Conditional Logics and Entropy

Kern-Isberner, Gabriele GND

The principles of maximum entropy and of minimum cross-entropy (ME-principles) provide an elegant and reasonable tool to represent quantified uncertainties within a probabilistic framework. The results the application of these principles yield are not only well-behaved in a statistical sense but prove to be inferentially sound. In this paper, we generalize the ME-approach by introducing a scheme for adapting a given prior distribution to new conditional information. This scheme is based on conditional-logic arguments, and the ME-adaptation is shown to be a special instance of it. Though the scheme ist far from capturing the whole inferential power of the ME-approach, it parallels it with regard to important features. In particular, independent and irrelevant information is dealt with in the same manner. Thus certain properties which are considered to be characteristic of ME-inference turn out to be due to its conditional-logic behavior.

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Kern-Isberner, Gabriele: Conditional Logics and Entropy. Hagen 1996. FernUniversität in Hagen.

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