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Re: Maximum cardinality of an RDF model

From: Dan Connolly <connolly@w3.org>
Date: Fri, 02 Feb 2001 17:26:22 -0600
Message-ID: <3A7B421E.CCCD9C5A@w3.org>
To: Miles Sabin <MSabin@interx.com>
CC: www-rdf-logic@w3.org
Miles Sabin wrote:
> Dan Connolly wrote,
> > pat hayes wrote:
> > > 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.
> Correct what? That the intended model is the graph/triplet model;
> or any implication that there's a model (in the model-theoretic
> sense) at all?

That there's a model-theoretic model in the RDF spec at all.

> > 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.
> That seems more or less right to me, with the following two
> qualifications,
> * There are no conjunctions in the way there are in typical
>   languages (tho', to be sure, you can get something like the
>   effect of asserting P&Q by asserting P and asserting Q).

well... ok...

> * Even if there's no explicit formal model, there's a fairly
>   clear indication in RDF M&S that the quantifiers range over
>   resources, ie. things which have a URI,

Huh? which part of the spec suggests that every resource
has a URI? Consider:

	  <foaf:workEmailAddress resource="mailto:connolly@w3.org"/>

	(exists (?x) (foaf:workEmailAddress ?x mailto:connolly@w3.org))

?x is me, right? i.e. the quantifiers might range over anything
you like.

I think I could construct descriptions of transcendental
numbers similarly.

I think the RDF spec leaves open the size (cardinality)
of the domain of discourse.

>   hence that the domain
>   of quantification is at most countably infinite ... because
>   there at most countably many URIs and no two distinct resources
>   can share a URI.

That would follow, but I don't accept the premise.

> BTW, if you're looking around for an interesting logical
> framework to embed RDF M&S, I'd recommend,
>   _A_Structuralist_Theory_of_Logic_, Arnold Koslow,
>   Cambridge University Press, 1992

er... ouch! $95.00 at amazon. Is there anything
online that explains it?

> _extremely_ highly. The salient point is that he manages to
> crank a variety of first order logics (both classical and non-
> classical) and a framework for building modal logics, out of
> resources which aren't all that different from what RDF M&S has
> to offer (I can elaborate on this if anyone's interested ... with
> the caveat that I'm an ex-philosopher, not a logician).
> Cheers,
> Miles

Dan Connolly, W3C http://www.w3.org/People/Connolly/
Received on Friday, 2 February 2001 18:26:25 UTC

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