Conditional Independence in Uncertainty Theories
This work provides a foundational extension for researchers in uncertainty reasoning, enabling consistent independence definitions across multiple calculi, though it is incremental as it builds on existing VBS frameworks.
The paper tackles the problem of defining independence and conditional independence within the valuation-based systems (VBS) framework, generalizing these concepts from probability theory to various uncertainty calculi such as Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory.
This paper introduces the notions of independence and conditional independence in valuation-based systems (VBS). VBS is an axiomatic framework capable of representing many different uncertainty calculi. We define independence and conditional independence in terms of factorization of the joint valuation. The definitions of independence and conditional independence in VBS generalize the corresponding definitions in probability theory. Our definitions apply not only to probability theory, but also to Dempster-Shafer's belief-function theory, Spohn's epistemic-belief theory, and Zadeh's possibility theory. In fact, they apply to any uncertainty calculi that fit in the framework of valuation-based systems.