- From: Michael Schneider <schneid@fzi.de>
- Date: Tue, 23 Oct 2007 23:42:55 +0200
- To: "Pat Hayes" <phayes@ihmc.us>
- Cc: <public-owl-dev@w3.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>, <jjc@hpl.hp.com>
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? 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..."? Cheers, Michael -- Dipl.-Inform. Michael Schneider FZI Forschungszentrum Informatik Karlsruhe Abtl. Information Process Engineering (IPE) Tel : +49-721-9654-726 Fax : +49-721-9654-727 Email: Michael.Schneider@fzi.de Web : http://www.fzi.de/ipe/eng/mitarbeiter.php?id=555 FZI Forschungszentrum Informatik an der Universität Karlsruhe Haid-und-Neu-Str. 10-14, D-76131 Karlsruhe Tel.: +49-721-9654-0, Fax: +49-721-9654-959 Stiftung des bürgerlichen Rechts Az: 14-0563.1 Regierungspräsidium Karlsruhe Vorstand: Rüdiger Dillmann, Michael Flor, Jivka Ovtcharova, Rudi Studer Vorsitzender des Kuratoriums: Ministerialdirigent Günther Leßnerkraus
Received on Tuesday, 23 October 2007 21:43:16 UTC