Re: Question about IS

>OK, I made it through (most of) the MT and one question especially
>lingers in my mind (along with a faint buzzing and some dark
>subtle whisperings... but that's probably not the MT's fault ;-)
>
>The question is about the mapping IS. As it has been pointed
>out, the MT (apparently) allows for there to actually be multiple,
>disjunct members of the vocabulary V (i.e. URIs) which map via IS to
>the very same resource node. Or have I missed something right off
>the bat?

One thing, yes. They don't map to a node. The nodes are part of the 
syntax. (In the example in figure 1, the node labels would be 'a', 
'b' and 'c'). IS maps from nodes (well, strictly, node labels) to 
resources, eg thing1 and thing2 .

>In your example 1.4 of 'Thing 1' and 'Thing 2' (which as you
>will recall tend to make quite a mess of things when one's
>mother is out ;-)  you define two graph nodes '1' and '2'

No, those are denotations of graph nodes.

Ah, I see that the figure may be misleading in a way that I hadn't 
thought of, since it looks like a graph.  I will try to explain this 
better in the next draft.

>and you map the labels (presumably equating to URIs) 'a'
>and 'b' both to node '1'.

To a single resource (not a single node, though: the graph syntax 
would require that 'a'  and 'b' be labels on different nodes, as you 
noted.)

An interpretation isn't itself an RDF graph; it is an interpretation 
OF a graph. The graph is the syntax. If you prefer, think of the 
interpretation as attached directly to an N-triples document, and 
just forget about the RDF graph. (We did it that way once, but to be 
precise you have to talk about quantifiers for bNode expressions, and 
the graph syntax seemed simpler.)

Does this make it clearer?

>......
>Just how do we end up with what is essentially a single
>node with two labels, 'a' and 'b'?

We don't. The IS mapping is not the node labelling.

>Or do we have two levels of representation here, where 'a',
>'b', and 'c' are the labeled nodes in the graph and '1' and
>'2' are "something else"

Yes, exactly; though its not really appropriate to describe an 
interpretation as a 'representation' in quite the same sense. Its 
better described as a possible world. Given that the representation 
(the RDF graph) is true, this is one way the world might be. Of 
course, there are many other ways the world could be, also, maybe 
infinitely many of them.

>(e.g. nodes at a higher level of
>abstraction)

Not *nodes*, necessarily, just things in some set (IR). Could be a 
set of anything.

If you are left with an unsatisfactory feeling that might be phrased: 
but what IS an interpretation, then, exactly?? Seems like it could be 
almost anything ?!!? The answer is, Yes, exactly: that is the point. 
The idea is not really to define a class of things called 
'interpretations' (like 'graphs' or 'Stone algebras' or whatever) so 
much as to give *minimal* conditions on what the world has to be 
like, in order to make an RDF graph true or false in it. The fact 
that these conditions make very few demands on what exactly a 'world' 
is, actually makes the overall theory more general-purpose as a 
theory of RDF meaning. So when the MT says 'an interpretation is...'. 
you can rephase this as 'in order to fix the truthvalues of an RDF 
graph, something has to at least provide the following, at a 
minimum....' What IS that 'something', exactly? I don't care. Talking 
in set-theory language is a mathematical way of saying, I don't care.

>Or have I just totally misunderstood the whole enchilada?

Perhaps slightly ;-).

Thanks for the feedback, I will try to rewrite the explanation to 
guard against this possible misunderstanding.

Pat

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Received on Friday, 5 October 2001 15:30:10 UTC