[DL] Question on the relation between ALCHOIQ and SROIQ

[Penaloza Nyssen Rafael]

Dear DLers,

  I am finding some papers, which provide methods for ALCHOIQ, and then mention something of the form "using well-known transformations, this extends to SROIQ." Unfortunately, this claim is not accompanied by any relevant reference to justify it. The closest I have found is the original SROIQ paper (Horrocks, Kutz, Sattler), where it is shown that one can reduce everything to a "role hierarchy" plus some restricted set of axioms. But such a role hierarchy still uses complex role inclusion axioms (i.e., beyond H).

  I trust the authors of all those papers, and do not doubt the veracity of the claim. But for someone like me that is not fluent in all the minutiae of SROIQ, it sounds like magic. For example, why doesn't that allow me to take any algorithm for ALCH and get one for SR? Where does the complexity jump happen? I want to understand it better (and, if possible, have a reference to cite if and when I ever make the same claim).

  Can anyone point me in the right direction?

  Thank you all in advance.

Cheers,
Rafael

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Prof. Rafael Peñaloza
University of Milano-Bicocca, Italy