- From: Jeremy Carroll <jjc@hplb.hpl.hp.com>
- Date: Thu, 4 Apr 2002 20:27:52 +0100
- To: "Pat Hayes" <phayes@ai.uwf.edu>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
- Cc: <dieter@cs.vu.nl>, <www-webont-wg@w3.org>
Basically agreeing with Pat, see on, Peter: > >I claim that this precisely captures the intuitive meaning of my example. > >Given an OWL KB, I need to be able to determine if an object in that KB > >satisfies a restriction that is not necessarily mentioned in the KB. > >I would be prepared to do this somewhat indirectly, as in > > > > <John, child, Joe>, <Joe, rdf:type, Person> > > |= <John, rdf:type, :_2>, <:2, owl:sameAs?, :_1>, > > <:_1, owl:onProperty, child>, <:_1, owl:hasClass, Person> > > > >However, I view any approach that does not come up with some way of doing > >the above as fundamentally broken. Pat: > Yes, this is a very intense disagreement between us. I view your way > of thinking here as itself totally broken. It insists on reducing all > of logic to inferences in set theory, a perspective I have never even > seen expressed before in any forum, logical or otherwise. I have > always thought of DLs as a restricted form of logic, but you seem to > have a completely different perspective, in which DL's are a branch > of set theory,and even elementary logical reasoning has been > eliminated in favor of set-theoretic constructions. > > Can you give us any reason at all why we should take this idea seriously? > > Pat > Set theory is believed to be a solved problem, but the best solutions (e.g. ZF) are complicated. I think in the sort of approaches that both Pat and I have been arguing for, the set theory is solved outside OWL. At some level the awkward examples occur because DAML+OIL (and OWL) embed a relatively naive way of talking about sets. If we try and construct a set theory in this naive way then we hit trouble. I don't see any harm in continuing to talk naively about sets within OWL, as long as we don't confuse what we are doing with actually replacing ZF. As I understand it, in a DL system with datatypes, the datatypes are represented as some sort of oracle that is invoked when needed. I can imagine a ZF oracle (hereafter ZFO) that logically corresponds to all purely set-theoretic DAML+OIL statements that are consistent with a given knowledge base. Thus in Peter's example, using my solipsistic reasoning and the oracle, <John, child, Joe>, <Joe, rdf:type, Person>, ZFO |= <John, child, Joe>, <Joe, rdf:type, Person> <:_1, owl:onProperty, child>, <:_1, owl:hasClass, Person> (because this set does exist because ZFO sees that its existence is consistent with the rest of the model) |= <John, rdf:type, :_1> (as my previous solipsistic message permitted). I don't believe that the set theoretic needs of an OWL implementation are so excessive that implementing such an oracle will be stressful in practice; and until we have feedback that indicates that that is a problem I think we should ignore the issue. [I suspect that Peter's paradox does indicate that the fully comprehensive ZFO is somewhat tricky - but I don't believe this will present real practical problems in realistic implementation scenarios.] Jeremy
Received on Thursday, 4 April 2002 14:28:40 UTC