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Re: RDF Semantics: use of functions IEXT / ICEXT

From: <herman.ter.horst@philips.com>
Date: Thu, 27 Feb 2003 15:18:25 +0100
To: pat hayes <phayes@ai.uwf.edu>
Cc: www-rdf-comments@w3.org
Message-ID: <OFFDD719E9.61852801-ON41256CDA.003C5014-C1256CDA.004EC133@diamond.philips.com>

>.....
>>  >>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

Pat, thank you for the explanation.
You now introduce in the proof an additional assumption.
What you prove is the following:
  If <x,y> is in IEXT(I(rdfs:range))
  AND IF x and y are in the range of the function IS
  then x is in IP and y is in IC.
However, this statement does not suffice:  the additional
assumption (AND IF ...) would need to be dropped.
However, I believe that it is not possible to prove that
  If <x,y> is in IEXT(I(rdfs:range))
  then x is in IP and y is in IC
(and similarly for rdfs:domain).

Therefore, my remark remains.
Let me recall in a slightly rephrased manner what I said in 
the first mail in this thread:

For each occurrence of IEXT(x) or ICEXT(x), it
should be clear that x is in the domain of the function
involved.  (For IEXT, this domain is the set IP. 
For ICEXT, the domain is the set IC, as you have now confirmed.)
For example, in Section 3.3 the semantic conditions on 
subClassOf and subPropertyOf take care of this explicitly.

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:

  If <x,y> is in IEXT(I(rdfs:range)) 
  [then x is in IP and y is in IC] and 
  [if, in addition,] <u,v> is in IEXT(x) then 
  v is in ICEXT(y)

  If <x,y> is in IEXT(I(rdfs:domain)) 
  [then x is in IP and y is in IC] and 
  [if, in addition,] <u,v> is in IEXT(x) then 
  u is in ICEXT(y)

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Herman
Received on Thursday, 27 February 2003 09:21:00 GMT

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