Re: Question on DL negation

On Mar 7, 2007, at 10:10 PM, Michael Schneider wrote:

> Vaughan Pratt wrote on Wed, 07 Mar 2007:
>> Bijan Parsia wrote:
>>> Well, disjointness is *weaker* than full negation. For example,  
>>> in OWL, A disjointWith B is just syntactic sugar for A subclassof  
>>> complementOf(B).
>> Are there technical (e.g. computational complexity) benefits to  
>> this definition over the more usual (and more constructive)  
>> definition in terms of emptiness of intersectionOf(A,B)?
>
> Thanks, Vaughan!
>
> That's an even more obvious example, how one can simulate a  
> disjointness axiom between two classes A and B within OWL-/Lite/.  
> Restated:
>
>   EquivalentClasses(owl:Nothing intersectionOf(A B))
>
> 'owl:intersectionOf' is explictly allowed vocabulary within OWL- 
> Lite, as long as the classes mentioned are named classes (or  
> restrictions), see
>
>   http://www.w3.org/TR/2004/REC-owl-features-20040210/#intersectionOf
>
> 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). See Jeremy's email. Perhaps I shouldn't have used the  
phrase "syntactic sugar". Many logical constructs are interdefinable,  
esp. via negation. With full negation you can easily define  
disjointWith. That's all. OWL Lite "has" aribitrary negation, not  
just disjointness. It (roughly) corresponds to SHIF. Thus adding  
explicit disjointness won't change its complexity.

> where 'owl:disjointWith' is given anyway. (But to be fair, keeping  
> within OWL-Lite wasn't the topic in Bijan's cited explanation -  
> this first came up in a later mail).

Yes.

Cheers,
Bijan.

Received on Wednesday, 7 March 2007 22:41:52 UTC