Re: comments on RDF MT

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


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