@inproceedings{KazSatZol:07:NonSimple,
  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. 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 demon-strate 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",
  author = "Yevgeny Kazakov and Ulrike Sattler and Evgeny Zolin",
  booktitle = "LPAR",
  doi = "10.1007/978-3-540-75560-9_23",
  pages = "303-317",
  publisher = "Springer",
  series = "Lecture Notes in Computer Science",
  title = "How Many Legs Do {I} Have? Non-Simple Roles in Number Restrictions Revisited",
  volume = "4790",
  year = "2007",
}