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Re: Mapping to RDF Graphs and reification

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Thu, 4 Dec 2008 14:26:44 +0000
Message-Id: <205BC8A2-A2EC-4375-A5A0-64D68B8E0A3A@cs.man.ac.uk>
Cc: Owl Dev <public-owl-dev@w3.org>
To: Pierre-Antoine Champin <swlists-040405@champin.net>

On 4 Dec 2008, at 14:11, Pierre-Antoine Champin wrote:
[snip]
> 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

Inferred what? This is just an interpretation that makes the sentence  
false. I believe that there are no interpretations that make it true,  
since this seems to be core to all of them, but I'm not sure about  
that. And I don't need to be. As long as there's a stable  
interpretation, we avoid paradox.

> (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. :-/

That's what I said. :)

> However, what bothers me here, is that you can not cut the ontology  
> into
> two consistent parts, whose respective consequences are contradictory.

Try:
	ClassAssertion(a owl:Nothing)

Also inconsistent. Also not partitionable into two consistent parts.

> 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...

Nope. Has nothing to do with paradox. Contradictions aren't problems.  
There's lots of them.

A paradox is the strange situation that the sentence is true iff it  
is false. That is, no matter how you interpret it, you interpration  
is "wrong". With a contradiction, there is a sensible interpretation:  
It's false.

Cheers,
Bijan.
Received on Thursday, 4 December 2008 14:23:45 GMT

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