Conditional Independence in Valuation-Based Systems

Abstract

This paper introduces the concept of conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define conditional independence in terms of factorization of the joint valuation. The definition of conditional independence in VBS generalizes the corresponding definition in probability theory. Besides probability theory, our definition applies also to Dempster-Shafer’s belief-function theory, Spohn’s epistemic-belief theory, and Zadeh’s possibility theory. In fact, it applies to any uncertainty calculi that fit in the VBS framework. We prove that our definition of conditional independence satisfies many of the usual properties associated with it. In particular, it satisfies Pearl and Paz’s graphoid axioms.