Assumptions, Beliefs and Probabilities

Abstract A formal equivalence is demonstrated between Shafer-Dempster belief theory and assumption-based truth maintenance with a probability calculus on the assumptions. This equivalence means that any Shafer-Dempster inference network can be represented as a set of ATMS justifications with probabilities attached to assumptions. A proposition's belief is equal to the probability of its label conditioned on label consistency. An algorithm is given for computing these beliefs. When the ATMS is used to manage beliefs, non-independencies between nodes are automatically and correctly accounted for. The approach described here unifies symbolic and numeric approaches to uncertainty management, thus facilitating dynamic construction of quantitative belief arguments, explanation of beliefs, and resolution of conflicts.

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