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

From: Peter F. Patel-Schneider <pfps@research.bell-labs.com>
Date: Mon, 28 Apr 2008 11:32:07 -0400 (EDT)
Message-Id: <20080428.113207.146739154.pfps@research.bell-labs.com>
To: schneid@fzi.de
Cc: public-owl-wg@w3.org

From: "Michael Schneider" <schneid@fzi.de>
Subject: RE: ISSUE-119: What can be done against the Russell paradox?
Date: Mon, 28 Apr 2008 16:49:41 +0200

[...]

> >The whole idea of Theorem 2 was to try to determine how close the
> >semantic meanings were between OWL 1 DL and OWL 1 Full.
> 
> I know that this was the idea, and I strongly agree that we need a
> criterion for this purpose. But I do not easily accept that the
> current formulation of Theorem 2 is an adequate approach to compare
> the semantic expressivity of OWL Full and OWL DL.

[...]

> When I want to construct an OWL 2 Full, which is at least as
> expressive as OWL 2 DL, then I should only ask for all those results
> which OWL 2 DL produces. I should not ask OWL Full for a cow, when I
> ask DL only for a glass of milk. If DL provides me from some given
> premise that Alice belongs to the /set/ of all self-lovers, then I
> cannot expect more than exactly this from OWL Full, too.

But this is precisely what Theorem 2 does.  In DL to ask whether Alice
belongs to the set of all self-lovers one asks whether the KB entails
Alice in SelfRestrition(loves).  In an RDF-based language, one asks the
same question couched in RDF-speak, i.e., does an RDF graph OWL
Full-entail an RDF graph stating that Alice is in the set of
self-lovers.
 
> The asymmetric demands, which Theorem 2 puts on OWL DL and OWL Full
> force OWL Full to include some very strong additional semantic conditions,
> namely the comprehension principles. A comprehension principle for
> self-restrictions will provide for every existing property p a class
> /resource/, which has the set {x|p(x,x)} as its class extension.
> Or more figuratively, comprehension principles provide me
> /precautionary/ a cow for milk, a fountain for water, and a brewery
> for beer, just for the case that I should ever become thirsty some
> day. :) This doesn't only lead to undesirable results (as I stated
> above), but also brings OWL Full near to its collapse, as one can see
> from the problem with the Russell paradox.
> 
> Bottom line: The "latent" collapse of OWL Full is not something which
> is inherent to an RDFS-based language which tries to compete with
> OWL DL w.r.t. semantic expressivity. Instead, this problem seems to
> result solely from the strong and (technically) unfair demands
> which Theorem 2 puts on OWL Full in comparison to OWL DL.

I'm open to other ways of doing this, but I don't see any.

[...]

> Cheers,
> Michael

peter
Received on Monday, 28 April 2008 15:35:45 GMT

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