CONDITIONAL-INDEPENDENCE IN VALUATION-BASED SYSTEMS

This study introduces the concept of conditional independence in valua tion-based systems (VBS). VBS is an axiomatic framework capable of rep resenting many different uncertainty calculi. We define conditional in dependence in terms of factorization of the joint valuation. The defin ition of conditional independence in VBS generalizes the corresponding definition in probability theory. Besides probability theory, our def inition applies also to Dempster-Shafer's belief-function theory, Spoh n's epistemic-belief theory, and Zadeh's possibility theory. In fact, it applies to any uncertainty calculi that fit in the VBS framework. W e prove that our definition of conditional independence satisfies many of the usual properties associated with it. In particular, it satisfi es Pearl and Paz's graphoid axioms.