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Re: Mapping to RDF Graphs and reification

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Thu, 4 Dec 2008 13:07:50 +0000
Message-Id: <7DA067ED-1F14-43BB-BD43-7CF2FB77CFCD@cs.man.ac.uk>
Cc: Owl Dev <public-owl-dev@w3.org>
To: Pierre-Antoine Champin <swlists-040405@champin.net>

I have no will power.

  I hate myself.

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 13:04:54 GMT

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