Uni cation of Concept Terms in Description

Uniication of concept terms is a new kind of inference problem for Description Logics, which extends the equivalence problem by allowing to substitute certain concept names by concept terms before testing for equivalence. We show that this inference problem is of interest for applications, and present rst decidability and complexity results for a small concept description language. 1 Motivation The rst motivation for considering uniication of concept terms comes from an application in chemical process engineering 4]. In this application, the DL system is used to support the design of a large terminology of concepts describing parts of chemical plants as well as processes that take place in these plants. Since several knowledge engineers are involved in deening new concepts, and since this knowledge acquisition process takes rather long (several years), it happens that the same (intuitive) concept is introduced several times, often with slightly diiering descriptions. Our goal was to use the reasoning capabilities of the DL system (in particular, testing for equivalence of concept terms) to support avoiding this kind of redundancy. However, testing for equivalence of concepts is not always suucient to nd out whether, for a given concept term, there already exists another concept term in the knowledge base describing the same notion. For example, assume that one knowledge engineer has deened the concept of all women having only daughters 1 by the concept term Woman u 8child:Woman: 1 We use an example from the family domain since examples from process engineering would require too much explanation. A second knowledge engineer might represent this notion in a somewhat more ne-grained way, e.g., by using the term Female u Human in place of Woman. The concept terms Woman u 8child:Woman and Female u Human u 8child:(Female u Human) are not equivalent, but they are meant to represent the same concept. The two terms can obviously be made equivalent by substituting the atomic concept Woman in the rst term by the concept term Female u Human. question whether two concept terms C; D can be made equivalent by applying an appropriate substitution , where a substitution replaces (some of the) atomic concepts by concept terms. A substitution is a uniier of C; D ii (C) (D) (where denotes equivalence of concept terms). Of course, it is not necessarily the case that uniiable concept terms are meant to represent the same notion. A uniiability test can, however, suggest to …