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
The emergence of ordered belief from initial ignorance
AAAI '94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 1)
Nonmonotonic inference based on expectations
Artificial Intelligence
System Z: a natural ordering of defaults with tractable applications to nonmonotonic reasoning
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Possibilistic logic, preferential models, non-monotonicity and related issues
IJCAI'91 Proceedings of the 12th international joint conference on Artificial intelligence - Volume 1
Plausibility measures and default reasoning
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 2
Numerical representations of acceptance
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
A big-stepped probability approach for discovering default rules
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - Intelligent information systems
Comparative uncertainty, belief functions and accepted beliefs
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
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The authors have proposed in their previous works to view a set of default pieces of information of the form, "generally, from αi deduce βi" as the family of possibility distributions satisfying constraints expressing that the situations where αiΛβi is true are more possible than the situations where αiΛ¬βi is true. A representation theorem in terms of this semantics, for default reasoning obeying the System P of postulates proposed by Kraus, Lehmann and Magidor, has been obtained. This paper offers a detailed analysis of the structure of this family of possibility distributions by exploiting two different orderings between them: Yager's specificity ordering and a new refinement ordering. It is shown that from a representation point of view, it is sufficient to consider the subset of linear possibility distributions which corresponds to all the possible completions of the default knowledge in agreement with the constraints. There also exists a semantics for system P in terms of infinitesimal probabilities. Surprisingly, it is also shown that a standard probabilistic semantics can be equivalently given to System P, without referring to infinitesimals, by using a special family of probability measures, that two of the authors have called acceptance functions, and that has been also recently considered by Snow in that perspective.