Rewriting Concepts Using Terminologies

The problem of rewriting a concept given a terminology can informally be stated as follows: given a terminology T (i.e., a set of concept deenitions) and a concept description C that does not contain concept names deened in T , can this description be rewritten into a \related better" description E by using (some of) the names deened in T ? In this paper, we rst introduce a general framework for the rewriting problem in description logics, and then concentrate on one speciic instance of the framework, namely the minimal rewriting problem (where \bet-ter" means shorter, and \related" means equivalent). We investigate the complexity of the decision problem induced by the minimal rewriting problem for the languages FL 0 , ALN, ALE, and ALC, and then introduce an algorithm for computing (minimal) rewrit-ings for the language ALE. (In the full paper , a similar algorithm is also developed for ALN.) Finally, we sketch other interesting instances of the framework. 1 Motivation In description logics (DLs), the standard inference problems, like the subsumption and the instance problem , are now well-investigated. More recently, new types of inference problems have been introduced and investigated, like matching In contrast to the standard inferences, algorithms that solve these nonstandard problems produce concept descriptions as output, which are then returned to the user for inspection. For example, in an application in chemical process engineering (Baader and Sattler, 1996; Sattler, 1998) we try to support the bottom-up construction of knowledge bases by computing most speciic concepts (msc) of individuals and least common subsumers (lcs) of concepts: instead of directly deening a new concept, the knowledge engineer introduces several typical examples as individuals, which are then generalized into a concept description by using the msc and the lcs operation (Baader and K usters, 1998; Baader et al., 1999b). This description is then ooered to the knowledge engineer as a possible candidate for a deenition of the concept. In such a framework, it is important that the returned description is as readable and comprehensible as possible. Unfortunately, the descriptions that are produced by the known algorithms for solving the nonstandard inference problems in general do not satisfy this requirement. The reason is that { like most algorithms for the standard inference problems { these algorithms work on unfolded descriptions, i.e., concept descriptions that do not contain names deened in the underlying terminology (TBox). Consequently, the descriptions that they …