Reasoning with Uncertainty in Continuous Domains

Continuous constraint programming has been widely used to model safe reasoning in applications where uncertainty arises. Constraint propagation propagates intervals of uncertainty among the variables of the problem, eliminating values that do not belong to any solution. However, to play safe, these intervals may be very wide and lead to poor propagation. We proposed a probabilistic continuous constraint framework that associates a probabilistic space to the variables of the problem, allowing to distinguish between different scenarios, based on their likelihoods. In this paper we discuss the capabilities of the framework for decision support in nonlinear continuous problems with uncertain information. Its applicability is illustrated in inverse and reliability problems, which are two different types of problems representative of the kind of reasoning required by the decision makers.