# Re: Maximum cardinality of an RDF model

From: Dan Connolly <connolly@w3.org>
Date: Fri, 02 Feb 2001 15:30:47 -0600
Message-ID: <3A7B2707.E5793CFD@w3.org>
To: pat hayes <phayes@ai.uwf.edu>
CC: Miles Sabin <MSabin@interx.com>, www-rdf-logic@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.

> 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.

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.

--
Dan Connolly, W3C http://www.w3.org/People/Connolly/
```
Received on Friday, 2 February 2001 16:31:05 UTC

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