- From: Pierre-Antoine Champin <swlists-040405@champin.net>
- Date: Thu, 04 Dec 2008 14:11:24 +0000
- To: Bijan Parsia <bparsia@cs.man.ac.uk>
- CC: Owl Dev <public-owl-dev@w3.org>, Michael Schneider <schneid@fzi.de>
Hi Bijan and Michael,
The time of a lunch break, and I'm not sure again.
(this is what is fun with paradoxes, even would-be paradoxes ;)
Let us take my first example.
>> _:x rdf:type owl:NegativePropertyAssertion
>> _:x owl:sourceIndividual _:x
>> _:x owl:assertionProperty owl:sourceIndividual
>> _:x owl:targetIndividual _:x
Bijan Parsia wrote :
> (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.
Ok, but if it is false, then you could not have inferred it in the first
place (because the 3 conditions above are not satisfied after all).
I guess you could simply say that no interpretation can possibly satisfy
the semantic conditions of table 5.15, so there is no model, so the
ontology is inconsistent. :-/
However, what bothers me here, is that you can not cut the ontology into
two consistent parts, whose respective consequences are contradictory.
I'm obviously reaching the limits of my understanding of model theory
here, but that is as close to a paradox as I can imagine...
Pierre-Antoine
Received on Thursday, 4 December 2008 14:12:11 UTC