Entailment in Probability of Thresholded Generalizations
Donald Bamber
Abstract:
A nonmonotonic logic of thresholded generalizations is presented. Given propositions A and B from a language L and a positive integer k, the thresholded generalization A=>B{k} means that the conditional probability P(BA) falls short of one by no more than c*d^k. A twolevel probability structure is defined. At the lower level, a model is defined to be a probability function on L. At the upper level, there is a probability distribution over models. A definition is given of what it means for a collection of thresholded generalizations to entail another thresholded generalization. This nonmonotonic entailment relation, called "entailment in probability", has the feature that its conclusions are "probabilistically trustworthy" meaning that, given true premises, it is improbable that an entailed conclusion would be false. A procedure is presented for ascertaining whether any given collection of premises entails any given conclusion. It is shown that entailment in probability is closely related to Goldszmidt and Pearl's SystemZ^+, thereby demonstrating that the conclusions of SystemZ^+ are probabilistically trustworthy.
Keywords: Nonmonotonic reasoning, probabilistic reasoning.
Pages: 5764
PS Link:
PDF Link: /papers/96/p57bamber.pdf
BibTex:
@INPROCEEDINGS{Bamber96,
AUTHOR = "Donald Bamber
",
TITLE = "Entailment in Probability of Thresholded Generalizations",
BOOKTITLE = "Proceedings of the Twelfth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI96)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1996",
PAGES = "5764"
}

