Re: update to MT document

>At 12:23 PM 1/28/02 -0600, Pat Hayes wrote:
>>An updated version of the MT document can be found at
>>
>>http://www.coginst.uwf.edu/users/phayes/w3-rdf-mt-draft-J.html
>
>Overall, I think this is looking very good.  I have some minor nits 
>and queries, but nothing that needs to delay publication, I think.
>
>Section 0.3:  Definition of instance, implies that:
>
>    :a :b :c .                   [1]
>
>is an instance of
>
>    _:x :b :c .                  [2]
>    _:y :d :e .
>
>Is this really what you meant?

Ouch, no it isn't.
Fixed.

>I think not:  it fails the instance lemma.  Suppose
>   <I(:a),I(:c)> in IEXT(I(:b)), but
>   NOT( <x,I(:e)> in IEXT(I(:d)) ) for all x.
>Then [1] does not entail [2].
>
>
>Section 1.6, final paragraph:  typo?

Fixed.

>
>Section 2, para starting "Any process ...":
>
>"S always entails E" took a couple of passes to unravel.  At first 
>glance, the "always" here is redundant ("S entails E" is defined 
>over all interpretations).  I think something like "... S entails E 
>for any application of the process, ..." would have been easier to 
>follow.

OK, fixed. I just deleted the 'always'.

>
>
>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. (?)

>Graph E:   _:x bbb ccc .
>
>Graph E':  aaa bbb ccc .
>
>E' is separable from E, but E is not separable from E'.  Right?

Right. Intuitively if you make E' true then E is forced to be (E not 
separable from E'), but not reverse.  This is now stated more 
explicitly.

>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]

Under that A it would, but then there would be a different A' with 
[I+A'] satisfying E. But in any case, the Herbrand lemma only 
establishes that *a* satisfying interpretation exists, and the 
construction of the Herbrand interpretation assigns true to that 
triple (if it occurs in the graph). So in your example, the Herbrand 
interpretation of E would look like this:

IR={ node(_:x), bbb, ccc}
IEXT(bbb)={<node(_:x), ccc>}, IEXT(node(_:x))=IEXT(ccc)={ }

Which satisfies E but makes E' false, since it doesn't assign any 
meaning to aaa.

>
>[mumble.  I think I'm losing the plot here.  It's getting late.]
>
>
>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?

Pat

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Received on Monday, 28 January 2002 19:18:25 UTC