Propagating belief functions through constraints systems

  • Jürg Kohlas
  • Paul-André Monney
1. Mathematical Theory Of Evidence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 521)


Constraint systems as used in temporal reasoning usually describe uncertainty by constraining variables into given sets. Viewing belief functions as random or uncertain sets, uncertainty in such models is quite naturally and more generally described by belief functions. Here a special class of constraint systems induced by the additive underlying group structure is considered. Belief functions are used to specify uncertain constraints on relations and constraint propagation can be applied to compute belief functions about relations between specified events.

The computations are as usual plagued by combinatorial explosion in the general case. Structural properties of the temporal knowledge base must therefore be exploited. It is explained that there are topological properties of the graph representing the model which can be used to reduce computational complexity. Series-parallel graphs are shown to be particularly simple with respect to computations. They play a role analogous to qualitative Markov trees in multivariate models. These methods are related to the use of reference events — a technique well known in temporal reasoning — to obtain a natural hierarchical structuring of the knowledge base.


Belief functions Dempster-Shafer Theory of Evidence Temporal Reasoning Reasoning under Uncertainty Constraint Propagation 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Davis E. (1987): Constraint Propagation With Interval Labels. Artificial Intelligence, 32, 281–331.CrossRefGoogle Scholar
  2. [2]
    Dean T. (1985): Temporal Imaginery: An Approach to Reasoning about Time for Planning and Problem Solving. Research Report 433, Yale University, New Haven, CT.Google Scholar
  3. [3]
    Dempster A.P. (1967): Upper and Lower Probabilities Induced by a Multivalued Mapping. Annals of Math. Stat., 38, 325–339.Google Scholar
  4. [4]
    Kohlas J. (1988): Models and Algorithms for Temporal Reasoning III: Combination and Propagation of Belief and Plausibility. Working Paper 158, Institute for Automation and O.R., University of Fribourg, Switzerland.Google Scholar
  5. [5]
    Kohlas J., Monney P.A. (1989): Propagating Belief Functions Through Constraint Systems. Working Paper 171, Institute for Automation and O.R., University of Fribourg, Switzerland. To appear in Int. J. of Approximate Reasoning.Google Scholar
  6. [6]
    Kohlas J., Monney P.A. (1989): Modeling and Reasoning with Hints. Working Paper 174, Institute for Automation and O.R., University of Fribourg, Switzerland.Google Scholar
  7. [7]
    Mackworth A.K. (1977): Consistency in Networks of Relations. Artificial Intelligence, 8, 99–118.CrossRefGoogle Scholar
  8. [8]
    Montanari U., Rossi F. (1988): Fundamental Properties of Networks of Constraints: A New Formulation. In: KANAL L., KUMAR V. (Eds.) Search in Artificial Intelligence, Springer, 426–449.Google Scholar
  9. [9]
    Shafer G. (1976): A Mathematical Theory of Evidence. Princeton Univ. Press.Google Scholar
  10. [10]
    Shafer G., Shenoy P., Mellouli K. (1986): Propagating Belief Functions in Qualitative Markov Trees. Int. J. of Approximate Reasoning, 1, 349–400.CrossRefGoogle Scholar
  11. [11]
    Vere S. (1983): Planning in Time: Windows and Durations for Activities and Goals. IEEE Trans. Patt. Anal. Mach. Intell., 5, 246–267.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Jürg Kohlas
    • 1
  • Paul-André Monney
    • 1
  1. 1.Institute for Automation and O.R.University of FribourgFribourgSwitzerland

Personalised recommendations