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RE: Maximum cardinality of an RDF model

From: Miles Sabin <MSabin@interx.com>
Date: Fri, 2 Feb 2001 22:09:06 -0000
Message-ID: <23CF4BF2C499D411907E00508BDC95E116FBD3@ntmews_01.interx.com>
To: www-rdf-logic@w3.org
Cc: connolly@w3.org
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? 

> 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).

* 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, 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.

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

_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

-- 
Miles Sabin                               InterX
Internet Systems Architect                5/6 Glenthorne Mews
+44 (0)20 8817 4030                       London, W6 0LJ, England
msabin@interx.com                         http://www.interx.com/
Received on Friday, 2 February 2001 17:09:47 GMT

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