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

From: "Michael Schneider" <schneid@fzi.de>
Subject: ISSUE-119: What can be done against the Russell paradox?
Date: Sat, 26 Apr 2008 00:07:50 +0200

> 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 thought that we already discussed this.  The trick is to fiddle with
the comprehension principle for self restrictions to not apply on rdf:type.

> 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. 

Yes, but what other options are there.  The RDF model is that everything
is a triple, and all triples have semantic weight.  Therefore syntax has
to have semantic weight, and you end up with comprehension principles.  

If another option was available then I'm sure that philosophers would
have used it to get around the Liar's paradox.

> 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. 

If you think that there is one, then please let people know.  The
comprehension principles were the only way that I could see to satisfy
the required 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,
> Michael

peter

Received on Friday, 25 April 2008 22:17:04 UTC