INFORMATIONAL INDEPENDENCE - MODELS AND NORMAL FORMS

The concept of informational independence plays a key role in most kno wledge-based systems. J. Pearl and his co-researchers analysed the bas ic properties of the concept and formulated an axiomatic system for in formational independence. This axiomatic system focuses on independenc es among mutually disjoint sets of variables. We show that in the cont ext of probabilistic independence a focus on disjoint sets of variable s can hide various interesting properties. To capture these properties , we enhance Pearl's axiomatic system with two additional axioms. We i nvestigate the set of models of the thus enhanced system and show that it provides a better characterization of the concept of probabilistic independence than Pearl's system does. In addition, we observe that b oth Pearl's axiomatic system and our enhanced system offer inference r ules for deriving new independences from an initial set of independenc e statements and as such allow for a normal form for representing inde pendence. We address the normal forms ensuing from the two axiomatic s ystems for informational independence. (C) 1998 John Wiley & Sons, Inc .