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ISSUE-119: What can be done against the Russell paradox?

From: Michael Schneider <schneid@fzi.de>
Date: Sat, 26 Apr 2008 00:07:50 +0200
Message-ID: <0EF30CAA69519C4CB91D01481AEA06A08BDDCA@judith.fzi.de>
To: "Peter F. Patel-Schneider" <pfps@research.bell-labs.com>
Cc: <public-owl-wg@w3.org>
Dear Peter!

Regrettably, I wasn't able to attend the last telco, so I haven't been able to 
discuss the Russell problem there.

The minutes cite you:

  Peter Patel-Schneider: one can do a patch to keep things the same...
  Peter Patel-Schneider: that might be adequate

Do you mean by this that you know about some method to restrict the semantics 
of the self restrictions in a way that we still have all OWL 2 DL entailments 
in OWL 2 Full?

I would be interested to see such an approach. I have tried several days now 
to find a "minimal invasive" modification of the semantics. But I did not 
succeed to find a solution which maintains this "Theorem 2" relationship 
between OWL DL and OWL Full.

On the other hand, as you know, I have become very skeptical to the 
comprehension principles within the last few weeks. I now regard comprehension 
principles to be a very heavy weight approach to make OWL Full an upper 
language of OWL DL. They make the OWL Full universe so amazingly complicated. 
If someone told me to prove or disprove consistency of OWL Full, my hypothesis 
would rather be that it is presumably inconsistent -- without the 
comprehension principles I would see a much better chance for consistency. But 
even if OWL Full really is internally consistent, it's hard for me to imagine 
how to come up with such a proof, when having all these comprehension 
principles around. (I tried myself a few times to find ideas how to prove or 
disprove consistency, but got almost crazy. ;-))

I even believe that there is an adequate alternative way to characterize the 
relationship between OWL DL and OWL Full. But if there is a save immediate 
bugfix for the Russell problem, which keeps the entailment-based relationship 
alive, then this will be the way to go. (Well there might be an OWL 3 some 
day... :))

All the best,

Received on Friday, 25 April 2008 22:08:29 UTC

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