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Conditional Independence in Valuation-Based Systems
Shenoy, Prakash P.
Shenoy, Prakash P.
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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.
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Date
1994-04
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Elsevier Science Publishers B. V.
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Keywords
Conditional independence, Valuation-based systems, Graphoid axioms, Factorization, Dempster-Shafer belief function theory, Possibility theory, Spohn's theory of epistemic beliefs
Citation
Shenoy, P. P., "Conditional Independence in Valuation-Based Systems," International Journal of Approximate Reasoning, Vol. 10, Nos 3, 1994, pp. 203--234.