Heller (2021) and Stefanutti et al. (2020) provided the mathematical foundation for the generalization of knowledge structure theory (KST) to polytomous items. Based on their works, the well-gradedness can be extended to polytomous knowledge structures. We propose the concepts of discriminative polytomous knowledge structure and well-graded polytomous knowledge structure. Then we show that every well-graded polytomous knowledge structure is discriminative. The basis of any polytomous knowledge space is formed by the collection of all the atoms. We discuss the sufficient and necessary conditions of polytomous knowledge structures to be well-graded polytomous knowledge spaces. Moreover, we provide an example to illustrate that a well-graded polytomous knowledge space is not necessarily a polytomous closure space.

Heller (2021) 和 Stefanutti 等人。(2020) 为将知识结构理论 (KST) 推广到多项式项目提供了数学基础。基于他们的工作，良好的分级性可以扩展到多元知识结构。我们提出了判别性多分知识结构和分级良好的多分知识结构的概念。然后我们证明每个分级良好的多知识结构都是有区别的。任何多知识空间的基础都是由所有原子的集合构成的。我们讨论了多元知识结构成为分级良好的多元知识空间的充分必要条件。此外，我们提供了一个例子来说明分级良好的多分知识空间不一定是多分闭包空间。