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Re: RDF Semantics: use of functions IEXT / ICEXT

From: pat hayes <phayes@ai.uwf.edu>
Date: Wed, 5 Mar 2003 09:26:15 -0500
Message-Id: <p05111b0bba8bb55ab670@[64.134.139.17]>
To: herman.ter.horst@philips.com
Cc: www-rdf-comments@w3.org

>  >
>>First, the truth of the axiomatic triple
>>
>>rdfs:range rdfs:domain rdf:Property .
>>
>>and the semantic conditions on rdfs:domain together require that
>>
>><x,y> inIEXT(I(rdfs:range)) implies x in ICEXT(I(rdf:Property))
>>
>>which in turn, by applying the condition (definition if you like :)
>>
>>IP= ICEXT(I(rdf:Property))
>>
>>means that
>>
>><x,y> in IEXT(I(rdfs:range)) implies x in IP
>>
>>Similarly y is in IC, using a different axiomatic triple.
>>
>>Is this more convincing?
>
>No: you use in this reasoning the conditions which
>I claimed are not complete in their statement.

I do not think that I do use them. I will present the argument in more detail.

1.    I |= rdfs:range rdfs:domain rdf:Property .         [axiomatic triple]
2.    <I(rdfs:range), I(rdf:Property)> in IEXT(I(rdfs:domain)) 
[1., basic RDF truthconditions]
3.   <x,y> in I(rdfs:range)  implies  x in ICEXT(I(rdf:Property)) 
[2., semantic conditions on rdfs:domain]
4.  <x,y> in I(rdfs:range)  implies x in IP  [3., definition of IP]

Note, step 3 does not depend on x being in any particular class; it 
simply uses the semantic conditions in the form they have in the 
document. None of this derivation implicitly assumes anything other 
than what is stated, and it has as a conclusion the 'assumption' that 
x is in IP. An exactly similar derivation (replace rdfs:domain by 
rdfs:range, rdf:Property by rdfs:Class and IP by IC) shows that y is 
in IC. So these assumptions are derivable, so are not needed.

>The domain and range conditions as they are now formulated
>implicitly assume that x is in IP and y is in IC,

If you still maintain that these assumptions are used implicitly, 
please give details of where the above derivation fails.

Best wishes

Pat


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Received on Wednesday, 5 March 2003 09:26:20 GMT

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