Knowledge Structures and Learning Spaces

Suppose that some complex system is assessed by an expert, who checks for the presence or absence of some revealing features. Ultimately, the state of the system is described by the subset of features, from a possibly large set, which are detected by the expert. This concept is very general, and becomes powerful only on the background of specific assumptions, in the context of some applications. We begin with the combinatoric underpinnings of the theory formalizing this idea.