- From: Pat Hayes <phayes@ihmc.us>
- Date: Thu, 4 Dec 2008 10:39:48 -0600
- To: Pierre-Antoine Champin <swlists-040405@champin.net>
- Cc: Owl Dev <public-owl-dev@w3.org>
On Dec 4, 2008, at 8:11 AM, Pierre-Antoine Champin wrote:
>
> 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).
Er... inferred it from what? By and large, one can often infer an
inconsistent set from another inconsistent set. In software
engineering its called GIGO, but the logical version might be called
IIIO.
> 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. :-/
Yes, exactly.
> However, what bothers me here, is that you can not cut the ontology
> into
> two consistent parts, whose respective consequences are contradictory.
True, but this isn't uncommon. But let me rephrase your possible
concern here in different words: there isn't a clear syntactic 'flag'
for this inconsistency (like being able to see both a P and a (not P),
or detecting a null clause, or something nice and neat like that.)
True, and this means that those who write inference engines have to be
aware of more kinds of syntactic inconsistency-markers to look out
for. But it can be done. Re. my earlier post, its harder still in IKL.
Pat
>
>
> 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
>
>
>
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Received on Thursday, 4 December 2008 16:52:15 UTC