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Re: Mapping to RDF Graphs and reification

From: Pat Hayes <phayes@ihmc.us>
Date: Thu, 4 Dec 2008 10:25:10 -0600
Cc: Pierre-Antoine Champin <swlists-040405@champin.net>, Michael Schneider <schneid@fzi.de>, Bijan Parsia <bparsia@cs.man.ac.uk>
Message-Id: <0C92B03B-B428-46D7-9591-1E9B2F9AB3EB@ihmc.us>
To: Owl Dev <public-owl-dev@w3.org>


On Dec 4, 2008, at 7:58 AM, Bijan Parsia wrote:

>
> On 4 Dec 2008, at 13:16, Pierre-Antoine Champin wrote:
>
>> Bijan Parsia wrote:
>>> I have no will power.
>>>
>>> I hate myself.
>>
>> :-D thanks anyway for digging faster than me in the document.
>>
>> As a matter of fact, I realized with Michael's and your mail that  
>> what I
>> *really* wanted to write was:
>>
>> _:x rdf:type owl:NegativePropertyAssertion   (1)
>> _:x owl:sourceIndividual _:x   (2)
>> _:x owl:assertionProperty rdf:type   (3)
>> _:x owl:targetIndividual owl:NegativePropertyAssertion   (4)
>>
>> However, reading the section you kindly pointed to, it seems to me  
>> that
>> there is no paradox either.
>>
>> Indeed, the belonging of I(_:x) to  
>> IEXT(owl:NegativePropertyAssertion)
>> seems to be *completely irrelevant* to the interpretation of triples
>> (2-4). So triple (1) says one thing, triples (2-4) say another  
>> thing...
>> this is a plain old contradiction.
>>
>> Cool. :-)
>
> Nice.
>

This general phenomenon, of classical paradoxes becoming simply new  
kinds of inconsistency, seems to be typical of the RDF 'style' of  
semantics, as we have discovered in the Common Logic [1] project  
(which uses the same basic semantic devices but in the context of a  
fully expressive first-order logic, in fact somewhat more than first- 
order in places.) In the IKL extension of common logic, the language  
becomes almost scarily expressive, with the full ability to refer to  
any proposition expressed by any of its own well-formed sentences,  
with full quantifying-in to any expression, and you can write  
"paradoxes" to your heart's content, including (IKL versions of) the  
Russell, Tarski, Liar and Kripke pragmatic paradoxes; and they all  
just turn out to be inconsistent sentences. What makes them have a  
paradoxical smell is that they all have the superficial syntactic form  
of definitions: for example, the Liar in IKL is

(= p (that (not (p))))

which is exactly how one would write a 'definition' of p, and the  
Russell is

(forall (x)(iff (R x)(not (x x)) ))

which is a 'definition' of R. If one were to call them definitions  
(rather than just logical sentences) and thereby implicitly insist  
that they could not possibly be false, in effect, then that would  
would make them genuinely paradoxical; but CL (and IKL, and RDF and  
OWL) don't have an explicit 'definition' syntax; which is their get- 
out-of-paradox-free ticket.

(Just a comment to help people's intuitions, probably best not pursued  
on this list.)

Pat
[1] http://cl.tamu.edu/
[2] http://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.html#liar
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Received on Thursday, 4 December 2008 16:27:36 GMT

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