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)


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.


Modal Logic Description Logic Conservative Extension Induction Base Undecidability Result 
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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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