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On the Krom Extension of \(\mathcal {CFDI}^{\forall -}_{nc}\)

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AI 2015: Advances in Artificial Intelligence (AI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9457))

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Abstract

We consider the consequences on basic reasoning problems of the Krom extension to the description logic dialect \(\mathcal {CFDI}^{\forall -}_{nc}\), that is, of allowing negated primitive concepts on left-hand-sides of inclusion dependencies. Specifically, we show that TBox consistency and concept satisfiability remain in PTIME, but that this extension leads to intractability for both knowledge base consistency and instance retrieval. We then trace the roots of intractability by presenting tight conditions that recover PTIME complexity for both of these problems. The conditions relate to the structure of functional constraints in \(\mathcal {CFDI}^{\forall -}_{nc}\) and to the unique name assumption.

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Notes

  1. 1.

    The widgets, in principle, can support 4-clauses. For 3-CNF we fixed concept membership of one of the objects to B.

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Authors and Affiliations

  1. Cheriton School of Computer Science, University of Waterloo, Waterloo, Canada

    David Toman & Grant Weddell

Authors
  1. David Toman
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  2. Grant Weddell
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Correspondence to David Toman .

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Editors and Affiliations

  1. The University of Waikato, Hamilton, New Zealand

    Bernhard Pfahringer

  2. The Australian National University, Canberra, Aust Capital Terr, Australia

    Jochen Renz

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Toman, D., Weddell, G. (2015). On the Krom Extension of \(\mathcal {CFDI}^{\forall -}_{nc}\) . In: Pfahringer, B., Renz, J. (eds) AI 2015: Advances in Artificial Intelligence. AI 2015. Lecture Notes in Computer Science(), vol 9457. Springer, Cham. https://doi.org/10.1007/978-3-319-26350-2_50

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  • DOI: https://doi.org/10.1007/978-3-319-26350-2_50

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26349-6

  • Online ISBN: 978-3-319-26350-2

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