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RE: Some basic questions about OWL-Full

From: Pat Hayes <phayes@ihmc.us>
Date: Tue, 23 Oct 2007 17:26:29 -0500
Message-Id: <p0623091bc34423b1b1ec@[10.100.0.25]>
To: "Michael Schneider" <schneid@fzi.de>
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"?

"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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Received on Tuesday, 23 October 2007 22:26:43 GMT

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