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RE: Anonymous individuals (again!)

From: Boris Motik <boris.motik@comlab.ox.ac.uk>
Date: Tue, 2 Dec 2008 17:58:18 -0000
To: <clu@tcs.inf.tu-dresden.de>
Cc: "'Jeff Z. Pan'" <jeff.z.pan@abdn.ac.uk>, <public-owl-wg@w3.org>
Message-ID: <4144856929564922BF8ECC18CC1FB867@wolf>

Hello,

Assume that you have the following ABox:

(1) R(a, _:x1)
(2) S(b, _:x1)
(3) T(_:x3, _:x1)

The global restrictions ensure that anonymous individuals occur in tree-shaped assertions, which is the case here.

Now you can eliminate these assertions by replacing these three assertions with the following one:

(4) \exists R.[(\exists S^-.{ b }) \sqcap (\exists T^-.\top)](a)

The problem is, however, that assertions containing anonymous individuals can be arbitrarily oriented; hence, you might need inverse
roles for rolling up. Since inverse roles are not available in OWL 2 EL, you can't make this encoding, which is why I thought one
cannot handle the damn thing in OWL 2 EL.

I'm open to suggestions if you have some other idea. 

Regards,

	Boris

> -----Original Message-----
> From: clu@tcs.inf.tu-dresden.de [mailto:clu@tcs.inf.tu-dresden.de]
> Sent: 02 December 2008 17:03
> To: Boris Motik
> Cc: 'Jeff Z. Pan'; public-owl-wg@w3.org
> Subject: Re: Anonymous individuals (again!)
> 
> Hi Boris,
> 
> Boris Motik wrote:
> > Hello,
> >
> > The general approach to handling anonymous individuals is that you should roll them up into a
> concept. Now, according to the
> > restrictions in the Syntax document, you might need inverse roles for that; OWL 2 EL doesn't have
> inverses, so there you go.
> 
> I am not sure I understand. I had assumed that anonymous individuals can easily
> be dealt with using the universal role and existential restrictions, both of which
> are present in OWL 2 EL. Can you explain what you mean with "rolling up"?
> 
> thanks,
> 		Carsten
> 
> > In OWL 2 QL, you can roll anonymous individuals into concepts. To decide satisfiability, you need
> to negate these concepts and put
> > them into the ontology; but then, existentials become universals, which you don't have in OWL 2 QL.
> There is another problem: if you
> > wanted to extend OWL 2 QL with functionality (which was deliberately left as a possibility), you
> must ensure that all individuals in
> > the ABox are interpreted under UNA if you want query answering to be first-order reducible. That's
> a problem for anonymous
> > individuals: they are not naturally interpreted under UNA, and, if you have such individuals
> distributed over imported ontologies,
> > you can't even axiomatize UNA yourself (because anonymous individuals are unique to the ontology
> they are contained in).
> >
> > Regards,
> >
> > 	Boris
> >
> >> -----Original Message-----
> >> From: Jeff Z. Pan [mailto:jeff.z.pan@abdn.ac.uk]
> >> Sent: 02 December 2008 15:16
> >> To: Boris Motik
> >> Cc: public-owl-wg@w3.org
> >> Subject: Re: Anonymous individuals (again!)
> >>
> >> Hi Boris,
> >>
> >> Thanks for the hard work. Are there any examples to illustrate why we
> >> can have anonymous individuals in OWL 2 RL but not the other two profiles?
> >>
> >> Thanks,
> >>
> >> Jeff
> >>
> >>
> >>
> >> Boris Motik wrote:
> >>> Hello,
> >>>
> >>> The problems with anonymous individuals that I noticed in the Profiles made me look again at the
> >> global restrictions on anonymous
> >>> individuals in Section 11.2. I noticed a slight error in the global restrictions, which I've
> fixed.
> >> After fixing this error, I
> >>> realized that
> >>>
> >>> - the restriction on no anonymous individuals in OWL 2 EL and OWL 2 QL is strictly needed if we
> 
> >>> computational properties;
> >>>
> >>> - however, in OWL 2 RL this restriction isn't needed -- that is, even with anonymous individuals
> >> reasoning in OWL 2 RL can be
> >>> implemented in polynomial time.
> >>>
> >>> Consequently, I've removed the restriction on no anonymous individuals in OWL 2 RL from the
> >> Profiles document.
> >>> I'm now done with all my changes to the spec -- we are ready to roll!
> >>>
> >>> Regards,
> >>>
> >>>       Boris
> >>>
> >>>
> >>>
> >>> The University of Aberdeen is a charity registered in Scotland, No SC013683.
> >>>
> >>>
> >>
> >>
> >> The University of Aberdeen is a charity registered in Scotland, No SC013683.
> >
> >
> 
> 
> --
> *  Carsten Lutz, FB Mathematik und Informatik, Universitaet Bremen   *
> * Office phone:++49 421 21864431 mailto:clu@informatik.uni-bremen.de *
Received on Tuesday, 2 December 2008 17:59:11 GMT

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