# Re: RDF Semantics: use of functions IEXT / ICEXT

From: <herman.ter.horst@philips.com>
Date: Wed, 5 Mar 2003 08:01:20 +0100
To: pat hayes <phayes@ai.uwf.edu>

Message-ID: <OFECF4FD86.19C7B47B-ONC1256CDE.0035E31A-C1256CE0.0026BAFD@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
>>>>>
>>>>>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.
>
>No, this is only an assumption of the way I presented the argument in
>the email. Let me rephrase the argument in full without trying to
>shorten it:
>
>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.
The domain and range conditions as they are now formulated
implicitly assume that x is in IP and y is in IC,
and my request is to make this explicit in the text.
See below the earlier, more complete description of
this point.

Herman

>
>-Pat
>
>>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 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
>>
>>   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
>
>
>--
>---------------------------------------------------------------------
>IHMC  (850)434 8903 or (650)494 3973   home
>40 South Alcaniz St.                                            (850)202
4416   office
>Pensacola               (850)202 4440   fax
>FL 32501             (850)291 0667    cell
>phayes@ai.uwf.edu                         http://www.coginst.uwf.edu/~phayes
>s.pam@ai.uwf.edu   for spam
>
>
```
Received on Wednesday, 5 March 2003 02:03:19 GMT

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