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One of the important topics under active investigation in the area of description logic (DL) is that of adding rules to the language. In this paper, we observe that the logic FO(ID), which was developed as an integration of ASP and classical logic, provides an interesting source of inspiration for such extensions. In particular, it seems well-suited as an upperbound to a hierarchy of increaslingly expressive extensions of DL with rules. We demonstrate this by defining two interesting sublogics of FO(ID), called ALCI(ID) and guarded ALCI(ID).doi:10.1007/s10472-010-9207-9 fatcat:z6x4g3fatbcsfi32qmllplqtei