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RE: Mapping to RDF Graphs and reification

From: Michael Schneider <schneid@fzi.de>
Date: Thu, 4 Dec 2008 13:14:19 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0EA6890@judith.fzi.de>
To: "Pierre-Antoine Champin" <swlists-040405@champin.net>
Cc: "Pat Hayes" <phayes@ihmc.us>, <public-owl-dev@w3.org>
Pierre-Antoine Champin wrote:

>Pat Hayes a écrit :
>> Well, someone could argue that since the negation construction
>involves
>> meta-description, iterating it gives you a kind of truth predicate, in
>a
>> sense. Kinda. But Tarski's paradox doesn't arise for other reasons,
>> having to do with how impoverished RDF is as an expressive logic.
>
>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) ?

This is simply a OWL 2 Full-inconsistent ontology.

>From interpreting the second triple, we get
 
  <I(_:x),I(_:x)> in IEXT(I(owl:sourceIndividual))

And from interpreting the whole graph by applying the OWL 2 Full semantic
conditions for negative property assertion, we get

  NOT [ <I(_:x),I(_:x)> in IEXT(I(owl:sourceIndividual)) ]

This is obviously a contradiction. But there is no paradox.

Michael

--
Dipl.-Inform. Michael Schneider
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Abtl. Information Process Engineering (IPE)
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Received on Thursday, 4 December 2008 12:15:02 GMT

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