The appeal of KST lies in the simplicity and generality of its basic notions. A domain of knowledge is characterized by a set of test items, and the knowledge state of an individual consists of the subset of items that the individual in principle masters. The collection of all the possible states then forms a knowledge structure. Due to dependencies between items, not all subsets of items will occur as knowledge states. Notice that mastering an item is to be distinguished from actually solving

A series of four papers is devoted to further developing the deterministic theory of knowledge structures.

In his contribution, Suck (2021) inverts the traditional KST perspective of going from items to skills, and starts out from a situation where a partially ordered set of skills is given. The mathematical tool of a set representation of a partial order is then used to construct a knowledge space or a learning space on a set of items. This approach is based on the notion of the basis of a

The remaining five contributions to the special issue consider probabilistic models defined on knowledge structures.

Based on the same parameter space as the BLIM, Doignon (2021) considers what he calls the Correct Response Model, which predicts the probability of a correct response to any single item. The paper investigates this model with respect to testability, identifiability and characterizability. Mainly drawing upon the theory of polytopes (Grünbaum, 2003, Ziegler, 1998) it either

The present special issue demonstrates that KST provides a general framework that, even after a history of almost four decades, offers plenty of potential for new theoretical developments as well as innovative applications. It paints a picture of KST as a many-faceted research strand drawing upon tools from different areas of mathematics (e.g., order theory, polyhedral combinatorics, probability theory and stochastic processes). The contributions document the current state of the art, showing

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