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RE: [OWLWG-COMMENT] Punning and the "properties for classes" use case

From: Michael Schneider <schneid@fzi.de>
Date: Mon, 5 Nov 2007 21:36:32 +0100
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A04A8F92@judith.fzi.de>
To: "Danny Ayers" <danny.ayers@gmail.com>
Cc: <public-owl-dev@w3.org>, "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Hi, Danny!

In addition to Peter's answer perhaps a few words about the RDF side (as far
as I have understood this myself, but if I am wrong in a point, others will
certainly intervene immediatly :)). There is really a distinction between a
"class resource itself", and its extension, i.e. the set of all the
resources which are rdf:type this class. And analog for properties, for
which their extension is a set of subject-object tuples. 

There is a nice (but somewhat confusing) figure demonstrating this "duality"
(so to speak) for properties in the RDF semantics document. It's figure 1 in
http://www.w3.org/TR/rdf-mt/#gddenot


There are two resources (in "IR"), the numbers "1" and "2", and "1" is
actually a property (in "IP"). Don't get confused: There are /two/ different
URIs "a" and "b" denoting this same property "1". The extension of property
"1" is the set

  IEXT(1) = {<1,2>, <2,1>}

(This is kind of curious, btw., because property "1" itself occurs once as a
subject, and once as an object in the tuples within the extension of "1".
But that's allowed.)

AFAICS, the distinction between a class resource C and its extension
ICEXT(C) is actually perceivable in OWL-Full. Say you have some property :p
assigned to some class :C (allowed in OWL-Full):

  :C a owl:Class .
  :p a owl:ObjectProperty .
  :x a owl:Thing .

  :C :p :x .

In OWL-Full you can have another class :D, which equals :C, by asserting

  :D owl:sameAs :C

and in this case you can entail

  :D :p :x .

because by owl:sameAs you declare :C and :D really to be the same, sharing
all their properties and extensions, so you also can entail:

  :D owl:equivalentClass :C .

because this "only" means that the extensions of :D and :C are the same.

But here's the interesting bit: If you just specify :D and :C to be
/equivalentClass/ instead of sameAs, i.e. if you just demand that only the
/extensions/ of :D and :C are equal, not the class resources denoted by :D
and :C themself, then you will /not/ get all the properties of :C also for
:D. I.e., asserting

  :D owl:equivalentClass :C

does *not* entail

  :D :p :x . # not entailed!

So the distinction between a class and its extension is not just
play-on-words, it's kind of "real", though AFAIK it can only be perceived
within OWL-Full [FIXME!], because only there you have the language features
and the semantical conditions to exploit this distinction directly.

Originally, I had a hard time to accept this distinction between a class
resource and its extension. The reason for this separation given somewhere
in the RDF semantics spec is, IIRC, that this allows a class C to be an
element of itself. Well... :) But in the meanwhile I like this distinction,
I find it very RDFish: It allows me to differentiate between comparing the
/descriptions/ of two classes (using sameAs), and the extensions of two
classes (using equivalentClass). I appreciate this, because two classes can
happen to have the same extension, even if they were defined with completely
different intentions in mind, i.e. described with different properties.

Cheers,
Michael


>-----Original Message-----
>From: Danny Ayers [mailto:danny.ayers@gmail.com] 
>Sent: Monday, November 05, 2007 10:49 AM
>To: Peter F. Patel-Schneider
>Cc: Michael Schneider; public-owl-dev@w3.org
>Subject: Re: [OWLWG-COMMENT] Punning and the "properties for 
>classes" use case
>
>Hi Peter,
>
>I'd be grateful if you could help me with this one point -
>
>On 02/11/2007, Peter F. Patel-Schneider 
><pfps@research.bell-labs.com> wrote:
>
>> Well, RDF overloads URIs already.  A URI in RDF denotes a 
>entity in the
>> domain of discourse as well as that entity's property 
>extension, which
>> also carries the entity's class extension.
>
>I assumed the resource identification here was (very loosely) like
>saying 'that bag of peanuts' - the peanuts inside are an implicit
>characteristic of the thing identified, even though you might not be
>able to see them. Perhaps you could contrast RDF's approach with
>another (OWL 1.1's?) which doesn't overload?
>
>Cheers,
>Danny.
>-- 
>
>http://dannyayers.com

>

--
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


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Received on Monday, 5 November 2007 20:36:50 GMT

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