New Axioms for Probability and Likelihood Ratio Measures

British Journal for the Philosophy of Science 64 (1):189-204 (2013)
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Probability ratio and likelihood ratio measures of inductive support and related notions have appeared as theoretical tools for probabilistic approaches in the philosophy of science, the psychology of reasoning, and artificial intelligence. In an effort of conceptual clarification, several authors have pursued axiomatic foundations for these two families of measures. Such results have been criticized, however, as relying on unduly demanding or poorly motivated mathematical assumptions. We provide two novel theorems showing that probability ratio and likelihood ratio measures can be axiomatized in a way that overcomes these difficulties



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Logic of Statistical Inference.Ian Hacking - 1965 - Cambridge, England: Cambridge University Press.
Probability and Evidence.Paul Horwich - 1982 - Cambridge: Cambridge University Press.

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