Artificial Intelligence
Reasoning with qualitative probabilities can be tractable
UAI '92 Proceedings of the eighth conference on Uncertainty in Artificial Intelligence
From Adams' conditionals to default expressions, causal conditionals, and counterfactuals
Probability and conditionals
Probability and conditionals
Asymptotic Conditional Probabilities: The Unary Case
SIAM Journal on Computing
The uncertain reasoner's companion: a mathematical perspective
The uncertain reasoner's companion: a mathematical perspective
From statistical knowledge bases to degrees of belief
Artificial Intelligence
Probabilistic Justification of Default Reasoning
KI '94 Proceedings of the 18th Annual German Conference on Artificial Intelligence: Advances in Artificial Intelligence
Random worlds and maximum entropy
Journal of Artificial Intelligence Research
Statistical foundations for default reasoning
IJCAI'93 Proceedings of the 13th international joint conference on Artifical intelligence - Volume 1
System-Z+: a formalism for reasoning with variable-strength defaults
AAAI'91 Proceedings of the ninth National conference on Artificial intelligence - Volume 1
AAAI'92 Proceedings of the tenth national conference on Artificial intelligence
| Hi-index | 0.00 |
A nonmonotonic logic of thresholded generalizations is presented. Given propositions a and β from a language L and a positive integer k, the thresholded generalization α →k β means that the conditional probability π(β|α) is at least 1 -ψδk. A two-level 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 System-Z+, thereby demonstrating that System-Z+'s conclusions are probabilistically trustworthy.