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RE: Defining cross products in OWL-1.1

From: Michael Schneider <schneid@fzi.de>
Date: Wed, 21 Nov 2007 18:16:17 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A053249A@judith.fzi.de>
To: "Jeremy Carroll" <jjc@hpl.hp.com>
Cc: "Owl Dev" <public-owl-dev@w3.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Thanks, Jeremy!

Related to the "non-empty universe" question, I have just read your new
Issue 73 in the OWL-WG list:

  ISSUE-73 (infinite universe): REPORTED: Should owl:Thing be necessarily

  In OWL 1.0 Full, the universe is necessarily infinite.

  In OWL 1.0 DL, the universe is required to be non-empty.

  The compatibility between OWL Full and OWL DL could be enhanced by
requiring the universe to be infinite in both cases.

As a public comment again :): I remember that I have read somewhere (don't
know where at the moment) that people sometimes restrict owl:Thing to be a
finite enumeration of certain instances:

  EquivalentClasses(owl:Thing oneOf(x1 ... xN))
The idea, AFAIR, was that by this people can approximate closed world
scenarios in connection with OWL (owl:Thing would then for instance stand
for a concretely given database, i.e. a finite(!) set of data entries). If
this should really be a reasonable pattern (I never used it, so I cannot
tell for sure), wouldn't it be a problem to demand that the OWL-DL-1.1
universe should be infinite?


>-----Original Message-----
>From: Jeremy Carroll [mailto:jjc@hpl.hp.com] 
>Sent: Wednesday, November 21, 2007 3:07 PM
>To: Michael Schneider
>Cc: Owl Dev; Peter F. Patel-Schneider
>Subject: Re: Defining cross products in OWL-1.1
>OWL does not permit an empty universe.
>Michael Schneider wrote:
>> Task: For given classes A and B give an OWL-1.1 axiom set, by which a
>> property pAXB is specified to be equivalent to the cross 
>product A X B.
>> Solution:
>>   (A0) ClassAssertion(w owl:Thing)
>>   (A1) SubClassOf(A ObjectHasValue(pA w))
>>   (A2) SubClassOf(B ObjectHasValue(pB w))
>>   (A3) SubObjectPropertyOf(
>>          SubObjectPropertyChain(pA InverseObjectProperty(pB))
>>          pAXB )
>>   (A4) ObjectPropertyDomain(pAXB A)
>>   (A5) ObjectPropertyRange(pAXB B)
>> There are a several points which need some further discussion here:
>> Second: About the "glue instance" w. The only real 
>requirement was that
>> there is /some/ instance in the universe (denoted by 
>owl:Thing), because
>> this alone suffices to use such an instance for glueing pA and pB^-1
>> together in the above sub role chain. Even the two 
>'ObjectHasValue' axioms
>> do not seem to put a dangerous restriction on 'w'. So it seems to be
>> possible for instance that I can reuse w for specifing the 
>"glue instance"
>> of a second role rCXD for other classes C and D without any 
>problem. Also,
>> if w occurs in other axioms of the ontology, this shouldn't be a big
>> problem, because it does not affect the fact that such a w 
>/exists/. Of
>> course, it must not happen that in the ontology's remaining 
>axioms one of
>> the "helper roles" 'pA' and 'pB' appears, but this can 
>always be avoided in
>> practice AFAICS. So the only thing which might be considered 
>to be at least
>> a /theoretical/ problem is that it will not be possible 
>anymore to interpret
>> such an OWL ontology over the /empty/ universe. But in 
>practice, no one will
>> really care about this lacking, and I am not even certain if 
>doing so is
>> allowed at all in OWL. 
>In OWL 1.0, the universe is restricted to have at least one member.

>EC(owl:Thing) = O ⊆ R, where O is nonempty and disjoint from LV
>I would expect this restriction to carry through to the next 
>version of OWL.

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
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Received on Wednesday, 21 November 2007 17:16:30 UTC

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