- From: Tim Berners-Lee <timbl@w3.org>
- Date: Fri, 29 Mar 2002 17:17:37 -0500
- To: "\"Peter F. Patel-Schneider\"" <pfps@research.bell-labs.com>
- Cc: <www-archive@w3.org>
Peter, I feel that I have, though lack of time, not to mention background and ability, failed to get mind loaded with the thinking behind your paradox. The most concise definition I could find with Google was in http://lists.w3.org/Archives/Public/www-webont-wg/2002Jan/0099.html and nearby. With respect to the set of triples > _:1 rdf:type owl:Restriction . > _:1 owl:onProperty rdf:type . > _:1 owl:maxCardinalityQ "0" . > _:1 owl:hasClassQ _:2 . > _:2 owl:oneOf _:3 . > _:3 owl:first _:1 . > _:3 owl:rest owl:nil . > _:1 rdf:type _: 1 . you say, "The question is whether the above collection of triples is entailed by an empty collection of triples." How would that be entailed? Certainly, the owl:first and owl:rest triples are axiomatically true. However, looking at it naively, that set of triples is indeed inconsistent, but I don't see why they should have the status of a paradox. Why should be inference engine believe them and more than it believes anything else inconsistent? Is there a set of rules for constructing classes which exist consistently from a vacuum? In Russell's paradox, why must one consider the class of classes which are not members of themselves? What forces one to fall prey to it? I thought it was the assumption that for every thing and every class that thing had to be either a member or not a member, akin to the idea that all sentences are either true or false. If you drop that requirement, then the paradox just sits there. I realize I'm asking you a big favor to reiterate this, and that I would probably know why had I studied the lists more effectively. Tim
Received on Friday, 29 March 2002 17:18:13 UTC