W3C home > Mailing lists > Public > semantic-web@w3.org > May 2008

Re: owl:Thing (was Re: Managing Co-reference)

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Wed, 21 May 2008 13:13:58 +0100
Message-Id: <A3B45F61-A4F9-4495-AB4F-57CE59C35A89@cs.man.ac.uk>
To: Semantic Web <semantic-web@w3.org>

Hi Peter,

On 21 May 2008, at 12:58, Peter Ansell wrote:

[snipped what I couldn't follow]

> [http://www.w3.org/2002/07/owl]
>
> <Class rdf:ID="Thing">
>   <rdfs:label>Thing</rdfs:label>
>   <unionOf rdf:parseType="Collection">
>     <Class rdf:about="#Nothing"/>
>     <Class>
>       <complementOf rdf:resource="#Nothing"/>
>     </Class>
>   </unionOf>
> </Class>
>
> <Class rdf:ID="Nothing">
>   <rdfs:label>Nothing</rdfs:label>
>   <complementOf rdf:resource="#Thing"/>
> </Class>

This isn't how they are defined. They are defined in terms of the  
model theory, to wit, in any interpretation (thus any model)  
owl:Thing contains all the elements of the interpretation  
(intuitively, all the individuals) and owl:Nothing is the empty set.  
Obviously, the universal set (or a given domain) and the empty set  
are complements, hence the tautologies/theorems you list above. You,  
of course, don't need such distinguished symbols, since you do have  
negation in OWL, you can always introduce them by a definition. Pick  
an arbitrary class name, C, then owl:Thing == (C or ~C) and  
owl:Nothing == (C and ~C). Obviously, once you have one, you could  
always define the other in the manner you list above.

> Sorry if this sounds like uninformed rambling and I am missing an
> important point why these two Classes need to obliquely reference each
> other using complement in this way as the basis for a consistent
> ontological system.

I hope I've clarified!

In many logics, the distinguished symbols are known as Top and  
Bottom, or \top and \bot

(see: <http://www.artofproblemsolving.com/LaTeX/ 
AoPS_L_GuideSym.php#others>)

Cheers,
Bijan.
Received on Wednesday, 21 May 2008 12:11:56 GMT

This archive was generated by hypermail 2.3.1 : Tuesday, 26 March 2013 21:45:22 GMT