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Re: Question on DL negation

From: Michael Schneider <m_schnei@gmx.de>
Date: Thu, 08 Mar 2007 09:16:10 +0100
Message-ID: <45EFC64A.6070103@gmx.de>
To: bparsia@cs.man.ac.uk
CC: semantic-web@w3.org, public-owl-dev@w3.org

Bijan Parsia wrote on Wed, 7 Mar 2007 at 22:41:

> On Mar 7, 2007, at 10:10 PM, Michael Schneider wrote:
>> Bijan's 'complementOf' construction only works in OWL-DL,
> 
> Sigh. I think you miss the point. Adding disjointWith to a language  
> that can simulate it directly or via complementOf doesn't increase  
> the expressiveness (in the sense of altering the worst case  
> complexity). 

You are right, I missed the point here, but only because I have missed 
it already before: In my previous mail to you, Ulrike and Evgeny, I 
misunderstood the example construct that you cited in another mail.

I wrote:

 > Bijan Parsia wrote on Wed, 7 Mar 2007 at 15:00:
> It stays EXPTIME-complete since you can polynomially encode class  
> disjointness in OWL-Lite.
> [...]
>> """ > > [1] An example construct, which Jeremy credits to Ian  
>> Horrocks, is as follows.
>>  > > >
>>  > > > Given a definition of a class C:
>>  > > >    Class(C complete <expr1>)
>>  > > >
>>  > > > The let P be a property which is not used elsewhere and define:
>>  > > >    Class(C complete restriction(minCardinality(P, 1))
>>  > > >    Class(C-co complete restriction(maxCardinality(P, 0))"""
> 
> Ok, "C-co" here is the "other" class, which can also have some 
> definition elsewhere:
> 
>    Class(C-co complete <expr2>)
> 
> The latter two number restriction (re)definitions are obviously 
> disjoint.

As you can see, I wrongly thought that this was an example for 
expressing /disjointness/ of the classes "C" and "C-co". But it actually 
turns out to be an example on how to define the /complement/ of a given 
class C within OWL-Lite!

I did not expect that this was possible at all (we were just talking 
about /disjointness/ all the time). But it works, and I have to admit 
that this really amazes me (hey, I am just an ordinary OWL user :))! And 
then, of course, getting disjointness from this result is just a corollary.

> See Jeremy's email. 

For completeness, perhaps someone else here in the list might be 
interested: I have found the place in the test cases document, which 
Jeremy was talking about (where the technique from the example above is 
used to formulate different non-Lite vocabulary within OWL-Lite):

 
http://www.w3.org/TR/owl-test/byIssue#issue-I5.2-Language-Compliance-Levels

Bye,
Michael
Received on Thursday, 8 March 2007 08:16:20 GMT

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