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Re: Mapping to RDF Graphs and reification

From: Pierre-Antoine Champin <swlists-040405@champin.net>
Date: Thu, 04 Dec 2008 13:16:17 +0000
Message-ID: <4937D821.3050309@champin.net>
To: Bijan Parsia <bparsia@cs.man.ac.uk>
CC: Owl Dev <public-owl-dev@w3.org>, Michael Schneider <schneid@fzi.de>

Bijan Parsia wrote:
> I have no will power.
> 
>  I hate myself.

:-D thanks anyway for digging faster than me in the document.

As a matter of fact, I realized with Michael's and your mail that what I
*really* wanted to write was:

_:x rdf:type owl:NegativePropertyAssertion   (1)
_:x owl:sourceIndividual _:x   (2)
_:x owl:assertionProperty rdf:type   (3)
_:x owl:targetIndividual owl:NegativePropertyAssertion   (4)

However, reading the section you kindly pointed to, it seems to me that
there is no paradox either.

Indeed, the belonging of I(_:x) to IEXT(owl:NegativePropertyAssertion)
seems to be *completely irrelevant* to the interpretation of triples
(2-4). So triple (1) says one thing, triples (2-4) say another thing...
this is a plain old contradiction.

Cool. :-)

  pa


> 
> On 4 Dec 2008, at 11:11, Pierre-Antoine Champin wrote:
> [snip]
>> Wouldn't
>>
>>  _:x rdf:type owl:NegativePropertyAssertion
>>  _:x owl:sourceIndividual _:x
>>  _:x owl:assertionProperty owl:sourceIndividual
>>  _:x owl:targetIndividual _:x
>>
>> a perfect example of that paradox (in OWL Full, of course) ?
>>
>> What am I missing?
> 
> Semantic conditions for negative property assertions are given by table
> 5.15:
>     <http://www.w3.org/2007/OWL/wiki/RDF-Based_Semantics#tab-semcond-negativeassertions>
> 
> 
> (Pretend the triples are numbered 1-4)
> 
> So, (and I'm just going to use "x"). Let's try the following
> interpretatioN"
> 
> D = {x, sI, aP, tI, NPA,type}
> 
> IEXT(NPA) = {x}
> IEXT(sI) = {<x,x>}
> IEXT(aP) = {<x, sI>}
> IEXT(tI) ={<x, x>}
> IEXT(type) = {<x, NPA>}
> 
> Now, looking at the conditions:
> 〈x,u〉 ∈ IEXT(I(owl:sourceIndividual)),
> 〈x,p〉 ∈ IEXT(I(owl:assertionProperty)),
> 〈x,w〉 ∈ IEXT(I(owl:targetIndividual))
> 
> u = x
> p = sI
> w = x
> From this it follows from the condition:
>     〈u,w〉 not in IEXT(sI)
> that
>     <x, x> not in IEXT(sI)
> which is false. Thus the assertion is false.
> 
> Not seeing any paradox. Just a contradiction like C&~C.
> 
> Cheers,
> Bijan.
> 
Received on Thursday, 4 December 2008 13:16:59 GMT

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