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Re: singleton sets

From: Richard H. McCullough <rhm@pioneerca.com>
Date: Wed, 13 Aug 2008 20:31:25 -0700
Message-ID: <7022784C63974C05B7FA1657BFA80C9C@rhm8200>
To: "Michael Schneider" <schneid@fzi.de>
Cc: "Semantic Web at W3C" <semantic-web@w3.org>, "Adam Pease" <adampease@earthlink.net>, "Pat Hayes" <phayes@ihmc.us>

Hi again Michael

I disagree with your reasoning here.
An individual is an "atomic" unit -- it can't have subClasses.

So if you're talking "nested classes", there can't be any
individuals in the middle of the nesting chain.
All the individuals have to be at the end of the nesting chain.

Dick McCullough
Ayn Rand do speak od mKR done;
mKE do enhance od Real Intelligence done;
knowledge := man do identify od existent done;
knowledge haspart proposition list;

----- Original Message ----- 
From: "Michael Schneider" <schneid@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>
Sent: Wednesday, August 13, 2008 2:38 AM
Subject: 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


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)
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
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Received on Thursday, 14 August 2008 03:34:19 UTC

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