A Generalization of Knowledge Space Theory to Problems with More Than Two Answer Alternatives

Abstract

In the theory of knowledge spaces (Doignon & Falmagne, 1985) a knowledge domain is represented by a setQof problems. The knowledge of a subject in the knowledge domain is described by the subset of problems from the domain that the subject is able to solve. A central assumption is therefore that the answer of a subject to a problem can be classified as either correct or incorrect. We show that the central concepts of the theory can be generalized to problem domains in which solutions can be evaluated on a linear scale concerning their quality.