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Semantical Considerations on Description Logics of MKNF

Published: 2013 Dezember
Institution: Institut AIFB
Erscheinungsort / Ort: Karlsruhe


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 $\mathcal{SROIQK}_\mathcal{NF}$.