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Re: An Axiomatic Semantics for RDF, RDF Schema, and DAML-ONT

From: Richard Fikes <fikes@KSL.Stanford.EDU>
Date: Wed, 29 Nov 2000 13:55:37 -0800
Message-ID: <3A257B59.4D73AC2D@ksl.stanford.edu>
To: Dan Connolly <connolly@w3.org>
CC: guha@guha.com, Ora Lassila <daml@lassila.org>, www-rdf-logic@w3.org
> That's good, since you can deduce that they're disjoint
> from this semantics
> 
> DAML-ONT Axioms
> http://www.ksl.stanford.edu/people/dlm/DAML-Ont-kif-axioms-001127.html
> Tue, 28 Nov 2000 05:16:36 GMT
> 
> er... at least I think you can... where did the
> axioms about what a class is (set of singletons)
> and what a property is (a set of pairs) go?
> They were in an earlier draft, no?

The earlier draft considered classes to be unary relations and
properties to be binary relations.  And, yes, from the definitions of
"unary relation" and "binary relation" one could infer that classes and
properties are disjoint.

However, the major step that was taken in the current axiomatization was
to drop all assumptions about what classes and properties are, and
simply give them the characteristics that are required of them by the
language specs.  One could consider them to be unary and binary
relations in addition to the axioms in the document if that were useful
in some settings, or one could consider classes and properties to be
sets (in a suitable set theory) in addition to the axioms in the
document if that were useful in some settings.  Or one could consider
classes to be concepts that are "thought objects".  Etc.  The claim of
the axiomatization is that such assumptions are not necessary.

So, there would be no way (that I see) of proving that classes and
properties are disjoint without explicitly stating that characteristic
as was done in axiom Ax8.

Richard
Received on Wednesday, 29 November 2000 16:54:59 UTC

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