Invited Speaker: Franz Baader

Formal Concept Analysis (FCA) and Description Logics (DL) are successful formalisms for structuring the terminological knowledge of an application domain. Both are based on the fundamental notion of a concept, which is a collection of objects sharing certain properties. Other than this communality, however, there are many differences between the two approaches. For example, FCA starts with a complete (extensional) description of the application domain (the context), and then derives the concepts of this fixed domain. In contrast, in DL one first defines (intensional) descriptions of concepts (in the TBox), and then uses them to give a partial description of the application domain (in the ABox).

This talk is concerned with bridging the gap between DL and FCA by employing FCA tools in the bottom-up construction of DL knowledge bases. Instead of directly defining a new concept, the knowledge engineer introduces several typical examples as objects, which are then automatically generalized into a concept description by the system. This description is offered to the knowledge engineer as a possible candidate for a definition of the concept.

From a technical point of view, this bottom-up construction motivates our interest in the following computation problems. Given a finite set S of description logic concepts, we are interested in computing the subsumption hierarchy of all least common subsumers of subsets of S as well as the hierarchy of all conjunctions of subsets of M. The point is to compute the first hierarchy without having to compute the least common subsumer for all subsets of M, and the second hierarchy without having to check all possible pairs of such conjunctions explicitly for subsumption. We will show that methods from formal concept analysis developed for computing concept lattices can be employed for this purpose.