How many legs do i have?: non-simple roles in number restrictions revisited

  • Authors:

  • Yevgeny Kazakov;Ulrike Sattler;Evgeny Zolin

  • Affiliations:

  • School of Computer Science, The University of Manchester, UK;School of Computer Science, The University of Manchester, UK;School of Computer Science, The University of Manchester, UK

  • Venue:
  • LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
  • Year:
  • 2007

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Abstract

The Description Logics underpinning OWL impose awell-known syntactic restriction in order to preserve decidability: they do not allow to use nonsimple 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 nonsimple 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.