- From: Richard Fikes <fikes@KSL.Stanford.EDU>
- Date: Wed, 29 Nov 2000 13:55:37 -0800
- 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