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

Date: Mon, 11 Nov 2002 22:50:43 -0600

Message-Id: <p05111b17b9f4f679a2bd@[10.0.100.86]>

To: herman.ter.horst@philips.com

Cc: www-rdf-comments@w3.org

Date: Mon, 11 Nov 2002 22:50:43 -0600

Message-Id: <p05111b17b9f4f679a2bd@[10.0.100.86]>

To: herman.ter.horst@philips.com

Cc: www-rdf-comments@w3.org

Herman, greetings. Responses below. > >- RDF closure lemma: since the definition of the set IP has been >changed (it is now part of the definition of a simple interpretation), >the last part of the proof of this lemma does not apply anymore: >the set IEXT(I(aaa)) can no longer be assumed to be nonempty. >(I fully support the change of the definition of IP, and considered >the old version of this definition to be a "weak spot" in the document.) Right. In fact, the changes to the semantic conditions for subclass and subproperty mean that the entire 'strategy' of the old proofs is no longer tenable; the closure lemmas as stated are no longer true. I have therefore gone back to a more traditional approach based directly on Herbrand's theorem, which makes the proofs somewhat more elegant in any case. >- There seems to be a problem with the proof of the second anonymity lemma. >Consider the sentence "Since E is lean, it contains no other triples >of the form S1 P1 O' or S2 P2 O'." This is true, when O' is assumed >to be a name. However, E may contain two other triples S1 P1 _:x3 >and S2 P2 _:x3. In this case, the last part of the proof does not >apply. Indeed. The problem here was the definition of 'lean', which had a mistaken restriction to *proper* instances. It now reads: a graph is lean if none of its triples is an instance of any other triple. The proof now applies as written. With the old definition of 'lean' the lemma was false, so it wasnt just an error in the *proof*. I have incorporated many of your other suggestions. Thanks again. Pat > >Herman ter Horst >Philips Research > >[1] http://www.coginst.uwf.edu/~phayes/RDF%20Model%20Theory_Oct_draft.html -- --------------------------------------------------------------------- IHMC (850)434 8903 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 spamReceived on Monday, 11 November 2002 23:50:14 UTC

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