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[OWLWG-COMMENT] Higher order quantification in OWL-DL with bNodes?

From: Michael Schneider <schneid@fzi.de>
Date: Sat, 10 Nov 2007 11:50:48 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A0531D9C@judith.fzi.de>
To: "Owl Dev" <public-owl-dev@w3.org>
Cc: <alanruttenberg@gmail.com>

[Comment to OWL-WG discussion; CC'ed to involved WG members]

Hi OWL-DEV list!

I just found the following mail by Alan Ruttenberg on the OWL-WG list

  Re: ISSUE-3: REPORTED: Lack of anonymous individuals
  http://lists.w3.org/Archives/Public/public-owl-wg/2007Nov/0214.html

where he notices that bNodes are used in both the RDF mapping for OWL-1.0
and for OWL-1.1, and Alan asks what consequences it would have to drop
bNodes from OWL-DL. Alan's question brought a related question up to my
mind, which I present below. 

BTW: No one has to read the complete thread there about "anonymous
individuals", my question doesn't depend on this discussion and is
self-contained.

Now my question:
  
OWL-DL-1.0 allows me to state that a class :C is the intersection of classes
:D1 and :D2. When I have to write such an axiom in RDF syntax, I generally
do it by means of Turtle in the following way:

  (1) :C a owl:Class .
  (2) :D1 a owl:Class .
  (3) :D2 a owl:Class .
  (4) :C owl:equivalentClass [ a owl:Class ;
          owl:intersectionOf ( :D1 :D2 )
      ].

where (4) is just a convenient Turtle shortcut for writing

  (4a) _:X a owl:Class .
  (4b) :C owl:equivalentClass _:X .
  (4c) _:X owl:intersectionOf ( :D1 :D2 ) . 

So we actually have a bNode "_:X" in our OWL-DL-1.0 ontology above.

Now OWL-DL-1.0 has both a "direct semantics" and an "RDF compatible
semantics", and for the DL sublanguage of OWL-1.0 they are intended to be
equivalent. This allows me to interprete the above OWL-DL-1.0 ontology by
using RDF compatible OWL-DL semantics. And because bNodes are interpreted in
RDF as /existential variables/, the meaning of axiom (4) is (in natural
language):

  "There exists some class ?X,
  to which class :C is equivalent, 
  and which is the intersection of the classes :D1 and :D2."   

So this statement is actually a quantification about a /class/ variable. But
I thought that OWL-DL was a First Order Logic dialect, where all universal
and existential quantifications must be asserted about /individual/
variables only? And in an RDF-mapped OWL-DL-1.0 ontology, I am not allowed
to regard such a class variable as an individual variable, because in OWL-DL
the OWL universe is strictly separated. So this looks to me like a problem
for the intended equivalence between Direct Semantics and RDF Compatible
Semantics for OWL-DL.

There is certainly some misunderstanding on my side, but maybe someone can
clarify?

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 Saturday, 10 November 2007 10:51:10 GMT

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