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Re: [ontolog-forum] Next steps in using ontologies as standards

To: "'[ontolog-forum] '" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: Matthew West <dr.matthew.west@xxxxxxxxx>
Date: Wed, 21 Jan 2009 22:48:23 -0000
Message-id: <4977a64c.04c2f10a.7b42.6321@xxxxxxxxxxxxx>
Dear Pat and Chris,    (01)

> > Is there somewhere we can find more details on this 'basic advance'?
> It was the development of non-well-founded set theory, written up in a
> Stanford CSLI monograph by Peter Aczel. There are articles on it on
> Wikipedia and other places, for a full account see
> http://plato.stanford.edu/entries/nonwellfounded-set-theory/
> . The key point is that set theories which do not use, and even which
> explicitly deny, the axiom of foundation, are not only possible, but
> can be proven to be relatively consistent with ZFC. So they are just
> as 'good' as a foundation as anything else. So, there is absolutely no
> reason to prohibit self-containing sets such as rdfs:Class. If you
> look at classical FOL in this light, you quickly end up with Common
> Logic.    (02)

[MW] As some of you (and Chris in particular) know, this is the approach we
took in ISO 15926. When just considering the names it sounds counter
intuitive, but well founded sets are of course a subset of non-well-founded
> Although they could have done, the RDF and CL model theories do not
> explicitly use Aczel's set theory, essentially for pedagogical
> reasons: to ask someone to swallow a new set theory     (03)

[MW] I can confirm from the abuse I have received from some quarters that
this is indeed true. However, it provides what I find to be the most elegant
solution, and it is not as if anyone has to give up well-founded sets, they
are still there.    (04)

Regards    (05)

Matthew West
http://www.matthew-west.org.uk/     (06)

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