Learning, forgetting, and the correlation of knowledge in knowledge space theory

In this work we introduce and study multiple properties and conditions related to the modeling of student knowledge in knowledge space theory (KST). We begin by looking at a property called forgetting consistency, which enforces a systematic way of forgetting within a knowledge structure. Next, we analyze in detail a concept we call positive knowledge correlation. This concept postulates that knowing more should not make it less likely that a student knows a particular concept. Among other things, we find that satisfying positive knowledge correlation implies the knowledge structure is closed under both union and intersection, and we also perform an empirical evaluation to assess the validity of the property. Finally, in the context of an adaptive assessment, we conclude with an analysis of the related concept of a positively correlated updating rule.