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

From: Antoine Zimmermann <antoine.zimmermann@gmail.com>
Date: Thu, 07 Apr 2011 21:53:05 +0200
Message-ID: <4D9E1621.8090005@insa-lyon.fr>
CC: public-rdf-wg@w3.org
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!

>
> peter
Received on Thursday, 7 April 2011 19:53:37 GMT

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