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RE: Maximum cardinality of an RDF model

From: Miles Sabin <MSabin@interx.com>
Date: Sat, 3 Feb 2001 00:01:38 -0000
Message-ID: <23CF4BF2C499D411907E00508BDC95E116FBD4@ntmews_01.interx.com>
To: Dan Connolly <connolly@w3.org>
Cc: www-rdf-logic@w3.org
Dan Connolly wrote,
> Miles Sabin wrote,
> > * 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?

From rdfms 2.1 Basic RDF Model,

  The basic data model consists of three object types:

  Resources

  All things being described by RDF expressions are called 
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  resources. A resource may be an entire Web page; such as the 
  ^^^^^^^^^
  HTML document "http://www.w3.org/Overview.html" for example. A 
  resource may be a part of a Web page; e.g. a specific HTML or 
  XML element within the document source. A resource may also be 
  a whole collection of pages; e.g. an entire Web site. A 
  resource may also be an object that is not directly accessible 
  via the Web; e.g. a printed book. Resources are always named by 
                                    ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  URIs plus optional anchor ids (see [URI]). Anything can have a 
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  URI; the extensibility of URIs allows the introduction of 
  identifiers for any entity imaginable. 

If I wanted to be picky, I'd have to observe that the last
sentence is clearly false because there aren't enought URI(-refs) 
to name all the reals, or all the points on a line.

> Consider:
>
> <rdf:Description>
>   <foaf:workEmailAddress resource="mailto:connolly@w3.org"/>
> </rdf:Descrption>
>
> aka
>  (exists (?x) (foaf:workEmailAddress ?x mailto:connolly@w3.org))
>
> ?x is me, right? i.e. the quantifiers might range over anything
> you like.

Oh, sure, but you've introduced new vocabulary which goes beyond
core RDF. An analogy ... the intended model of first-order
arithmetic has a countable domain; intended models of first-order
arithmetic+set theory are quite a bit bigger.

> I think I could construct descriptions of transcendental numbers 
> similarly.

Agreed, you could quantify over all the points on a line. But,
again you'd need extra vocabulary.

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

Careful here. It leaves open the cardinality of the domain of
discource of RDF+X (fill in with your favourite 'X'). But the
domain of bare RDF is at most uncountably infinite (thanks to the
clause from 2.1 quoted above) and at least uncountably infinite
(thanks to rdf:_1, rdf:_2, ...).

> > _A_Structuralist_Theory_of_Logic_, Arnold Koslow,
> > Cambridge University Press, 1992
>
> er... ouch! $95.00 at amazon. Is there anything online that 
> explains it?

Not that I can find. Don't you have access to a decent academic
library? Failing that I could have a stab at a sketch, but I
doubt that I'd do it any kind of justice, and it'd take a _very_
long mail.

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 19:02:19 GMT

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