A symbolic generalization of probability theory
A symbolic generalization of probability theory
An axiomatic treatment of three qualitative decision criteria
Journal of the ACM (JACM)
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference
A Comparison of Axiomatic Approaches to Qualitative Decision Making Using Possibility Theory
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Reasoning about Uncertainty
A decision theory for non-probabilistic uncertainty and its applications
A decision theory for non-probabilistic uncertainty and its applications
Decision making with partially consonant belief functions
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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This paper proposes a decision theory for a symbolic generalization of probability theory (SP). Darwiche and Ginsberg [2, 3] proposed SP to relax the requirement of using numbers for uncertainty while preserving desirable patterns of Bayesian reasoning. SP represents uncertainty by symbolic supports that are ordered partially rather than completely as in the case of standard probability. We show that a preference relation on acts that satisfies a number of intuitive postulates is represented by a utility function whose domain is a set of pairs of supports. We argue that a subjective interpretation is as useful and appropriate for SP as it is for numerical probability. It is useful because the subjective interpretation provides a basis for uncertainty elicitation. It is appropriate because we can provide a decision theory that explains how preference on acts is based on support comparison.