Qualitative Bayesian Networks with logical constraints

Abstract

An important feature of Qualitative Bayesian Networks is that they describe conditional independence models. However, they are not able to handle models involving logical constraints among the given variables. The aim of this paper is to show how this theory can be extended in such a way to represent also the logical constraints in the graph through an enhanced version of Qualitative Bayesian Networks. The relative algorithm for building these graphs (which is a generalization of the well-known algorithm based on D-separation criterion) is given. This theory is particularly fit for conditional probabilistic independence models based on the notion of cs-independence. This notion avoids the usual critical situations shown by the classic definition when logical constraints are present.