Modeling of, and Reasoning with Recurrent Events with Imprecise Durations

  • Stanislav Kurkovsky
  • Rasiah Loganantharaj
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1821)


In this paper we study how the framework of Petri nets can be extended and applied to study recurrent events. We use possibility theory to realistically model temporal properties of the recurrent processes being modeled by an extended Petri net. Such temporal properties include time-stamps stored in tokens and durations of firing the transitions. We apply our method to model the recurrent behavior of an automated manufacturing cell.


Recurrent Event Possibilistic Distribution Possibility Theory Input Place Firing Transition 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Allen. Maintaining Knowledge about Temporal Intervals. Communications of the ACM, 26:832–843, 1983.zbMATHCrossRefGoogle Scholar
  2. [2]
    I. Bestuzheva, V. Rudnev. Timed Petri Nets: Classification and Comparative Analysis. Automation and Remote Control, 51(10):1308–1318, Consultants Bureau, New York, 1990.Google Scholar
  3. [3]
    C. Brown, D. Gurr. Temporal Logic and Categories of Petri Nets. In A. Lingass, R. Karlsson, editors, Automata, Languages and Programming, pp. 570–581, Springer-Verlag, New York, 1993.Google Scholar
  4. [4]
    J. Cardoso, H. Camargo, editors. Fuzziness in Petri Nets, Physica Verlag, New York, NY, 1999.zbMATHGoogle Scholar
  5. [5]
    J. Cardoso, R. Valette, D. Dubois. Fuzzy Petri Nets: An Overview. In G. Rosenberg, editor, Proceedings of the 13th IFAC World Congress, pp. 443–448, San Francisco CA, 30 June–5 July 1996.Google Scholar
  6. [6]
    J. Cardoso, R. Valette, D. Dubois. Possibilistic Petri nets. IEEE transactions on Systems, Man and Cybernetics, part B: Cybernetics, October 1999, Vol. 29, N 5, p. 573–582CrossRefGoogle Scholar
  7. [7]
    J. Carlier, P. Chretienne. Timed Petri Net Schedules. In G. Rozenberg, editor, Advances in Petri Nets, pp. 642–666, Springer-Verlag, New York, 1988.Google Scholar
  8. [8]
    J. Coolahan. N. Roussopoulos. Timing Requirements for Time-driven Systems Using Augmented Petri Nnets. IEEE Transactions on Software Engineering, 9(5):603–616, 1983.CrossRefGoogle Scholar
  9. [9]
    R. Dechter, I. Meiri, J. Pearl. Temporal Constraint Networks. Artificial Intelligence, 49:61–95, 1991.zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    M. Diaz, P. Senac. Time Stream Petri Nets: a Model for Timed Multimedia Information. In R. Valette, editor, Application and Theory of Petri Nets-94, pp. 219–238, Springer-Verlag, New York, 1994.Google Scholar
  11. [11]
    D. Dubois, H. Prade. Possibility Theory. Plenum Press, New York, 1988.zbMATHGoogle Scholar
  12. [12]
    D. Dubois, H. Prade. Processing Fuzzy Temporal Knowledge. IEEE Transactions on Systems, Man and Cybernetics, 19(4), July/August 1989.Google Scholar
  13. [13]
    D. Dubois, J. Lang, H. Prade. Timed Possibilistic Logic. Fundamenta Informaticae. 15(3,4):211–234, 1991.MathSciNetzbMATHGoogle Scholar
  14. [14]
    D. Dubois, H. Prade. Processing Fuzzy Temporal Knowledge. IEEE Transactions on Systems, Man and Cybernetics, 19(4):729–744, 1989.CrossRefMathSciNetGoogle Scholar
  15. [15]
