Skill map based knowledge structures: some considerations about their identifiability

In this article identification of skill multi map based knowledge structures is studied. It is shown how some possible modifications to the skill map may lead the probabilistic knowledge structure to be not identifiable. More specifically, we refer to particular modifications such as adding skills, or adding competencies for an item q. We demonstrate how these changes in the skill map lead the derived knowledge structure to be backward-graded or forward-graded respectively, and how these two particular kinds of structures are not identifiable.