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Probabilistic satisfiability and decomposition

  • Guy-Blaise Douanya Nguetsé
  • Pierre Hansen
  • Brigitte Jaumard
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 946)

Abstract

Given a set of logical sentences together with probabilities that these sentences are true, the probabilistic satisfiability (psat) problem consists, in its decision version, in finding whether these probabilities are consistent, and in its optimization version in determining best possible lower and upper bounds on the probability that an additional sentence be true. Van der Gaag recently proposed a partially quantified belief network model which may be viewed as a decomposition-oriented version of psat. Both models give the same bounds, which implies that psat implicitly takes into account some independence relations. A column-generation algorithm is proposed for the decomposition form of psat and shown to have several advantages over a similar algorithm for the usual form, mainly in the exploitation of the sparsity of the matrix of coefficients.

Keywords

Probabilistic Satisfiability Decomposition Belief Network 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Guy-Blaise Douanya Nguetsé
    • 1
  • Pierre Hansen
    • 2
  • Brigitte Jaumard
    • 3
  1. 1.École Polytechnique de MontréalCanada
  2. 2.GERAD and École des Hautes Études Commerciales de MontréalCanada
  3. 3.GERAD and École Polytechnique de MontréalCanada

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