Probabilistic Reasoning with Continuous Constraints

Continuous constraint reasoning assumes the uncertainty of numerical variables within given bounds and propagates such knowledge through a network of constraints, reducing the uncertainty. In some problems there is also information about the plausibility distribution of values within such bounds. However, the classical constraint framework cannot accommodate that information. This paper describes how the continuous constraint programming paradigm may be extended, in order to accommodate some probabilistic considerations, bridging the gap between the pure interval-based approach, that does not consider likelihoods, and the pure stochastic approach, that does not guarantee the safety of the obtained results.