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Rules having rare exceptions may be interpreted as assertions of high conditional probability. In other words, a rule If X then Y may be interpreted as meaning that Pr(Y∣X) 1. A general approach to reasoning with such rules, based on second-order probability, is advocated. Within this general...
One of the major ideas of Shafer's mathematical theory of evidence is the introduction of uncertainty descriptions on different representation domains of phenomena, called families of compatible frames of discernment. Here we are going to analyze these families of frames from an algebraic point...
In previous work [V. Biazzo, A. Gilio, T. Lukasiewicz and G. Sanfilippo, Probabilistic logic under coherence, model-theoretic probabilistic logic, and default reasoning in System P, Journal of Applied Non-Classical Logics 12(2) (2002) 189–213.], we have explored the relationship between...
This paper is concerned with the reliable inference of optimal tree-approximations to the dependency structure of an unknown distribution generating data. The traditional approach to the problem measures the dependency strength between random variables by the index called mutual information. In...
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