

  12. Marsan, M.A.: Stochastic petri nets: an elementary introduction. In: Miola, A. (ed.) DISCO 1990. LNCS, vol. 429, pp. 1–29. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  13. Marsan, M.A., Chiola, G.: On Petri Nets with deterministic and exponentially distributed firing times. In: Rozenberg, G. (ed.) Advances in Petri Nets 1987. LNCS, vol. 266, pp. 132–145. Springer, Heidelberg (1987)

    Chapter  Google Scholar 

  14. Mazigh, B., Abbas-Turki, A.: Specifying and Verifying Holonic Multi-Agent Systems Using Stochastic Petri Net and Object-Z: Application to Industrial Maintenance Organizations. In: Petri Nets – Manufacturing and Computer Science. InTech (2012)

    Google Scholar 

  15. Babczyński, T., Magott, J.: PERT based approach to performance analysis of multi–agent systems. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 1040–1049. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  16. Lopes, B., Benevides, M., Haeusler, E.H.: Extending Propositional Dynamic Logic for Petri Nets. Electronic Notes in Theoretical Computer Science 305(11), 67–83 (2014)

    Article  Google Scholar 

  17. Lopes, B., Benevides, M., Haeusler, E.H.: Propositional dynamic logic for petri nets. Logic Journal of the IGPL 22(5) (2014)

    Google Scholar 

  18. Feldman, Y.A.: A decidable propositional probabilistic dynamic logic. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC 1983, pp. 298–309. ACM (1983)

    Google Scholar 

  19. Feldman, Y.A., Harel, D.: A probabilistic dynamic logic. Journal of Computer and System Sciences 28(2), 193–215 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  20. Kozen, D.: A probabilistic pdl. In: Proceedings of the Fifteenth Annual ACM Symposium on Theory of Computing, STOC 1983, pp. 291–297. ACM (1983)

    Google Scholar 

  21. Tiomkin, M., Makowsky, J.: Propositional dynamic logic with local assignment. Theoretical Computer Science 36, 71–87 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  22. Tiomkin, M., Makowsky, J.: Decidability of finite probabilistic propositional dynamic logics. Information and Computation 94(2), 180–203 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  23. Lopes, B., Benevides, M., Haeusler, E.H.: Verifying properties in multi-agent systems using Stochastic Petri Nets and Propositional Dynamic Logic. In: Annals of the X Encontro Nacional de Inteligência Artificial e Computacional (2013)

    Google Scholar 

  24. Pujari, S., Mukhopadhyay, S.: Petri Net: A tool for modeling and analyze multi-agent oriented systems. International Journal of Intelligent Systems and Applications 10, 103–112 (2012)

    Article  Google Scholar 

  25. de Almeida, E.S., Haeusler, E.H.: Proving properties in ordinary Petri Nets using LoRes logical language. Petri Net Newsletter 57, 23–36 (1999)

    Google Scholar 

  26. Nalon, C., Lopes, B., Haeusler, E.H., Dowek, G.: A calculus for automatic verification of Petri Nets based on Resolution and Dynamic Logics. Electronic Notes in Theoretical Computer Science (in press)

    Google Scholar 

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Lopes, B., Benevides, M., Haeusler, E.H. (2015). Reasoning about Multi-Agent Systems Using Stochastic Petri Nets. In: Bajo, J., et al. Trends in Practical Applications of Agents, Multi-Agent Systems and Sustainability. Advances in Intelligent Systems and Computing, vol 372. Springer, Cham. https://doi.org/10.1007/978-3-319-19629-9_9

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  • DOI: https://doi.org/10.1007/978-3-319-19629-9_9

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