Polytomous Knowledge Structures Based on Entail Relations

In knowledge structure theory (KST), an individual’s knowledge state represents the items that the individual can completely solve. Based on the differences in individuals’ latent cognitive competence, polytomous knowledge states can be used to partially represent individuals to solve items. This paper explores the construction of polytomous knowledge states and polytomous knowledge structures on a polytomous knowledge domain Q×L. A quasi-ordinal polytomous knowledge space and a polytomous knowledge space can be induced by two different entail relations, respectively. When the polytomous knowledge structure (Q,L,K) on Q×L is determined, accurately evaluating an individual’s polytomous knowledge state is the key to providing learning guidance and taking teaching remedial measures for the individual. Therefore, we study the basic assessment procedure for a given polytomous knowledge structure, and a concrete example is designed to illustrate the method presented in this paper.