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Re: RDF Recommendation Set comments (re agenda for 6th April)

From: Peter Frederick Patel-Schneider <pfps@research.bell-labs.com>
Date: Thu, 7 Apr 2011 16:09:48 -0400
Message-ID: <20110407.160948.1559061203962047566.pfps@research.bell-labs.com>
To: <antoine.zimmermann@insa-lyon.fr>, <antoine.zimmermann@gmail.com>
CC: <public-rdf-wg@w3.org>
From: Antoine Zimmermann <antoine.zimmermann@gmail.com>
Subject: Re: RDF Recommendation Set comments (re agenda for 6th April)
Date: Thu, 7 Apr 2011 14:53:05 -0500

> Le 07/04/2011 18:35, Peter Frederick Patel-Schneider a écrit :
>> From: Antoine Zimmermann<antoine.zimmermann@insa-lyon.fr>
>> Subject: Re: RDF Recommendation Set comments (re agenda for 6th April)
>> Date: Thu, 7 Apr 2011 10:40:37 -0500
>>
>>> Le 07/04/2011 15:31, Peter Frederick Patel-Schneider a écrit :
>>>> Well, it is possible to derive contradictions in RDFS all by itself, so
>>>> the answer to your question is obvious.
>>>
>>>
>>> Then, let us consider RDFS without datatypes. In this case, it is not
>>> possible to derive contradictions. However, by adding owl:sameAs, it is
>>> possible to derive contradictions even in absence of datatypes.
>>>
>>> :x owl:sameAs "abc" .
>>> :x owl:sameAs "xyz" .
>>>
>>> or, even better:
>>>
>>> rdf:type owl:sameAs owl:sameAs .
>>>
>>>
>>> AZ.
>>
>> It would be interesting to see the derivation of inconsistency from the
>> last.
> 
> Sure:
> 
> An interpretation I that satisfies
> 
> rdf:type owl:sameAs owl:sameAs .
> 
> has a set LV that contains the plain literals. For all plain literal L 
> in LV, IEXT(rdf:type^I) must include (L,rdfs:Literal^I). So, in 
> particular, it must contain ("abc",rdfs:Literal^I) and 
> ("xyz",rdfs:Literal^I). Moreover, since I satisfies the triple above, 
> then rdf:type^I = owl:sameAs^I (by definition of the semantics of 
> owl;sameAs), so IEXT(rdf:type^I) = IEXT(owl:sameAs^I). So 
> ("abc",rdfs:Literal^I) and ("xyz",rdfs:Literal^I) both belongs to 
> IEXT(owl:sameAs^I). But again, by definition of the semantics of 
> owl:sameAs, this means that "abc" = rdfs:Literal^I = "xyz". Inconsistency!

Cute.

peter
Received on Thursday, 7 April 2011 20:10:36 GMT

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