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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: Fri, 25 Apr 2008 19:34:01 -0400 (EDT)
Message-Id: <20080425.193401.265607449.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: Sat, 26 Apr 2008 01:12:27 +0200

> Hi, Peter!
> 
> Peter F. Patel-Schneider wrote:
> 
> >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.
> 
> Before I answer the rest of you mail, I will first want to make sure that I
> correctly understand you in this point.
> 
> Do you mean the following or a variant of it:
> 
>     "Guarded" Comprehension Principle:
>     ----------------------------------
> 
>     IF
>         p rdf:type owl:ObjectProperty .
> -->     p owl:differentFrom rdf:type .
>     THEN
>         _:x rdf:type owl:SelfRestriction .
>         _:x owl:onProperty p .
> 
> where "_:x" is an existential variable?

Well that is not a comprehension principle, you need something like

     IF  p belongs to the class extension of owl:ObjectProperty
         and p is not equal to the denotation of rdf:type
     THEN there must be a domain element x such that
          x belongs to the class extension of owl:SelfRestriction
	  and x and the denotation of p is in the property extension of owl:SelfRestriction

> But if you have the following two graphs G_L and G_R:
> 
>     G_L := { 
>         :alice rdf:type owl:Thing .
>         :loves rdf:type owl:ObjectProperty .
>         :alice :loves :alice .
>     }
> 
>     G_R := {
>         :alice rdf:type _:s .
>         _:s rdf:type owl:SelfRestriction .
>         _:s owl:onProperty :loves .
>     }
> 
> AFAICT, G_L entails G_R in OWL 2 DL, right? 

> But with the guarded comprehension principle above, this won't be an
> entailment in OWL 2 Full anymore. 

Yes, as you state below you also need a premise of something like

	:loves owl:differentFrom rdf:type

> The reason is that the guarded comprehension principle now only "fires" on
> property :loves, if :loves can be entailed to be owl:differentFrom rdf:type.
> But without giving more information in graph G_L, there will exist a
> satisfying interpretation for G_L in which the URI ':loves' happens to
> denote the same individual as the URI 'rdf:type' (making :alice actually
> into a class, but this doesn't matter in OWL Full). So, a self restriction
> class on property :loves does not exist, at least not deduced from the
> guarded comprehension principle.
> 
> The guard in the guarded comprehension principle does not only protect
> against the "real" rdf:type, but also against most other properties within
> an ontology. This approach is too strong for maintaining Theorem 2.

Well you also have to fiddle a bit more.

You could fiddle with Theorem 2, for example by adding something like

	... O augmented with suitable distinctness conditions, i.e., all
	properties in O are distinct from rdf:type entails ...

You could also fiddle with the semantic conditions, adding something
like the denotation of all names that are not rdf:type are different
from the denotaiton of rdf:type.

But, again, what did you expect in OWL Full?   OWL 1 Full was dancing
right up against the cliff.   Adding useful expressive power to OWL
requires delicate work so that OWL Full doesn't fall into the abyss.
As an alternative, I suppose that the WG could just go the N3 way with
OWL Full.

> Cheers,
> Michael

peter
Received on Friday, 25 April 2008 23:36:15 GMT

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