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

From: Pat Hayes <phayes@ihmc.us>
Date: Sat, 10 Nov 2007 09:22:17 -0600
Message-Id: <p06230902c35b790da638@[192.168.1.2]>
To: "Michael Schneider" <schneid@fzi.de>
Cc: "Owl Dev" <public-owl-dev@w3.org>, <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.

Note however that you could have done a 
translation with a URIref instead of a bnode 
(invent some random "skolem" URI for the purpose)

>
>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?

Well, just for clarification, OWL-Full and RDFS 
are also first-order, but allow quantification 
over classes. One can quantify over 
reasonably-sized universes of classes (or indeed 
anything else) in first-order frameworks. (What 
one cannot quantify over is the set of all 
mathematically definable classes, but nobody 
wants to do that.)

But your point can still be made, since OWL-DL is 
a *segregated* first-order language which does 
not permit individuals and classes to be 
intermixed, and prohibits quantification over the 
latter. But see below.

>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.

True, but what is the problem? That variable only 
arises in the RDF translation: it is not a 
variable in OWL-DL itself. The direct semantic 
meaning of the intersection statement is clear, 
and mentions three classes. The RDF meaning of 
the OWL/RDF is also clear, and also mentions (the 
same) three classes, but uses two names (the URI 
":C" and the bnode) to refer to one of them. So? 
The fact that the RDF uses a name in a way that 
is syntactically prohibited in the DL says 
nothing about their semantic equivalence.

Pat

>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
>Tel.: +49-721-9654-0, Fax: +49-721-9654-959
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Received on Saturday, 10 November 2007 15:22:43 GMT

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