Extensions of concept languages for a mechanical engineering application

We shall consider an application in mechanical engineering, and shall show that the adequate modeling of the terminology of this problem domain in a conventional concept language poses two main representation problems. The first requires access to concrete domains, such as real numbers, while the second asks for a construct which can be used to represent sequences of varying length. As shown in recent papers by the authors there exist extended concept languages--equipped with sound and complete reasoning algorithms--that satisfy the respective representation demands separately. The main result presented in this paper is that the combination of both extensions leads to undecidable terminological inference problems. In particular, the important subsumption problem is undecidable. It should be noted that the need for these extensions is not particular to the considered problem domain; similar representation demands are likely to occur in other non-toy applications