From: <herman.ter.horst@philips.com>

Date: Wed, 5 Mar 2003 08:01:20 +0100

To: pat hayes <phayes@ai.uwf.edu>

Cc: www-rdf-comments@w3.org

Message-ID: <OFECF4FD86.19C7B47B-ONC1256CDE.0035E31A-C1256CE0.0026BAFD@diamond.philips.com>

Date: Wed, 5 Mar 2003 08:01:20 +0100

To: pat hayes <phayes@ai.uwf.edu>

Cc: www-rdf-comments@w3.org

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 >>>>>>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. > >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 >>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) >> >>>-- >>>--------------------------------------------------------------------- >>>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 >>> >>> >> >>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 UTC

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