Abstract

The set of all knowledge spaces on a given set of items or questions is investigated with respect to order theoretic and metrical properties. It is argued that a generalization of properties of the subspaces of a finite dimensional Euclidean vector space yields the material for defining a metric which satisfies certain requirements. The fact that the lattice of knowledge spaces is not modular is the reason for most of the difficulties. It turns out that a Hausdorff metric based on the Hamming distance satisfies the postulated conditions.

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