How Many Legs Do I Have? Non-Simple Roles in Number Restrictions Revisited
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.
Unable to display preview. Download preview PDF.
- 3.Börger, E., Grädel, E., Gurevich, Y.: The Classical Decision Problem. Perspectives in Mathematical Logic. Springer, Heidelberg (1997)Google Scholar
- 5.Horrocks, I., Patel-Schneider, P.F., van Harmelen, F.: From SHIQ and RDF to OWL: The making of a web ontology language. Journal of Web Semantics 1(1), 7–26 (2003)Google Scholar
- 7.Kazakov, Y., Sattler, U., Zolin, E.: Is Your RBox Safe? Technical report. The University of Manchester (2007), available at http://www.cs.man.ac.uk/~ezolin/pub/