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Re: Some basic questions about OWL-Full

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Wed, 24 Oct 2007 04:40:44 -0400 (EDT)
Message-Id: <20071024.044044.166862332.pfps@research.bell-labs.com>
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 GMT

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