# Re: Maximum cardinality of an RDF model

From: pat hayes <phayes@ai.uwf.edu>
Date: Mon, 5 Feb 2001 23:30:56 -0600
Message-Id: <v04210125b6a53a914746@[205.160.76.246]>
To: Dan Connolly <connolly@w3.org>

```>pat hayes wrote:
>[...]
> > >4. RDF models can contain at most countably many statements:
> > >   becauce they're subsets of,
>[...]
> >
> > Yes, you are right to infer that. However, your question raises
> > another, related, issue: according to several members of the group
> > which developed RDF, the 'graph model' of a set of RDF triplets is
> > intended itself to be *the* model (in the sense from model theory) of
> > those triplets.
>
>Really? can you cite a source for that? I'd like to correct it.
>
>The use of the term "model" in the RDF spec has
>nothing to do with model theory, as far as I know.
>
>I think it was you, Pat, that explained that
>what the RDF specs call a model is usually called
>an abstract syntax in logic literature.

Yes, I did, and when I had done so I got a phone call from Guha and
an email from Ora (as I recall from memory: sorry if I am making the
wrong attribution here) telling me why I was wrong, and that the
right way to think about it was as I described above, ie that the
graph model is, indeed, a model in the sense of model theory. It
seemed kind of crazy to me also, but I wasnt there when this was
decided, so I took it as authoritative (and gave up trying to make a
model theory for RDF, since it already had one: a damn silly one, but
then....)

> > It follows that all RDF models of any RDF ontology
> > (that could be stored on any web page, at any rate) must be not only
> > countable, but finite. Now, since the finite-model restriction is not
> > expressible in first-order (or any complete semi-decideable) logic,
> > this would appear to indicate that RDF must have a semantics which
> > has no semidecision procedure (and hence no proof procedure.)
>
>I'm just sort of teaching myself all this model theory stuff
>as I go, but as far as I understand it, the semantics
>of RDF are just like the semantics of first-order logic,
>where the only terms are URIs (constant symbols) and
>existentially quantified variables, and the only formulas are
>ground propositions, conjuctions, and existentially quantified
>formulas.
>
>At least, that's one logic, and it's sort of implicitly
>in the RDF 1.0 spec.

Yes, that is what I would have guessed from the spec; it is kind of
what it suggests. I was trying to do was put reification into the
model theory as well, which is trickier. Maybe I should get back to

>Things get more interesting when you start using the
>RDF model/abstract-syntax with extensions to that
>logic with stuff like =, not, KIF's wtr, lambda, etc.

Er, yes, they would. Rather in the way that a pavement gets more
interesting when the St Patricks Day parade walks on it.

Pat

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Received on Tuesday, 6 February 2001 00:28:04 UTC

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