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Re: Question about problems with top/bottom property

From: Rinke Hoekstra <hoekstra@uva.nl>
Date: Fri, 30 May 2008 10:24:34 +0200
Cc: "Boris Motik" <boris.motik@comlab.ox.ac.uk>, <public-owl-wg@w3.org>
Message-Id: <DE6F402E-FF34-410D-BCFE-76FF4A64FE70@uva.nl>
To: Michael Schneider <schneid@fzi.de>

Tracker, this is related to ISSUE-112

-Rinke

On 29 mei 2008, at 23:31, Michael Schneider wrote:

> Hi Boris!
>
> Many thanks for this clear explanation. I think I now understand  
> what your
> concerns are.
>
> To point 2: What I at least can imagine is that adding U to OWL R  
> Full would
> result in a mess. So let's better not have it in this particular  
> profile.
>
> To point 1: I was surprised that the encoding of U was so simple (I  
> myself
> only found a complicated encoding based on sub property chains a few  
> months
> ago). And I can see that it is even simpler, because the reflexivity  
> axiom
> (2) is redundant: For each x in owl:Thing we have U(x,ni) by axiom  
> (1). So
> we have U(ni,x) by symmetry (3). And then U(x,x) follows from  
> transitivity
> (4). This means that the top property can already be expressed in  
> OWL 1.
>
> Cheers,
> Michael
>
>> -----Original Message-----
>> From: Boris Motik [mailto:boris.motik@comlab.ox.ac.uk]
>> Sent: Thursday, May 29, 2008 1:52 PM
>> To: Michael Schneider
>> Cc: public-owl-wg@w3.org
>> Subject: RE: Question about problems with top/bottom property
>>
>> Hello,
>>
>> Here is the executive summary of this rather long e-mail:
>>
>> 1. The universal property can already be expressed in OWL 2 in a
>> straightforward way.
>> 2. This straightforward encoding (suggested in most papers),  
>> however, is
>> quite inefficient in practice.
>> 3. It might be possible to come up with a more efficient  
>> implementation
>> technique. This technique, however, would not be completely
>> trivial.
>> 4. It is currently unclear how any of these techniques would fare in
>> practice.
>> 5. It is currently unclear that the potential "dangers" outweigh the
>> benefits of adding the universal property.
>> 6. Therefore, we might want to wait before we add this feature to  
>> OWL 2.
>>
>> And now for the details.
>>
>> = 
>> = 
>> = 
>> =====================================================================
>> =================
>>
>> Point 1.
>> --------
>>
>> You can use existing OWL 2 axioms to encode universal role. The
>> following axioms make U universal (ni is a new individual -- that
>> is, an individual that does not occur elsewhere in your ontology):
>>
>> (1)  SubClassOf( owl:Thing hasValue( U ni ) )
>> (2)  ReflexiveProperty( U )
>> (3)  SymmetricProperty( U )
>> (4)  TransitiveProperty( U )
>>
>> Axiom (1) makes every individual in the interpretation domain  
>> connected
>> through U to ni, and axioms (2), (3), and (4) then ensure
>> that you have a connection between all possible individuals. This  
>> is the
>> encoding suggested as an encoding in most papers: one
>> simply adds these axioms to an ontology and treats U as an ordinary
>> object property.
>>
>> Point 2.
>> --------
>>
>> The problem with this encoding is that axioms (1)--(4) connect
>> everything with everything. Consider what would happen if you added
>> (1)--(4) to an ontology containing a large number of assertions.  
>> Then,
>> your reasoner would have to deal with the extension of U
>> which is at least quadratic in the number of individuals occurring in
>> the ontology. This is likely to cause problems for indexing
>> and memory storage management in general.
>>
>>
>> Point 3.
>> --------
>>
>> I had a quick chat with Ian, and we noticed that there might be a  
>> way to
>> implement the universal property more efficiently, without
>> the explicit maintenance of the extension of U. Here is a very rough
>> sketch how this might work.
>>
>> The only way that U does something from a logical point of view is
>> through universals, and in such cases, U is connected to
>> everything; hence, you might find a suitable reformulation of
>> AllValuesFrom( U CE ) and simulate it though axioms of the form
>> SubClassOf( owl:Thing CE ). In fact, the two constructs are "quite
>> close" semantically.
>>
>> The complication here is with the role hierarchy: one would have to
>> ensure that the used encoding does not mess up some interaction
>> w.r.t. complex role inclusions.
>>
>> Thus, there is some conceptual work to be done, albeit this work is
>> probably not hard and/or interesting from a purely theoretical
>> point of view.
>>
>>
>> Point 4.
>> --------
>>
>> We should be careful when extending OWL 2 with new features that have
>> not been extensively tested in practice.
>>
>> If we don't have the universal property in OWL 2, then it is user's
>> fault if he adds the axioms (1)--(4) to an ontology and
>> everything suddenly runs slowly. In fact, if a user complains that my
>> reasoner is running slowly on his ontology, I can tell him
>> "it's your fault because you are using an ontology which is hard".
>>
>> If we allow for the universal property, then users will use it (even
>> though they might not really need it). But then, if my
>> implementation technique for an official feature of OWL 2 is flaky  
>> (and,
>> in particular, if this flakiness occurs in even rather
>> simple cases), the user has every right to complain.
>>
>>
>> Point 5.
>> --------
>>
>> On the one hand, I see that the universal property might be  
>> intuitively
>> appealing: it would allow make the language symmetric when
>> compared with classes (which have owl:Thing), and it would allow us  
>> to
>> "hang" the property hierarchy off of the universal role.
>>
>> On the other hand, I don't see what expressivity benefits we gain by
>> adding the construct to the language. As I already mentioned,
>> AllValuesFrom( U CE ) and SubClassOf( owl:Thing CE ) are "very close"
>> semantically.
>>
>> Thus, the added expressivity of the universal property does not  
>> seem to
>> outweigh the potential risks identified in Point 4.
>>
>>
>>
>> Point 6.
>> --------
>>
>> My preferred course of action would be to let someone demonstrate
>> (either by using the simple encoding (1)--(4) or by developing a
>> more efficient implementation approach) that adding universal  
>> property
>> does not really cause problems in practice. Assuming this is
>> done, adding the feature to the language should not be contentious.
>>
>>
>> Regards,
>>
>> 	Boris
>>
>>> -----Original Message-----
>>> From: public-owl-wg-request@w3.org [mailto:public-owl-wg-
>> request@w3.org] On Behalf Of Michael
>>> Schneider
>>> Sent: 29 May 2008 09:32
>>> To: Boris Motik
>>> Cc: public-owl-wg@w3.org
>>> Subject: Question about problems with top/bottom property
>>>
>>> Hi Boris!
>>>
>>> In yesterday's telco you expressed some concerns about the
>> introduction of
>>> the top/bottom properties into OWL. But I did not understand what  
>>> the
>>> problem was. Can you please elaborate on this topic.
>>>
>>> Thanks,
>>> Michael
>>
>

-----------------------------------------------
Drs. Rinke Hoekstra

Email: hoekstra@uva.nl    Skype:  rinkehoekstra
Phone: +31-20-5253499     Fax:   +31-20-5253495
Web:   http://www.leibnizcenter.org/users/rinke

Leibniz Center for Law,          Faculty of Law
University of Amsterdam,            PO Box 1030
1000 BA  Amsterdam,             The Netherlands
-----------------------------------------------
Received on Friday, 30 May 2008 08:25:10 GMT

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