G. Kern-Isberner.
**A conditional-logical approach to minimum cross-entropy**.
In Proceedings 14th Symposium on Theoretical Aspects of Computer Science
STACS'97, pages 237-248, Berlin Heidelberg New York, 1997.
Springer.

#### Abstract:

The principle of minimum cross-entropy (ME-principle) is often used in the
AI-areas of knowledge representation and uncertain reasoning as an elegant and
powerful tool to build up complete probability distributions when only partial
knowledge is available. The inputs it may be applied to are a prior
distribution *P* and some new information *R*, and it yields as
a result the one distribution *P*^{*} that satisfies *R*
and is closest to *P* in an information-theoretic sense. More generally,
it provides a "best" solution to the problem "How to adjust *P* to
*R*"

In this paper, we show in a rather direct and constructive manner that
adjusting *P* to *R* by means of this principle follows a
simple and intelligible conditional-logical pattern. The scheme that underlies
ME-adjustment is made obvious, and in a generalized form, it provides a
straightforward conditional-logical approach to the adaptation problem. We
introduce the idea of a *functional concept* and show how the demands
for *logical consistency* and *representation invariance*
influence the functions involved. Finally, the ME-distribution arises as the
only solution which follows the simple adaptation scheme given and satisfies
these three assumptions. So a characterization of the ME-principle within a
conditional-logical framework will have been achieved, and its logical
mechanisms will be revealed clearly.

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