On the applicability of maximum entropy to inexact reasoning
International Journal of Approximate Reasoning
An analysis of first-order logics of probability
Artificial Intelligence
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Representing and reasoning with probabilistic knowledge: a logical approach to probabilities
Asymptomatic conditional probabilities for first-order logic
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Entailment in probability of thresholded generalizations
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Generating new beliefs from old
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
Probabilistic description logics
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
A logic for default reasoning about probabilities
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
Using first-order probability logic for the construction of Bayesian networks
UAI'93 Proceedings of the Ninth international conference on Uncertainty in artificial intelligence
Limiting disclosure of sensitive data in sequential releases of databases
Information Sciences: an International Journal
Modelling relational statistics with Bayes Nets
Machine Learning
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An intelligent agent uses known facts, including statistical knowledge, to assign degrees of belief to assertions it is uncertain about. We investigate three principled techniques for doing this. All three are applications of the principle of indifference, because they assign equal degree of belief to all basic "situations" consistent with the knowledge base. They differ because there are competing intuitions about what the basic situations are. Various natural patterns of reasoning, such as the preference for the most specific statistical data available, turn out to follow from some or all of the techniques. This is an improvement over earlier theories, such as work on direct inference and reference classes, which arbitrarily postulate these patterns without offering any deeper explanations or guarantees of consistency. The three methods we investigate have surprising characterizations: there are connections to the principle of maximum entropy, a principle of maximal independence, and a "center of mass" principle. There are also unexpected connections between the three, that help us understand why the specific language chosen (for the knowledge base) is much more critical in inductive reasoning of the sort we consider than it is in traditional deductive reasoning.