A Dimension-Related Metric on the Lattice of Knowledge Spaces

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. Copyright 1999 Academic Press.