We present a critical analysis of the maximal prime decomposition of Bayesian networks (BNs). Our analysis suggests that it may be more useful to transform a BN into a hierarchical Markov network.

Previous work seemed to suggest that the logical implication of non-numeric constraints in database systems exactly coincides with that of numeric constraints in probabilistic expert systems, provided that restrictions are imposed on the given set of constraints. In this paper, we dispel this suggestion by showing that the logical implication differs in database systems and probabilistic expert systems even with a restriction imposed on the given set of constraints. Our restriction is a granular representation, called hierarchical Markov networks, which have shown great promise as a new representation of Bayesian networks. This work is then significant as it provides a lower upper-bound on where the logical implication of nonnumeric and numeric constraints diverge.