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Re: OWL semantics

From: Christopher Welty <welty@us.ibm.com>
Date: Tue, 6 Aug 2002 11:29:52 -0400
To: Ian Horrocks <horrocks@cs.man.ac.uk>
Cc: www-webont-wg@w3.org, www-webont-wg-request@w3.org
Message-ID: <OF551E005F.12C8F032-ON85256C0D.005262A7@pok.ibm.com>

WIth regards to Ians two basic points:

1a) Classes as instances:

This is, to me, a fascinating issue, and I'm not willing to take Ian and 
Peter's word on it yet.  It is certainly a useful feature to have.  Pat 
and Chris Menzel worked out a way to make the semantics of this 
first-order for KIF/CL/whatever it's called now, however to my knowledge 
they have never shown any of the (algorithmic) consequences for reasoning. 
 Pat shrugs and says it should be no problem since it's all first order, 
and the syntax prevents paradoxes.  I'm not willing to take their word for 
it, either.

Applying this result (assuming there is an algorithm) to OWL may not be 
trivial, however, since much computation in description logics occurs over 
the class descriptions - even if it the reasoner is model based.  So, at 
least from what I understand, a lot hinges on the fact that the extension 
of a class does not include other classes.  Still, what are the 
consequences of including classes in the extension of classes?  An 
inference may add more to the description of a class?  As long as that 
addition is monotonic, is it really that bad?

So Ian, Peter, are you objecting prima facie to the fact that "classes of 
classes" is inherently second order, or do you have examples in mind that 
would break the reasoner?

1b) Using OWL to change the syntax of OWL

I strongly agree with Ian's position here.   It is well known that when 
you use a logical system to *talk about itself* you are introducing 
incompleteness.  This was part of Godel's theorem.  In every system that 
permitted this I've ever seen, it was a trivial matter to create 
incomplete and infinite proofs, so trivial that naive users did it all the 
time.  Unless you break processing into two discrete steps, the way 
compilers/loaders do (i.e. compile time and run time) you are also 
introducing a huge amount of machinery to support this.  Machinery that no 
one really knows how to build. 

Adding such a class of  features reduces the space of possible 
implementors for the full language from a handful to none.  It may be 
interesting to create that as "OWL level three" and make it a challenge 
problem for Computer Science.

-ChrisW


Dr. Christopher A. Welty, Knowledge Structures Group
IBM Watson Research Center, 19 Skyline Dr.
Hawthorne, NY  10532     USA 
Voice: +1 914.784.7055,  IBM T/L: 863.7055
Fax: +1 914.784.6078, Email: welty@us.ibm.com
Received on Tuesday, 6 August 2002 11:31:14 GMT

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