RE: singleton sets

Richard H. McCullough wrote:

>I think nested lists are more common that nested sets.
>Both can be useful in complex data structures.

Ok, and these "nested sets" are just what Pat and others were referring to when they were talking about

  "classes which are individuals"

In RDFS, you can build "nested classes", where a class X is an instance of another class Y:

  // X used as a subclass of another class --> X is a class
  X rdfs:subClassOf rdfs:Resource 

  // X used as an instance of another class --> X is an individual
  X rdf:type Y                    

That's essentially your "2." point in your original mail

  <http://lists.w3.org/Archives/Public/semantic-web/2008Aug/0031.html>

You asked there what one can do with this "neat property". Now, you gave the answer yourself: You can build "nested classes", where, for example, Y is the singleton class of X. Actually, you cannot define such a singleton class in RDFS, but it's possible in OWL Full, which is an extension of RDFS.

So, it looks to me that you and Pat have talked about different things all the time. "Classes being individuals" has nothing to do with "singletons being equal to their contained instance" (yes, this would be nonsense in most situations). It's just about that "classes can themselves be instances of *other* classes", i.e. you can build "nested classes".

Cheers,
Michael

--
Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
Tel  : +49-721-9654-726
Fax  : +49-721-9654-727
Email: Michael.Schneider@fzi.de
Web  : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555

FZI Forschungszentrum Informatik an der Universität Karlsruhe
Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe
Tel.: +49-721-9654-0, Fax: +49-721-9654-959
Stiftung des bürgerlichen Rechts
Az: 14-0563.1 Regierungspräsidium Karlsruhe
Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi Studer
Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus