Knowledge Spaces and Formal Concept Analysis

Abstract

J.-P. Doignon and J.-C. Falmagne have introduced a formal notion of knowledge space to develop a scientific approach to the assessment of knowledge. They define a knowledge space as a (finite) set Q of questions together with a collection K, of subsets of Q representing different knowledge states; in addition, they assume that K is closed under set unions. The theory of knowledge spaces can be effectively connected with formal concept analysis. The connection is established by the definition of a knowledge context as a triple (P, Q, I) where P is a finite set of persons, Q is a finite set of questions, and I is a binary relation between P and Q such that plq means: the person p cannot solve the question q. For each knowledge context there is a corresponding knowledge space which consists of the complements of all intents of this context; conversely, each knowledge space can be derived in this way. Via the described connection, methods of formal concept analysis can be successfully applied to the theory of knowledge spaces. In particular, the attribute exploration as a method of conceptual knowledge acquisition yields a new approach for building knowledge spaces.