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RE: interpretation of instance and subclass

From: David Menendez <zednenem@psualum.com>
Date: Fri, 14 May 2004 01:33:10 -0400
To: "Burkett, Bill" <WBurkett@modulant.com>
Cc: Benja Fallenstein <b.fallenstein@gmx.de>, www-rdf-interest@w3.org
Message-id: <r02000200-1033-3011EFC6A56811D8AC0B000393758032@[]>

Burkett, Bill writes:

> "(-" = "member of"
> "<" = "subclass of"
> Using my example again: 
>   m (- M
>   M (- C
>   M  < C
> The problem I have is an apparent contradiction in the latter two
> statements with respect to m. As a member of C, members of M are
> *not* also members of C.  As a subclass of C, members of M *are* also
> members of C.  Is this where we find the Incompleteness of our
> rdf/rdfs representational langauge?  Is this an inherent
> paradox/contradiction that we just have to live with?

The problem is the assumption that instances of M cannot be instances of
C. In RDF, a class is an entity associated with a set of instances, not
the set of instances itself.

Consider this:

    ex:Species rdf:type rdfs:Class.
    ex:Species rdfs:subClassOf rdfs:Class.
    ex:Orangutan rdf:type ex:Species.
    ex:koko rdf:type ex:Orangutan.

If we write the extension of the class C as IEXT(C), we have:

IEXT(rdfs:Resource) = { rdfs:Resource, rdfs:Class, ex:Species,
                        ex:Orangutan, ex:koko, ... }
IEXT(rdfs:Class)    = { rdfs:Resource, rdfs:Class, ex:Species,
                        ex:Orangutan, ... }
IEXT(ex:Species)    = { ex:Orangutan }
IEXT(ex:Orangutan)  = { ex:koko }
David Menendez <zednenem@psualum.com> <http://www.eyrie.org/~zednenem/>
Received on Friday, 14 May 2004 01:37:17 GMT

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