FIRST INTERNATIONAL SYMPOSIUM ON
IMPRECISE PROBABILITIES AND THEIR APPLICATIONS

Ghent, Belgium
30 June - 2 July 1999

ELECTRONIC PROCEEDINGS

Pierre Hansen, Brigitte Jaumard, Marcus Poggi de Aragão, Fabien Chauny, and Sylvain Perron

Probabilistic Satisfiability with Imprecise Probabilities

Abstract

Treatment of imprecise probabilities within the probabilistic satisfiability approach to uncertainty in knowledge-based systems is surveyed and discussed. Both probability intervals and qualitative probabilities are considered. Analytical and numerical methods to test coherence and bound the probability of a conclusion are reviewed. They use polyhedral combinatorics and advanced methods of linear programming.

Keywords. Satisfiability, Probability intervals, Qualitative probabilities, Polyhedra, Linear programming, Column generation, Nonlinear 0--1 programming.

The paper is available in the following formats:

Authors addresses:

Pierre Hansen

GERAD and École des Hautes Études Commerciales, Montréal, Canada

Brigitte Jaumard

GERAD and École Polytechnique de Montréal, Canada

Marcus Poggi de Aragão

Catholic University of Rio de Janeiro, Brasil

Fabien Chauny

GERAD and École des Hautes Études Commerciales, Montréal, Canada

Sylvain Perron

École Polytechnique de Montréal, Canada

E-mail addresses:

Pierre Hansen pierreh@crt.umontreal.ca
Brigitte Jaumard brigitt@crt.umontreal.ca
Marcus Poggi de Aragão poggi@inf.puc-rio.br
Fabien Chauny fabien@crt.umontreal.ca
Sylvain Perron sylvain@crt.umontreal.ca

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