Knowledge space

In mathematical psychology, a knowledge space is a combinatorial structure describing the possible states of knowledge of a human learner. To form a knowledge space, one models a domain of knowledge as a set of concepts, and a feasible state of knowledge as a subset of that set containing the concepts known or knowable by some individual. Typically, not all subsets are feasible, due to prerequisite relations among the concepts. The knowledge space is the family of all the feasible subsets. Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne and have since been studied by many other researchers. They also form the basis for two computerized tutoring systems, RATH and ALEKS.