Belief structures, possibility theory and decomposable confidence measures on finite sets
Computers and Artificial Intelligence
Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Nonmonotonic reasoning, preferential models and cumulative logics
Artificial Intelligence
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Artificial Intelligence
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A preference-based approach to default reasoning: preliminary report
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
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Artificial Intelligence
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Artificial Intelligence
An axiomatic treatment of three qualitative decision criteria
Journal of the ACM (JACM)
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IPMU '92 Proceedings of the 4th International Conference on Processing and Management of Uncertainty in Knowledge-Based Systems: Advanced Methods in Artificial Intelligence
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AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
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Comparative uncertainty, belief functions and accepted beliefs
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Generalized qualitative probability: savage revisited
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Artificial Intelligence - Special issue: Fuzzy set and possibility theory-based methods in artificial intelligence
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Electronic Notes in Theoretical Computer Science (ENTCS)
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ACM Transactions on Computational Logic (TOCL)
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Proceedings of the 2006 conference on ECAI 2006: 17th European Conference on Artificial Intelligence August 29 -- September 1, 2006, Riva del Garda, Italy
Conditional and Preferential Logics: Proof Methods and Theorem Proving
Proceedings of the 2010 conference on Conditional and Preferential Logics: Proof Methods and Theorem Proving
Qualitative test-cost sensitive classification
Pattern Recognition Letters
Preferences in AI: An overview
Artificial Intelligence
Answer set programming for computing decisions under uncertainty
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
Leximax relations in decision making through the dominance plausible rule
ECSQARU'11 Proceedings of the 11th European conference on Symbolic and quantitative approaches to reasoning with uncertainty
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JELIA'06 Proceedings of the 10th European conference on Logics in Artificial Intelligence
Representing and reasoning with qualitative preferences for compositional systems
Journal of Artificial Intelligence Research
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This paper investigates to what extent a purely symbolic approach to decision making under uncertainty is possible, in the scope of artificial intelligence. Contrary to classical approaches to decision theory, we try to rank acts without resorting to any numerical representation of utility or uncertainty, and without using any scale on which both uncertainty and preference could be mapped. Our approach is a variant of Savage's where the setting is finite, and the strict preference on acts is a partial order. It is shown that although many axioms of Savage theory are preserved and despite the intuitive appeal of the ordinal method for constructing a preference over acts, the approach is inconsistent with a probabilistic representation of uncertainty. The latter leads to the kind of paradoxes encountered in the theory of voting. It is shown that the assumption of ordinal invariance enforces a qualitative decision procedure that presupposes a comparative possibility representation of uncertainty, originally due to Lewis, and usual in nonmonotonic reasoning. Our axiomatic investigation thus provides decision-theoretic foundations to the preferential inference of Lehmann and colleagues. However, the obtained decision rules are sometimes either not very decisive or may lead to overconfident decisions, although their basic principles look sound. This paper points out some limitations of purely ordinal approaches to Savage-like decision making under uncertainty, in perfect analogy with similar difficulties in voting theory.