Based on the celebrated Birkhoff theorem, Doignon and Falmagne (1985) establish a one-to-
one correspondence between certain binary relations on a domain of (dichotomous) items …

Abstract Heller (2021) generalized quasi‐ordinal knowledge spaces to polytomous items.
Inspired by this paper, we propose CD‐polytomous knowledge space and its polytomous …

Abstract Concept-cognitive learning has been widely used in simulating the human brain to
learn concepts. However, the existing concept-cognitive learning models mainly focused on …

The dichotomous knowledge structure theory was introduced to polytomous items, which is
proved meaningful in representing individuals' partial mastery of items. Given that different …

Skills represent the underlying cognitive abilities, which consist in methods, algorithms or
tricks etc. Skills can be used to interpret individuals' knowledge states. A skill map assigns a …

In knowledge space theory (KST), knowledge structure is an effective feature to evaluate
individuals' knowledge and guide future learning. How to construct knowledge structures is …

Abstract Knowledge structure is a valid characteristic for assessing individuals' knowledge
and guiding their future learning. Based on formal context, there are methods to construct a …

Abstract Stefanutti et al.(2020) and Heller (2021) have recently done significant work on the
polytomous extensions of knowledge space theory (KST), which opens the field for …

The present article lays out the foundations of an axiomatic theory of attribute maps, an
extension of skill maps to polytomous knowledge structure theory. A deterministic …

As an important mathematical theory in intelligent learning and assessment system,
knowledge space theory merely cares about items are mastered or non-mastered. Thus it …