*Gabriele Kern-Isberner and Jens Fisseler*

In a very basic sense, the aim of knowledge discovery is to reveal structures of knowledge which can be seen as being represented by structural relationships. In this paper, we make this notion more precise and present a method how to extract structural information from statistical data. There are two key ideas underlying our approach: First, knowledge discovery is understood as a process which is inverse to inductive knowledge representation. So the relevance of discovered information is judged with respect to the chosen representation method. Second, the link between structural and numerical knowledge is established by an algebraic theory of conditionals, which considers conditionals as agents acting on possible worlds. By applying this theory, we develop an algorithm that computes sets of probabilistic rules from distributions. In particular, we show how sparse information can be dealt with appropriately in our framework. The inductive representation method used here is based on information theory, so that the discovered rules can be considered as being most informative in a strict, formal sense.

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