Re: Question about problems with top/bottom property

Alan Ruttenberg wrote:
> 
> Is there any reason not to include bottom role? There is a debugging 
> benefit to computing equivalentProperty to bottom role.
> 

I must admit I do not understand what you mean here.

In general, I would like to understand the clear benefit the top and 
bottom role would bring to OWL users. At the moment, it is unclear to me.

Ivan

> Also, where we discuss computational properties and reasoning services - 
> should role subsumption (and with bottom role, role satisfiability) be 
> mentioned?
> 
> 
> -Alan
> 
> On May 29, 2008, at 7:52 AM, Boris Motik wrote:
> 
>>
>> 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
>>
>>
>>
> 
> 

-- 

Ivan Herman, W3C Semantic Web Activity Lead
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