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

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 )

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 )

(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?

Best,
Michael

>> -----Original Message-----
>> From: Michael Schneider [mailto:schneid@fzi.de]
>> Sent: 27 June 2009 01:52
>> To: Boris Motik
>> Cc: OWL 1.1
>> Subject: RE: question on "forest-like anonymous individuals"
>restriction of
>> OWL 2 DL
>>
>> Hi Boris!
>>
>> The second counter example states
>>
>>   ObjectPropertyAssertion( a:hasChild _:b1 _:b2 )
>>   ObjectPropertyAssertion( a:hasDaughter _:b1 _:b2 )
>>
>> But shouldn't it be
>>
>>   ObjectPropertyAssertion( a:hasChild _:b1 _:b2 )
>>   ObjectPropertyAssertion( a:hasDaughter _:b2 _:b1 )
>>                                          ^^^^^^^^^
>>
>> in order to build a circular structure?
>>
>> Cheers,
>> Michael
>>
>> >-----Original Message-----
>> >From: Boris Motik [mailto:boris.motik@comlab.ox.ac.uk]
>> >Sent: Friday, June 26, 2009 1:29 PM
>> >To: Michael Schneider; 'OWL 1.1'
>> >Subject: RE: question on "forest-like anonymous individuals"
>restriction
>> >of OWL 2 DL
>> >
>> >Hello,
>> >
>> >In response to Michael's comment, Ian and I have made the following
>> >changes to
>> >the Syntax document:
>> >
>>
>>http://www.w3.org/2007/OWL/wiki/index.php?title=Syntax&diff=24654&oldid
>=
>> >24647
>> >
>> >I hope things are clearer now. Please let me know should you have any
>> >comments.
>> >
>> >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 2009 20:46
>> >> To: OWL 1.1
>> >> Subject: question on "forest-like anonymous individuals"
>restriction
>> >of OWL 2
>> >> DL
>> >>
>> >> Hi all!
>> >>
>> >> I had to explain to someone the "forest-like anonymous individuals"
>> >> restriction of OWL 2 DL (Section 11.2 of the Structural Spec), but
>I
>> >found
>> >> myself uncertain about it. In particular, I'm unclear how "fixed"
>the
>> >variable
>> >> "OPE" is in the set of conditions.
>> >>
>> >> But it's easier to show my problem by an example: It's clear to me
>> >(also from
>> >> the example following the formal definition) that the following is
>> >/not/
>> >> allowed in OWL 2 DL:
>> >>
>> >>   _:x :p _:y
>> >>   _:y :p _:x
>> >>
>> >> But what about
>> >>
>> >>   _:x :p _:y
>> >>   _:y :q _:x
>> >>
>> >> with /different/ properties?
>> >>
>> >> Michael

--
Dipl.-Inform. Michael Schneider
Research Scientist, Dept. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: michael.schneider@fzi.de
WWW  : http://www.fzi.de/michael.schneider
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