Properties of Weak Conditional Independence

Object-oriented Bayesian networks (OOBNs) facilitate the design of large Bayesian networks by allowing Bayesian networks to be nested inside of one another. Weak conditional independence has been shown to be a necessary and sufficient condition for ensuring consistency in OOBNs. Since weak conditional independence plays such an important role in OOBNs, in this paper we establish two useful results relating weak conditional independence with weak multivalued dependency in relational databases. The first result strengthens a previous result relating conditional independence and multivalued dependency. The second result takes a step towards showing that the complete axiomatization for weak multivalued dependency is also complete for full weak conditional independence.