Re: Question about the topProperty

On Mittwoch, 30. April 2008, Markus Krötzsch wrote:
> On Freitag, 25. April 2008, Carsten Lutz wrote:
> > On Thu, 24 Apr 2008, Michael Schneider wrote:
> > > Hi!
> > >
> > > I have a question regarding the topProperty and the bottomProperty. If
> > > these properties are going to be introduced into OWL 2, would they only
> > > go into OWL-DL/Full, or can they also be included into each of the
> > > profiles? Do these properties add to the semantic expressivity or to
> > > the computational complexity of the profiles?
> >
> > For the case of EL++: the top and bottom properties can be included. They
> > do add to the expressivity, but do not increase computational complexity.
> > The latter is very easy to see by looking at existing EL++ algorithms,
> > and I think it also follows from Markus' rule-extension of EL++.
>
> Yes, and this is still the case if you add things like role disjointness
> and local reflexivity. If you add only universal properties, it is indeed
> very easy to modify the existing algorithms.
>
> Anything above OWL DL can easily axiomatise a top property (using DL
> pseudo-notation here, sorry):
>
> TOP SUBCLASSOF EXISTS R1.{a}
> TOP SUBCLASSOF EXISTS R2.{a}
> R1 o R2 SUBPROPOF U
Typo. It should of course be:

R1 o R2- SUBPROPOF U

R1, R2 (properties) and a (individual) are of course new names, not used 
anywhere else.

-- Markus

>
> Then U is the universal. In other words: when you have defined your
> semantics for TOP (thing), you also can define an according "cross product"
> TOP x TOP easily. BottomProperties are even easier (see previous telco
> logs).
>
> Cheers,
>
> Markus
>
> > greetings,
> >  		Carsten
> >
> > --
> > *      Carsten Lutz, Institut f"ur Theoretische Informatik, TU Dresden
> >  * *     Office phone:++49 351 46339171  
> > mailto:lutz@tcs.inf.tu-dresden.de *



-- 
Markus Krötzsch
Institut AIFB, Universität Karlsruhe (TH), 76128 Karlsruhe
phone +49 (0)721 608 7362          fax +49 (0)721 608 5998
mak@aifb.uni-karlsruhe.de          www  http://korrekt.org