Probabilistic continuous constraint satisfaction problems

Constraint programming has been used in many applications where uncertainty arises to model safe reasoning. The goal of constraint propagation is to propagate intervals of uncertainty among the variables of the problem, thus only eliminating values that assuredly do not belong to any solution. However, to play safe, these intervals may be very wide and lead to poor propagation. In this paper we present a framework for probabilistic constraint solving that assumes that uncertain values are not all equally likely. Hence, in addition to initial intervals, a priori probability distributions (within these intervals) are defined and propagated through the constraints. This provides a posteriori conditional probabilities for the variables values, thus enabling the user to select the most likely scenarios.