Re: Nothing in App. B of OWL Language Reference 31 March 2003

re: any Class, I meant some class with an extension of size > 0.
Given any such class, ABC.

<Class rdf:ID="Thing">
   <rdfs:label>Thing</rdfs:label>
   <unionOf rdf:parseType="Collection">
     <Class rdf:about="#ABC"/>
     <Class>
       <complementOf rdf:resource="#ABC"/>
     </Class>
   </unionOf>
 </Class>

Strictly speaking, Nothing is the class of things that don't exist.
I don't think it's a good idea to base your axioms on Nothing.

Dick McCullough
knowledge := man do identify od existent done;
knowledge haspart proposition list;

----- Original Message ----- 
From: "Guus Schreiber" <schreiber@cs.vu.nl>
To: "Richard H. McCullough" <rhm@cdepot.net>
Cc: "webont-comments at W3C" <public-webont-comments@w3.org>
Sent: Friday, May 09, 2003 5:39 AM
Subject: Re: Nothing in App. B of OWL Language Reference 31 March 2003


> Dear Richard,
> 
> Thanks for your comment. Responses in-line.
> 
> Richard H. McCullough wrote:
> 
> > Appendix B says
> > 
> > <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>
> > 
> > Since the 2nd group implies that complementOf Nothing is Thing,
> > the first group is equivalent to
> > 
> > <Class rdf:ID="Thing">
> >   <rdfs:label>Thing</rdfs:label>
> >   <unionOf rdf:parseType="Collection">
> >     <Class rdf:about="#Nothing"/>
> >     <Class rdf about="#Thing"/>
> >   </unionOf>
> > </Class>
> 
> The class axiom for owl:Thing in Appendix B of Reference defines its 
> class extension to be the extension of owl:Nothing plus its complement, 
> which means all individuals in the universe of discourse. owl:Nothing is 
> its complement, so its class extension is the empty set.
> 
> Your revised axiom uses owl:Thing to define itself. We would prefer to 
> refrain from such recursive definitions and thus keep to the axioms as 
> they currently are.
> 
> > which is probably what you want to say,
> > or else omit it all together.  
> > 
> > Even better would be to replace "Nothing" with
> > some variant of "any Class" -- which I believe
> > is what the document says elsewhere.
> 
> I'm not sure I understand your point. The extension of owl:Nothing is 
> the empty set, so it is not "any Class".   owl:Thing and owl:Thing 
> fulfill a special role, namely as root resp. leaf of the class lattice, 
> cf. Sec. 3.1:
> 
> [[
> Consequently, every OWL class is a subclass of owl:Thing and owl:Nothing 
> is a subclass of every class.
> ]]
> 
> Please let us know whether this response is satisfactory.
> 
> Regards,
> Guus Schreiber
> 
> > ============ 
> > Dick McCullough 
> > knowledge := man do identify od existent done;
> > knowledge haspart proposition list;
> > 
> > 
> 
> -- 
> NOTE: new affiliation per April 1, 2003
> 
> Free University Amsterdam, Computer Science
> De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands
> Tel: +31 20 444 7739/7718
> E-mail: schreiber@cs.vu.nl
> Home page: http://www.cs.vu.nl/~guus/ [under construction]
> 
>

Received on Friday, 9 May 2003 09:00:06 UTC