Semantical Considerations on Description Logics of MKNF

Description logics of minimal knowledge and negation as failure (MKNF-DLs) are formalisms which augment description logics (DLs) with the modal operators K representing `knowledge' and A representing `default assumption'. Such hybrid formalisms are useful in characterizing many nonmonotonic features which can not captured in pure DLs. The traditional semantics employed for MKNF-DLs is based on the possible world approach where each world corresponds to a DL interpretation. Further, the semantics requires the interpretations to share a common domain and to interpret constants rigidly across the worlds. In this paper we argue that these restrictions lead to unintended effects when an expressive MKNF-DL like \mathcal{SROIQK}_\mathcal{NF} is considered. We thus propose employing the extended semantics, introduced recently, for \mathcal{SROIQK}_\mathcal{NF}. We then provide a comparison between the traditional and the extended semantics including a comparison from first-order modal logic perspective. In addition, we present a methodology for performing reasoning tasks in \mathcal{SROIQK}_\mathcal{NF}.