Coarsening a Knowledge Structure

This paper describes an assessment procedure which does not deal explicitly with the whole knowledge structure, but rather operates on a faithful summary of the structure. The summary is achieved through the notion of coarsening of a structure, where the knowledge states are grouped into equivalence classes. We first define a stochastic assessment procedure running on the coarsening. Then we specify a set of possible properties for the equivalence relation. In particular, we define a notion of convexity for a knowledge structure. The results are justified by a simulation study.