Nonstandard Concepts of Similarity in Case-Based Reasoning

The present paper is motivated by the author’s work in learning, by his work on case-based learning and by his machine learning work in the case-based reasoning research project FABEL, in particular. The presentation is focussed on case-based classification, but the paper is more specific in one respect and more general in another. The core of the paper is more specific, as it is driven by investigations in learning, and it is more general, as the nonstandard concepts developed are of importance for case-based reasoning, in general. It seems that a much too restricted view at similarity is one of the basic drawbacks of recent research in case-based reasoning. A rigorous criticism is intended to set the stage for new approaches to similarity which may contribute to a considerable progress in the similarity-based use of cases. New generation approaches to similarity should allow both non-symmetric similarity concepts and similarity of more than two objects. Those concepts exist already in certain specific versions mainly in the cognitive sciences area. The present paper is introducing nonstandard concepts of similarity in a quite formal setting which allows an integration of well-known procedures like unification algorithms.

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