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Re: Question on DL negation

From: Bijan Parsia <bparsia@cs.man.ac.uk>
Date: Wed, 7 Mar 2007 22:35:02 +0000
Message-Id: <4138166B-3A1E-4CC1-893C-44F76CD6CCDE@cs.man.ac.uk>
Cc: public-owl-dev@w3.org, semantic-web@w3.org
To: pratt@cs.stanford.edu

On Mar 7, 2007, at 8:28 PM, Vaughan Pratt wrote:

> 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)?
[snip]

I'd really prefer to keep to the context of the discussion. The point  
behind this was that if you can encode arbitrary negation, then  
adding an explicit disjointWith constructor isn't going to alter the  
complexity. Hence the point that "mere" disjointness is (generally)  
*weaker* than full negation.

As I've pointed out, I believe in this thread, that if you can avoid  
the arbitrary use of full negation, there's a good chance at having  
lower complexity. EL++ demonstrates that. That's part of what it is  
for it to be *weaker* than (and definable in terms of) full negation.

As for constructive/nonconstructive...I don't see at all what you're  
getting at. All of this is in the context of fragments of first order  
logic. If you are going to depart from that context, you need to  
supply a lot more detail than I've seen thus far.

Cheers,
Bijan.
Received on Wednesday, 7 March 2007 22:35:53 GMT

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