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Re: singleton sets

From: Richard H. McCullough <rhm@pioneerca.com>
Date: Wed, 13 Aug 2008 22:33:24 -0700
Message-ID: <18B864EC65D542A4B360817B362D96AC@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>, "KR-language" <KR-language@YahooGroups.com>

Eureka!!!

Question: If an individual is an "atomic" unit, and can't have subClasses,
what class can't have subClasses?
Answer: singleton-set class (and empty-set class)

So it is only a singleton-set class that might be considered to be an 
individual.
And the Barwise, Etchemendy textbook IS advising against the
class-individual.

As I have said previously, I view it as an individual, not a class.
Also, I view anything with subClasses as a class, not an individual.

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;
http://mKRmKE.org/

----- Original Message ----- 
From: "Richard H. McCullough" <rhm@pioneerca.com>
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>
Sent: Wednesday, August 13, 2008 8:31 PM
Subject: Re: singleton sets


> 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;
> http://mKRmKE.org/
>
> ----- 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
>
>  <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
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>
> 
Received on Thursday, 14 August 2008 05:36:01 GMT

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