This paper is to introduce Propagation nets as a kind of Petri nets whose flowing objects are uncertain values. The approach is influenced by Bayesian networks (J. Pearl [10]) and probabilistic Horn abduction (D. Pool [12]). In contrast to Bayesian networks, the algorithms are not ”hidden” but part of the nets. The net structure together with a simple firing rule allows uncertain reasoning in backward and forward direction, where backward and forward direction are dual to each other in terms of a Petri net duality. Propagation nets allow to deal with several kinds of uncertainties. This is shown for probabilities, intervals and fuzzy numbers.


Bayesian Network Fuzzy Number Interval Arithmetic Horn Clause Input Place 
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.
    Lautenbach, K.: Exakte Bedingungen der Lebendigkeit für eine Klasse von Petri-Netzen. Gesellschaft für Mathematik und Datenverarbeitung Bonn, Bericht Nr. 82 (1973)Google Scholar
  2. 2.
    Lautenbach, K.: Simple Marked-graph-like Predicate/Transition Nets. Arbeitspapiere der GMD Nr. 41. In: Informatik Fachberichte 66, Bonn (1983)Google Scholar
  3. 3.
    Lautenbach, K.: Reproducibility of the empty marking. In: Esparza, J., Lakos, C.A. (eds.) ICATPN 2002. LNCS, vol. 2360, pp. 237–253. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  4. 4.
    Lautenbach, K.: Logical Reasoning and Petri Nets. In: van der Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 276–295. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Lautenbach, K., Pinl, A.: Probability Propagation in Petri Nets. Fachberichte Informatik 16–2005, Universität Koblenz-Landau, Institut für Informatik, Universitätsstr. 1, D-56070 Koblenz (2005)Google Scholar
  6. 6.
    Lautenbach, K., Pinl, A.: Probability Propagation Nets. Arbeitsberichte aus dem Fachbereich Informatik 20–2007, Universität Koblenz-Landau, Institut für Informatik, Universitätsstr. 1, D-56070 Koblenz (2007)Google Scholar
  7. 7.
    Lautenbach, K., Pinl, A.: A Petri net representation of Bayesian message flows: importance of Bayesian networks for biological applications. Natural Computing 10, 683–709 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Lautenbach, K., Susewind, K.: Probability Propagation nets and Duality. Fachberichte Informatik 11–2012, Universität Koblenz-Landau, Institut für Informatik, Universitätsstr. 1, D-56070 Koblenz (2012)Google Scholar
  9. 9.
    Neapolitan, R.E.: Probabilistic Reasoning in Expert Systems – Theory and Algorithms. Wiley (1990)Google Scholar
  10. 10.
    Pearl, J.: Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann Publishers Inc., San Francisco (1988)zbMATHGoogle Scholar
  11. 11.
    Pinl, A.: Probability Propagation Nets – Unveiling Structure and Propagations of Bayesian Networks by means of Petri Nets. Ph.D. thesis, Universität Koblenz-Landau, Campus Koblenz (2007)Google Scholar
  12. 12.
    Poole, D.: Probabilistic horn abduction and bayesian networks. Artificial Intelligence 64, 81–129 (1993)CrossRefGoogle Scholar
  13. 13.
    Ren, J., Xu, D.L., Yang, J.B., Jenkinson, I., Wang, J.: An offshore risk analysis method using fuzzy bayesian network. J. Offshore Mech. Arct. Eng. 131(4), 12 (2009)CrossRefGoogle Scholar
  14. 14.
    Ren, J., Wang, J., Jenkinson, I.: Fuzzy bayesian modelling in maritime risk analysis. In: GERI Annual Research Symposium, Liverpool John Moores University, UK (2005)Google Scholar
  15. 15.
    Ren, J., Wang, J., Jenkinson, I., Xu, D., Yang, J.B.: A methodology to model human and organisational errors on offshore risk analysis. In: IEEE International Conference on Automation Science and Engineering, October 8-10, pp. 144–149 (2006) ISBN 1-4244-0310-3 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Kurt Lautenbach
    • 1
  1. 1.University of Koblenz-LandauKoblenzGermany

Personalised recommendations