- From: Bijan Parsia <bparsia@cs.man.ac.uk>
- Date: Wed, 21 May 2008 13:13:58 +0100
- 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 UTC