Heller (2021) generalized quasi-ordinal knowledge spaces to polytomous items. Inspired by this paper, we propose CD-polytomous knowledge space and its polytomous surmise system. A Galois connection is established between the collection $\mathfrak{K}$ of all polytomous knowledge structures and the collection ${\mathfrak{F}}_1$ of particular polytomous attribute functions. The closed elements of the Galois connection are CD-polytomous knowledge spaces in $\mathfrak{K}$ and polytomous surmise functions in ${\mathfrak{F}}_1$, respectively. With the help of these, this paper provides a characterization of the polytomous knowledge structure corresponding to the polytomous surmise function that is weakly factorial. Based on the finite sets of items and response values, these results generalize the previous approaches for polytomous knowledge spaces.

中文翻译：

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CD-多元知识空间和对应的多元推测系统

Heller (2021) 将准序数知识空间推广到多项式。受本文启发，我们提出了CD-多元知识空间及其多元推测系统。集合之间建立伽罗华联系$\mathfrak{钾}$所有多元知识结构和集合${\mathfrak{F}}_{\mathrm{1个}}$特定的多属性函数。Galois 连接的封闭元素是 CD 多分知识空间$\mathfrak{钾}$和多项猜测功能${\mathfrak{F}}_{\mathrm{1个}}$， 分别。借助于这些，本文提供了对应于弱阶乘的多元推测函数的多元知识结构的表征。基于项目和响应值的有限集，这些结果概括了先前的多元知识空间方法。