How Many Legs Do I Have? Non-Simple Roles in Number Restrictions Revisited

  • Yevgeny Kazakov
  • Ulrike Sattler
  • Evgeny Zolin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4790)

Abstract

The Description Logics underpinning OWL impose a well-known syntactic restriction in order to preserve decidability: they do not allow to use non-simple roles—that is, transitive roles or their super-roles—in number restrictions. When modeling composite objects, for example in bio-medical ontologies, this restriction can pose problems.X

Therefore, we take a closer look at the problem of counting over non-simple roles. On the one hand, we sharpen the known undecidability results and demonstrate that: (i) for DLs with inverse roles, counting over non-simple roles leads to undecidability even when there is only one role in the language; (ii) for DLs without inverses, two transitive and an arbitrary role are sufficient for undecidability. On the other hand, we demonstrate that counting over non-simple roles does not compromise decidability in the absence of inverse roles provided that certain restrictions on role inclusion axioms are satisfied.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Yevgeny Kazakov
    • 1
  • Ulrike Sattler
    • 1
  • Evgeny Zolin
    • 1
  1. 1.School of Computer Science, The University of ManchesterUK

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