    M. Felder, A. Morzenti. A Temporal Logic Approach to Implementation and Refinement of Timed Petri Nets. In D. Gabbay, editor, Proceedings of 1 st international conference on Temporal Logic ICTL-94, Bonn, Germany, July 11–14, pp. 365–381, Springer-Verlag, New York, 1994.Google Scholar
  16. [16]
    P. Fortemps. Jobshop Scheduling with Imprecise Durations: A Fuzzy Approach. IEEE Transactions on Fuzzy Systems, 5(4):557–569, 1997.CrossRefGoogle Scholar
  17. [17]
    L. Godo, L. Vila. Possibilistic Temporal Reasoning Based on Fuzzy Temporal Constraints. In C. Mellish, editor, Proceedings of IJCAI-95, pp. 1916–1922, Montreal, Canada, 20–25 August, Morgan Kaufmann, San Francisco, CA, 1995.Google Scholar
  18. [18]
    H. Hanisch. Analysis of Place/Transition Nets with Timed Arcs and Its Application to Batch Process Control. In M. Marsan, editor, Application and Theory of Petri Nets-93, pp. 282–299, Springer-Verlag, 1993.Google Scholar
  19. [19]
    E. Kindler, T. Vesper. ESTL: A Temporal Logic for Events and States. In J. Desel, M. Silva, editors, Application and Theory of Petri Nets-98, pp. 365–384, Springer-Verlag, New York, 1998.CrossRefGoogle Scholar
  20. [20]
    S. Kurkovsky. Possibilistic Temporal Propagation. Ph.D. dissertation. University of Southwestern Louisiana, 1999.Google Scholar
  21. [21]
    P. Ladkin. Time Representation: A Taxonomy of Interval Relations. Proceedings of fifth national conference on Artificial Intelligence, pp. 360–366. American Association for Artificial Intelligence, 1996.Google Scholar
  22. [22]
    R. Loganantharaj, S Giambrone. Probabilistic Approach for Representing and Reasoning with Repetitive Events. In J. Stewman, editor, Proceedings of FLAIRS-95, pp. 26–30, Melbourne, FL, 27–29 April 1995.Google Scholar
  23. [23]
    R. Loganantharaj, S. Giambrone. Representation of, and Reasoning with, Near-Periodic Recurrent Events. In F. Anger, H. Guesgen, J. van Benthem, editors, Proceedings of IJCAI-95 Workshop on Spatial and Temporal Reasoning, pp. 51–56, Montreal, Canada, 20–25 August 1995, Morgan Kaufmann, San Mateo, CA, 1995.Google Scholar
  24. [24]
    P. Merlin, D. Farber. Recoverability of Communication Protocols. IEEE Transactions on Communications, 24(9):541–580, 1989.MathSciNetGoogle Scholar
  25. [25]
    J. Peterson. Petri Net Theory and The Modeling of Systems. Prentice Hall, 1981.Google Scholar
  26. [26]
    C. Ramamoorthy, G. Ho, Performance Evaluation of Asynchronous Concurrent Systems Using Petri Nets. IEEE Transactions on software Engineering, 6(5):440–449, 1980.CrossRefMathSciNetGoogle Scholar
  27. [27]
    M. Tanabe. Timed Petri Nets and Temporal Linear Logic. In P. Azema, G. Balbo, editors, Application and Theory of Petri Nets-97, pp. 156–174, Springer-Verlag, New York, 1997.Google Scholar
  28. [28]
    M. Woo, N. Qazi, A. Ghafoor. A Synchronization Framework for Communication of Preorchestrated Multimedia Information. IEEE Networks, 8(1)52–61, 1994.CrossRefGoogle Scholar
  29. [29]
    Y. Yao. A Petri Net Model for Temporal Knowledge Representation and Reasoning. IEEE Transactions on Systems, Man, and Cybernetics, 24(9):1374–1382, 1994.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Stanislav Kurkovsky
    • 1
  • Rasiah Loganantharaj
    • 2
  1. 1.Department of Computer ScienceColumbus State UniversityColumbus
  2. 2.Automated Reasoning Laboratory, Center for Advanced Computer StudiesUniversity of Louisiana at LafayetteLafayette

Personalised recommendations