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Re: Some basic questions about OWL-Full

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 23 Oct 2007 08:58:28 -0500
Message-Id: <p06230913c343ad57c4e1@[192.168.1.2]>
To: Jeremy Carroll <jjc@hpl.hp.com>
Cc: public-owl-dev@w3.org

>Peter F. Patel-Schneider wrote:
>>
>>For homework:  Is EquivalentProperties(owl:sameAs owl:differentFrom)
>>    	       itself inconsisten?
>>
>
>I'm afraid I'm several years' late on my (easier) homework of:
>    Is (*empty*) itself inconsistent?

Yes, in RDF (and conventional FOL). This is the 
only assumption of Tarskian semantic theory, that 
there is something in the universe. One can build 
a 'free' logic which allows an empty universe, 
but then its proof theory can't have the usual 
rules of instantiation and generalization, which 
allow the inferences

(forall (x) (foo x))  |==   (foo A) for some 
'new' name A |==  (exists (x)(foo x))

Pat

>
>Jeremy


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Received on Tuesday, 23 October 2007 13:58:42 GMT

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