RE: Set Theory (NBG)

> 
> 
> I am puzzled by RDF's treatment of containers.  It seems to me that
> RDF provides a way to talk about collections of objects without
> requiring that collections have the semantics one normally attaches to
> them.  The standard practice in mathematics is to use set theory for
> that purpose, so why not restrict the models of RDF statements to
> those consistent with set theory?  One could do this by allowing
> reasoning systems to assume the axioms of set theory.
> Von-Neumann-Bernays-Godel (NBG) set theory is well suited for this
> purpose.  You can read more about NBG and mechanized mathematics in
> W. M. Farmer, "STMM: A Set Theory for Mechanized Mathematics", Journal
> of Automated Reasoning, 2000, Vol 26, No. 3, pp. 269-289,
> http://imps.mcmaster.ca/doc/stmm.pdf.
> 

RDF, as far as I can make out from the W3C spec, relates solely to what
may be termed "enumerated sets" -- that is, (apparently finite) sets
whose members are explicitly listed, as in something like:

<rdf:Bag>
	<rdf:li resource="http://mycollege.edu/students/Amy"/>
	<rdf:li resource="http://mycollege.edu/students/Tim"/>
	<rdf:li resource="http://mycollege.edu/students/John"/>
	<rdf:li resource="http://mycollege.edu/students/Mary"/>
	<rdf:li resource="http://mycollege.edu/students/Sue"/>
 </rdf:Bag>


This is an extremely weak "set theory", if one can call it that, which
hardly seems to require the full semantic power of NBG axiomatic set
theory -- the difficulties that systems such as NBG and ZFC set out to
struggle with only rear their heads once one enters the realm of
infinities, transitive sets, well-founded sets, sets whose members are
sets, and all those other subjects fondly remembered from axiomatic set
theory lectures.

Cheers,

Ziv