Institute for Mathematical Behavioral Sciences

Abstract. Pedagogically sound axioms are given for a particular case of knowledge space, called a “learning space.” However, in realistic applications, such structures are typically very large (often containing > 100,000 knowledge states) which create a problem of storage and communication. The answer to the problem can be found in Media Theory. It turns out that any learning space can be represented as an ”oriented closed medium.” This type of semigroup has a convenient representation as an isometric subgraph of Nk for some positive integer k, and a unique base—the precedence diagram—which is an oriented medium. The reconstruction of the full oriented medium from its base (and thus also the learning space) is particularly simple.