Re: question on "forest-like anonymous individuals" restriction of OWL 2 DL

On 27 Jun 2009, at 22:11, Michael Schneider wrote:

> Hi again!
>
>> -----Original Message-----
>> From: Boris Motik [mailto:boris.motik@comlab.ox.ac.uk]
>> Sent: Saturday, June 27, 2009 2:01 AM
>> To: Michael Schneider
>> Cc: 'OWL 1.1'
>> Subject: RE: question on "forest-like anonymous individuals"  
>> restriction
>> of OWL 2 DL
>>
>> Hello,
>>
>> No, not really: since OWL 2 has inverse roles, the actual  
>> directionality
>> of the
>> property assertions doesn't matter. That is, the role assertion
>>
>> ObjectPropertyAssertion( a:hasDaughter _:b1 _:b2 )
>>
>> is equivalent to
>>
>> ObjectPropertyAssertion( InverseObjectProperty(a:hasDaughter) _:b2  
>> _:b1
>> )
>>
>> Now if the latter is circular, the former should be circular as well,
>> given that
>> the two assertions are semantically equivalent.
>>
>> Regards,
>>
>> 	Boris
>
> Ok, thanks, I see it now! I admit that I didn't see when writing my  
> previous
> main, and I guess that I won't be the last one who will be  
> puzzled. :) So
> can we please just have a more obvious example, where the circular  
> structure
> is being made explicit?
>
> But from what you say above, a second issue seems to arise: It  
> looks to me
> that OWL 2 DL now does not even allow to state /single/ property  
> assertions
> with blank nodes in both subject and predicate position. Because,  
> as you
> said, with
>
>   ObjectPropertyAssertion( ex:p _:s _:o )
>
> one will always also have
>
>   ObjectPropertyAssertion( InverseObjectProperty(ex:p) _:o _:s )

The restrictions are about syntax. You won't always have the second  
triple in the *syntax* of the ontology, even if the existence of such  
an inverse relationship can be inferred.

>
> and so there are in fact always /two/ triples (though only one of them
> explicitly stated) with their contained blank nodes building a  
> circular
> structure.
>
> Even worse, since blank nodes are /existentially/ interpreted in  
> OWL 2 DL, I
> would expect that the following entailment holds (as in OWL 2 Full):
>
>   ObjectPropertyAssertion( ex:p ex:s ex:p )
>   |=
>   ObjectPropertyAssertion( ex:p _:s _:o )

Seems reasonable (modulo the typo in the first assertion).

>
> (Stating that if ex:s is in ex:p-relationship with ex:o, then  
> something
> ("_:s") is in ex:p-relationship with something else ("_:o").)
>
> So if this is really the case, than it wouldn't even be allowed to  
> have
> *any* object property assertions in an ontology, since an arbitrary  
> property
> assertion would entail another property assertion with two blank  
> nodes,
> which will then entail yet another property assertion with the inverse
> property, leading to a circular blank node structure.
>
> Of course, this sounds absurd to me, but where is my error?

You are forgetting that such restrictions apply to the syntax of the  
ontology and not to its semantics (what can be entailed).

Ian


>
> Best,
> Michael

[snip]

Received on Saturday, 27 June 2009 22:24:11 UTC