Re: model theory for RDF/S

>From: Dan Connolly <connolly@w3.org>
>Subject: Re: model theory for RDF/S
>Date: Thu, 27 Sep 2001 10:40:57 -0500
>
>>  "Peter F. Patel-Schneider" wrote:
>>  [...]
>>  > Syntax:
>>  >
>>  > URI is the collection of URI names, i.e., some collection of strings
>>  >
>>  >   [NB:  This ignores all aspects of the structure of URIs.]
>>  >
>>  > L is the collection of literals, i.e., some collection of strings,
>>  > disjoint from URI
>>
>>  I think the mention of "string" here is a misnomer/red-herring, no?
>>
>>  i.e. take the string "http://example/". It's a URI, and
>>  you say URIs are disjoint from literals... hence it's not a literal.
>>
>>  But it's a perfectly legal property value in RDF:
>>
>>	<rdf:Description rdf:about="#something">
>>	  <dc:identifier>http://example/</dc:identifier>
>>	</rdf:Description>
>>
>>  I think if you just say URI and L are disjoint, denumerable
>>  sets, you've said what you need to say.
>
>Yes, that should mostly work, at least for the purposes of this
>discusssion.  I don't know if you even need to say denumerable.

True. It would be a normal assumption, though.

>
>>  > 3. if <f,g> is in E
>>  >    then I(E) = true
>>
>>  you mean I(<f,g>) rather than I(E), no?
>
>Correct.  I have this typo in several other places also.
>
>>  > Claim 1:
>>  >
>>  > A core RDF interpretation that is a model of a basic untidy RDF graph R
>>  > contains everything (and more) that is in the intended core RDF (i.e., RDF
>>  > without reification or containers) meaning of R.  In other words, a model
>>  > contains all the information implicitly (or explicity) in the graph, and
>>  > maybe more, and contradicts nothing that is implicitly (or explicitly) in
>>  > the graph.
>>
>>  Hmm... at this point, the formality fails me. I would need
>>  an example to provide intiutions about whether I believe this
>>  or not.
>
>Think of this as a very informal way of stating that we need only consider
>the models of a graph, not the graph itself, to get all the results we
>want, whatever they are.  For example, we would say that one graph implies
>another precisely when all the models of the second graph are also models
>of the first.

That is the *definition* of 'implies' (well, entails, to be strict), 
so there doesn't seem to be much to prove :-)

>We would also say that the results of a query operation can be
>determined by looking only at the models of a graph.

I think this way of talking about 'looking at' the models is 
potentially misleading, since it suggests some kind of computational 
process on the models rather than the graphs.

>
>>  > Claim 2:
>>  >
>>  > A core RDF interpretation that is not a model of a basic untidy 
>>RDF graph R
>>  > has something that is not compatible the intended core RDF meaning of R.
>>  > In other words, a non-model is missing or incorrect on something that is
>>  > implicitly (or explicitly) in the graph.
>>
>>  That makes sense relative to claim 1 (though I don't have
>>  a good feel for claim 1 itself).
>>
>>  > Claim 3:
>>  >
>>  > For every basic untidy RDF graph R there is a core RDF interpretation that
>>  > captures exactly the closure of the intended core RDF meaning of 
>>R and that
>  > > is a model for R.  That is, roughly, that there is a model that makes
>  > > everything implicitly (or explicitly) in the graph true, and everything
>  > > else false.
>  >
>  > I have no idea what the significance of this claim is, let
>>  alone any sense of whether I agree or disagree with it.
>
>This claim roughly says that there is a ``canonical'' model.  That is you
>don't need to worry about the fact that there are multiple models for a
>graph, you can just work with this canonical model.

There is a canonical model (its the one that is constructed in the 
proof of the strong Herbrand lemma; its universe is the graph 
vocabulary plus the bNodes, and the extensions are just enough to 
make all the triples in the graph true, and that's all.) However, its 
not quite right to say that you don't need to consider any other 
models, since you may need to check entailment of a graph with some 
new anonymous nodes in it. Still, its clear from the interpolation 
lemma that you don't need to look very far beyond that model.

Pat


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Received on Thursday, 27 September 2001 21:05:39 UTC