Eliminating nonmonotonic DL-Atoms in description logic programs

  • Authors:

  • Yisong Wang;Thomas Eiter;Jia-Huai You;LiYan Yuan;Yi-Dong Shen

  • Affiliations:

  • Department of Computer Science, Guizhou University, Guiyang, China;Institute of Information Systems, Vienna University of Technology, Austria;Department of Computing Science, University of Alberta, Canada;Department of Computing Science, University of Alberta, Canada;State Key Laboratory of Computer Science,Institute of Software, Chinese Academy of Sciences, China

  • Venue:
  • RR'13 Proceedings of the 7th international conference on Web Reasoning and Rule Systems
  • Year:
  • 2013

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Abstract

Nonmonotonic description logic programs (dl-programs) are a well-known formalism for combining rules and ontologies, where rules interact with an underlying ontology via dl-atoms that allow queries to the ontology under a possible update of its assertional part. It is known that dl-atoms may be nonmonotonic and dl-programs without nonmonotonic dl-atoms have many desirable properties. In this paper, we show that it is possible to remove nonmonotonic dl-atoms from a dl-program while preserving its strong/weak answer set semantics. Though the translation is faithful, it relies on the knowledge about monotonicity of dl-atoms. We then thoroughly investigate the complexity of deciding whether a dl-atom is monotonic under the description logics DL-Lite$_{\mathcal R}$, ${\mathcal{EL}}^{++}$, ${\mathcal{SHIF}}$ and ${\mathcal{SHOIN}}$, which is of independent interest for computing strong answer sets. We show that the problem is intractable in general, but tractable for dl-atoms with bounded queries in DL-Lite$_{\mathcal R}$.