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Re: Settheoretical interpretation of the RDF-schema possible?

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Tue, 05 Jun 2001 12:17:42 -0400
To: kruggel@kbs.uni-hannover.de
Cc: www-rdf-interest@w3.org
Message-Id: <20010605121742Z.pfps@research.bell-labs.com>
From: Christian Kruggel <kruggel@kbs.uni-hannover.de>
Subject: Re: Settheoretical interpretation of the RDF-schema possible? 
Date: Tue, 05 Jun 2001 16:29:24 +0200

> Hi!
> I['m] try[ing] to figure out w[h]ether a settheoretical interpretation of the
> RDF-schema is possible or not. I refer to both schema specifications
> from 3. March 1999 and from 27. March 2000 as well. They show rdfs:Class
> to be subClassOf rdfs:Resource and an instance (type) of itself.

It would be possible to interpret instance in a non-standard set theory.
It is also possible to interpreset instance as just a relationship between
objects in the model, not as set membership.  But, yes, you can't have an
set being a member of itself in standard set theory.

> This raises the question if then rdfs:Resource is also an instance of
> itself for the property of being instance of oneself is a property of a
> class and such properties are inherited along the subClassOf-relation.
> If there was just one class that's an instance of itself this would be
> no surprise. All objectoriented programminglanguages have to define such
> a class. But it would be useless and confusing if the RDF-schema
> specifies at least two classes to be instances of themselves.
> At the moment I think that the RDF-schema enforces the equalization of
> instances and classes for any subClassOf rdfs:Resource inherits the
> propery of being instance of itself. Am I doing wrong?
> Christian

I don't think that subclasses of resource are necessarily instances of
themselves, as this is not something that is generally inheritable.  Of
course, the RDFS specification is not written in a clear-enough manner to
provide definitive answers to questions like this.

Peter F. Patel-Schneider
Received on Tuesday, 5 June 2001 12:18:38 UTC

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