Conservative Extensions in the Lightweight Description Logic $\mathcal{EL}$

  • Authors:
  • Carsten Lutz;Frank Wolterinst

  • Affiliations:
  • Institute for Theoretical Computer Science, TU Dresden, Germany;Department of Computer Science, University of Liverpool, UK

  • Venue:
  • CADE-21 Proceedings of the 21st international conference on Automated Deduction: Automated Deduction
  • Year:
  • 2007

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Abstract

We bring together two recent trends in description logic (DL): lightweight DLsin which the subsumption problem is tractable and conservative extensionsas a central tool for formalizing notions of ontology design such as refinement and modularity. Our aim is to investigate conservative extensions as an automated reasoning problem for the basic tractable DL $\mathcal{EL}$. The main result is that deciding (deductive) conservative extensions is ExpTime-complete, thus more difficult than subsumption in $\mathcal{EL}$, but not more difficult than subsumption in expressive DLs. We also show that if conservative extensions are defined model-theoretically, the associated decision problem for $\mathcal{EL}$ is undecidable.