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Re: update to MT document

From: Graham Klyne <Graham.Klyne@MIMEsweeper.com>
Date: Tue, 29 Jan 2002 09:43:07 +0000
Message-Id: <>
To: Pat Hayes <phayes@ai.uwf.edu>
Cc: w3c-rdfcore-wg@w3.org
At 06:18 PM 1/28/02 -0600, Pat Hayes wrote:

>>Section 2:  Chewing over separability and strong Herbrand lemma...
>OK, I have added a brief explanation of separability and put this 
>definition more where it belongs, nearer the front of the section. I hope 
>this makes things clearer.
>If I were doing this in a more 'mathematical' way, I would start by 
>constructing Herbrand interpretations and defining  minimality, then prove 
>the interpolation lemma directly and then derive everything else from it. 
>But I think that wouldn't be so useful to a non-math readership. Even 
>though some of these lemmas follow from others, proving most of the 
>directly from first principles gives a better feel for how to use MT in 
>analysing inferences, i think. (?)

Yes... I think it's helpful to build some intuitive feel for what's going 
before leaping off into pure mathematical structures

>>I think I'm satisfied that it might work, but I'm not happy with the 
>>explanation.  If an interpretation assigns false to any ground triple not 
>>in E, then what triple will have the value TRUE so that E (above) is satisfied?
>The point is that there could still be something in a universe that you 
>could map _:x to and have that triple come out true, even though there was 
>no uriref that denoted that thing. There can be things in the universe 
>that don't have a uriref referring to them, right? All the triple says is 
>that *something* exists (whose bbb is ccc), but that something might not 
>have a name in the form of a uriref.


>>It's not clear to me in the Herbrand lemma construction of I, what value 
>>is assigned to IEXT(bbb) corresponding to the triple in graph E.  I 
>>suppose it is
>>     <node(_:x),ccc>
>>where node(_:x) is the blank graph node corresponding to _:x in the 
>>triples above.
>Right. The blank nodes are themselves considered to be things in the 
>universe. The A mapping where they denote themselves (identity map) then 
>has [I+A] satisfying all the triple with blank nodes in them, so....
>>In this case, assigning false to the ground triple:
>??? That isn't a ground triple.
>>     node(_:x) bbb ccc .
>>would also cause graph E to be false under that [I+A]

... I was confusing triples with denotations.  Still.  :-(

Getting that straight, the rest is fine.


>>Section 6:
>>rdfs2, rdfs4a, rdfs6, rdfs7, rdfs8, rdfs9: do you mean to allow literals 
>>in the subject positions here?
>No. Well, it depends what you mean to 'allow'. I don't exclude them 
>because there is no need to, since they can never occur in those positions 
>in the LHS of those rules. The rdfs3 and 4b cases need to be restricted 
>since a literal could legally appear there in the LHS patterns but would 
>produce a syntactically illegal triple on the RHS.
>Should I put a sentence of explanation?

Probably not ... just checking that was what you meant.  If I weren't in 
"reviewer mode" it wouldn't have caused me to pause.


Graham Klyne                    MIMEsweeper Group
Strategic Research              <http://www.mimesweeper.com>
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Received on Tuesday, 29 January 2002 05:07:54 UTC

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