Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Independence concepts for convex sets of probabilities
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Independence with lower and upper probabilities
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
About Conditional Belief Function Independence
ECSQARU '01 Proceedings of the 6th European Conference on Symbolic and Quantitative Approaches to Reasoning with Uncertainty
Separation properties of sets of probability measures
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
Credal networks under maximum entropy
UAI'00 Proceedings of the Sixteenth conference on Uncertainty in artificial intelligence
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This paper investigates Walley's concepts of irrelevance and independence, as applied to the theory of closed convex sets of probability measures. Walley's concepts are analyzed from the perspective of axioms for conditional independence (the so-called semi-graphoid axioms). Two new results are demonstrated in discrete models: first, Walley's concept of irrelevance is an asymmetric semi-graphoid; second, Walley's concept of independence is an incomplete semi-graphoid. These results are the basis for an understanding of irrelevance and independence in connection to the theory of closed convex sets of probability measures, a theory that has received attention as a powerful representation for uncertainty in beliefs and preferences.