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

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?

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. 

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.

Cheers,
Michael