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RE: singleton sets

From: Michael Schneider <schneid@fzi.de>
Date: Wed, 13 Aug 2008 11:38:58 +0200
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0AD977C@judith.fzi.de>
To: "Richard H. McCullough" <rhm@pioneerca.com>
Cc: "Semantic Web at W3C" <semantic-web@w3.org>, "Adam Pease" <adampease@earthlink.net>, "Pat Hayes" <phayes@ihmc.us>
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


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".


Dipl.-Inform. Michael Schneider
FZI Forschungszentrum Informatik Karlsruhe
Abtl. Information Process Engineering (IPE)
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Received on Wednesday, 13 August 2008 09:39:40 UTC

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