[DL] Local/global consequence and DL

Franz Baader baader at tcs.inf.tu-dresden.de
Thu May 25 14:03:42 CEST 2006

>   Could anyone tell me whether a TBox is (by default) seen as a set of local
> axioms?

No, TBoxes and the more general GCIs (general concept inclusion axioms)
are gobal. This follows immediately from the definition of the semantics:
In a model I of A = C , you must have A^I = C^I, i.e., for every individual d of
the domain (in modal logic speak: for every world of the Kripke structure),
d in A^I iff s in C^I. This shows that A = C corresponds to a global axiom of
the form a <-> phi.

Best regards,

-Franz Baader

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