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Re: RDF Semantics: use of functions IEXT / ICEXT

From: pat hayes <phayes@ai.uwf.edu>
Date: Wed, 26 Feb 2003 15:23:29 -0600
Message-Id: <p05111b06ba82dfa0a063@[10.0.100.86]>
To: herman.ter.horst@philips.com
Cc: www-rdf-comments@w3.org

.....
>  >>The semantic conditions on rdfs:range and rdfs:domain in Section 3.3
>>>do not yet incorporate explicit domain assumptions as just
>>>discussed.  It seems that additions such as the following need
>>>therefore to be made:
>>
>>The additions suggested are not required, since they follow from the
>>axiomatic triples in the next table and the other conditions on range
>>and domain.
>>
>>It is probably easiest to express the reasoning in terms of triples
>>that must be satisfied by an interpretation I. For example, suppose
>><x,y> is in IEXT(I(rdfs:range)), ie that
>>
>>I |= (x) rdfs:range (y)
>
>I do not understand this step.  In these two lines x/y have a different
>origin.  In "<x,y> is in IEXT(I(rdfs:range))", x and y are in IR.
>In the triple "(x) rdfs:range (y)", x and y are uri's or blank nodes
>(y may also be a literal).  So this conclusion ("ie that")
>is not clear.

Sorry, I was using an unstated convention. Let me rephrase it more carefully.

Suppose <x,y> is in IEXT(I(rdfs:range)) and suppose that I(aaa)=x and 
I(bbb)=y. Then

I |= aaa rdfs:range bbb .

Now, since

I |= rdfs:range rdfs:domain rdf:Property .  (axiomatic triple)

it follows by the semantic conditions on rdfs:domain that

I |= aaa rdf:type rdf:Property .

and hence that I(aaa)=x is in IP.

Similarly for bbb, the axiomatic triple defining the range of 
rdfs:range, and IC.

Pat
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Received on Wednesday, 26 February 2003 16:23:33 GMT

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