ABSTRACT
This chapter develops an extension of Doignon and Falmagne’s knowledge structures theory by integrating it into a competence-performance conception. The aim is to show one possible way in which the purely behavioral and descriptive knowledge structures approach could be structurally enriched in order to account for the need of explanatory features for the empirically observed solution behavior. Performance is conceived as the observable solution behavior of a person on a set of domain-specific problems. Competence (ability, skills) is understood as a theoretical construct accounting for the performance. The basic concept is a mathematical structure termed a diagnostic, that creates a correspondence between the competence and the performance level. The concept of a union-stable diagnostic is defined as an elaboration of Doignon and Falmagne’s concept of a knowledge space. Conditions for the construction and several properties of union-stable diagnostics are presented. Finally, an empirical application of the competence-performance conception in a small knowledge domain is reported that shall illustrate some advantages of the introduced modeling approach.
