- From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
- Date: Wed, 24 Oct 2007 04:40:44 -0400 (EDT)
- To: schneid@fzi.de
- Cc: public-owl-dev@w3.org
From: "Michael Schneider" <schneid@fzi.de> Subject: RE: Some basic questions about OWL-Full Date: Tue, 23 Oct 2007 23:42:55 +0200 > Pat Hayes wrote: > > >>From: Pat Hayes <phayes@ihmc.us> > >>Subject: Re: Some basic questions about OWL-Full > >>Date: Tue, 23 Oct 2007 08:58:28 -0500 > >> > >>> > >>> >Peter F. Patel-Schneider wrote: > >>> >> > >>> >>For homework: Is EquivalentProperties(owl:sameAs > >owl:differentFrom) > >>> >> itself inconsisten? > >>> >> > >>> > > >>> >I'm afraid I'm several years' late on my (easier) homework of: > >>> > Is (*empty*) itself inconsistent? > >>> > >>> Yes, in RDF (and conventional FOL). This is the > >>> only assumption of Tarskian semantic theory, that > >>> there is something in the universe. One can build > >>> a 'free' logic which allows an empty universe, > >>> but then its proof theory can't have the usual > >>> rules of instantiation and generalization, which > >>> allow the inferences > >>> > >>> (forall (x) (foo x)) |== (foo A) for some > >>> 'new' name A |== (exists (x)(foo x)) > >>> > >>> Pat > >> > >>I think Jeremy meant an empty KB, i.e., whether OWL Full is trivial or > >>not. > > > >Ah, I see. Sorry. Yes, that question amounts to > >whether the OWL semantic conditions are > >internally consistent when transcribed into > >common logic (or FOL using the holds/app style). > >Good question! > > Hm, seems to me that I did not understand neither Jeremy, nor Peter, nor > you. :) What is meant by "whether OWL Full is trivial or not"? Is this the > question about whether empty OWL-Full ontologies are inconsistent or not? > I.e. whether an empty OWL-Full ontology entails contradictory statements? Yes. Or, equivalently, an empty OWL-Full ontology has no models (satisfying OWL-Full interpretations). > But if I have some arbitrary non-empty ontology O := {A1,...,An}, then O > contains the empty ontology as a sub-ontology. So I would assume that every > statement which is entailed by the empty OWL-Full ontology will also be > entailed by O itself. And if the empty OWL-Full ontology would entail > contradictory statements, then /every/ OWL-Full ontology would entail > contradictory statements, and then OWL-Full semantics would be totaly > broken! Is it this what you (Pat) mean by "whether the OWL semantic > conditions are internally consistent..."? Yes, again. > Cheers, > Michael An early formulation of set theory (by Frege) was quickly shown to be self-contraditory by Russell. (See http://en.wikipedia.org/wiki/Russell%27s_paradox for more information.) peter
Received on Wednesday, 24 October 2007 08:49:06 UTC