Re: Some basic questions about OWL-Full

Well you could certainly ask the same question about RDF, or RDFS.

Indeed, some care has to be taken with D-entailment when XML Schema
datatypes are considered, as the XML Schema datatype document, read
normally, is internally inconsistent. 

* The value space of decimal is the set of numbers that can be
  obtained by multiplying an integer by a non-positive power of ten, i.e.,
  expressible as i x 10^-n where i and n are integers and n >= 0

So, the integer 2 is in the value space of xsd:decimal.

* The basic value space of float consists of the values m x 2^e, where m
  is an integer whose absolute value is less than 2^24, and e is an
  integer between -149 and 104, inclusive. 

So, the integer 2 is in the value space of xsd:float.

* The value spaces of all primitve datatypes are disjoint.

Contradiction.

This contradiction is "resolved" by making the overall value space
contain the disjoint union of the value spaces of the primitive
datatypes, and thus "2"^^xsd:decimal is not equal to "2"^^xsd:float.

peter


From: "Giorgos Stoilos" <gstoil@image.ece.ntua.gr>
Subject: RE: Some basic questions about OWL-Full
Date: Thu, 25 Oct 2007 10:15:54 +0300

> Hi all,
> 
> Does this question/discussion apply also to RDF or only to OWL Full. If so
> why is there a difference?
> 
> Best,
> Giorgos
> 
> > -----Original Message-----
> > From: public-owl-dev-request@w3.org [mailto:public-owl-dev-request@w3.org]
> > On Behalf Of Pat Hayes
> > Sent: Wednesday, October 24, 2007 1:26 AM
> > To: Michael Schneider
> > Cc: public-owl-dev@w3.org; Peter F. Patel-Schneider; jjc@hpl.hp.com
> > Subject: RE: Some basic questions about OWL-Full
> > 
> > 
> > >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"?
> > 
> > "Trivial" in this context means that there would
> > be no OWL-Full interpretations which satisfy
> > anything, so everything would be OWL-Full
> > unsatisfiable. Put another way, the OWL-Full
> > semantic conditions would be internally
> > contradictory.
> > 
> > >  Is this the
> > >question about whether empty OWL-Full ontologies are inconsistent or not?
> > 
> > That is another way to put it, yes.
> > 
> > >I.e. whether an empty OWL-Full ontology entails contradictory statements?
> > 
> > And that is another, yes.
> > 
> > >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!
> > 
> > Quite. Which is what Peter meant by "trivial". I
> > am confident that this is not the case, but even
> > if it were I would say they would indeed be
> > broken, but because in that case the OWL semantic
> > conditions were themselves broken. And not
> > necessarily totally, since the next task would be
> > to see how to weaken them so that they weren't
> > broken. IMO they are too strong in some ways in
> > any case, e.g. the intensional view of classes
> > seems better than the extensional one, c.f.
> > terHorst's version of OWL.
> > 
> > >Is it this what you (Pat) mean by "whether the OWL semantic
> > >conditions are internally consistent..."?
> > 
> > Yes.
> > 
> > Pat
> > 
> > >
> > >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
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> > 
> > 
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> 
>

Received on Thursday, 25 October 2007 09:32:31 UTC