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Re: Question on DL negation

From: Richard H. McCullough <rhm@PioneerCA.com>
Date: Wed, 7 Mar 2007 14:21:40 -0800
Message-ID: <02c901c76107$1d8e2a30$6401a8c0@rhm8200>
To: "Michael Schneider" <m_schnei@gmx.de>
Cc: <bparsia@cs.man.ac.uk>, <matthew.williams@cancer.org.uk>, <semantic-web@w3.org>, <public-owl-dev@w3.org>

I'm not saying that disjointness is assumed, I'm saying that disjointness is 
a fact.
In real-world concept formation, all species of a genus are mutually 
exclusive
and mutually exhaustive.
I don't know what terminology you use.  Perhaps you would call this
a taxonomy, instead of an ontology.

I consider non-disjointness to be "bad", because that means that units
in the intersection have multiple genii -- which means you are mixing
together two different definitions (contexts) for these units.

Dick McCullough
mKE do enhance od "Real Intelligence" done;
knowledge := man do identify od existent done;
knowledge haspart proposition list;
http://mKRmKE.org/

----- Original Message ----- 
From: "Michael Schneider" <m_schnei@gmx.de>
To: <rhm@PioneerCA.com>
Cc: <bparsia@cs.man.ac.uk>; <matthew.williams@cancer.org.uk>; 
<semantic-web@w3.org>; <public-owl-dev@w3.org>
Sent: Wednesday, March 07, 2007 6:22 AM
Subject: Re: Question on DL negation


> Hi, Dick!
>
> Richard H. McCullough wrote on Tue, 6 Mar 2007:
>
>> Your BTW3 really intrigues me.  You say that "disjointness" increases the 
>> "complexity" of a DL, presumably a "bad" thing.
>
> I wrote:
>
>>> BTW3: I cannot see a feature "disjointness", neither for concepts, nor 
>>> for roles. Doesn't the addition of disjointness adds significantly to 
>>> the complexity of a DL? I thought that at least it would, when adding 
>>> concept disjointness to OWL-Lite. Or can disjointness be expressed in 
>>> terms of the other mentioned features? At least, I do not see how this 
>>> were possible for /role/ disjointness, when only having the features of 
>>> OWL1.0.
>
> By "complexity", I really meant /computational/ complexity, in the sense 
> of:
>
>   http://en.wikipedia.org/wiki/Computational_complexity_theory
>
> This is a general runtime (or space) measure for a given computational 
> problem.
>
> The complexity navigator at
>
>   http://www.cs.man.ac.uk/~ezolin/logic/complexity.html
>
> which Bijan pointed me to, shows the computational complexity (if already 
> known) for the (computational) problem of deciding, if a given ontology is 
> satisfiable or not. You can choose the different language features of the 
> description logic you are interested in, and then you can see how the 
> complexity class changes.
>
> Adding some language feature to a given language, for instance the feature 
> "class disjointness" to OWL-Lite, always has the /potential/ to increase 
> the computational complexity of the satisfiability problem, because every 
> reasoner for the augmented language (OWL-Lite+disj) now has to solve this 
> problem for all possible ontologies of the old language (OWL-Lite) PLUS 
> all those ontologies which contain the additional language feature 
> (disjointness axioms). But such an increase in complexity doesn't always 
> happen, I just /supposed/ that this was the case for the step from 
> OWL-Lite to OWL-Lite+disjointness.
>
> Unluckily, I cannot check this with the navigator, because there is no 
> such "concept disjointness" checkbox. It seems that all I can do is 
> comparing the complexity classes of OWL-Lite and OWL-DL, which is an 
> upper-language of OWL-Lite+disj:
>
>    * Complexity( OWL-Lite )  = ExpTime (complete)
>    * Complexity( OWL-DL )    = NExpTime (complete)
>
> And according to
>
>    http://en.wikipedia.org/wiki/EXPTIME
>
> it is currently unknown if ExpTime and NExpTime are different or not (most 
> probably different, so this approach does not really provide me much 
> help).
>
> Anyway, you see now that I had a very specific (and very technical) notion 
> of "complexity" in mind.
>
>> In real-world concept formation, all species of a genus are disjoint,
>> and I believe this is a "good" thing -- a major factor contributing to 
>> the
>> "simplicity" and the "power"of hierarchical classification.
>> Perhaps it's only partial disjointness that is "bad"?
>> I consider any intersection between species to be "bad".
>
> But you can use DLs like OWL to model whatever you want, not only "natural 
> species". And when comparing two general concepts, you cannot simply 
> assume disjointness (it would often be wrong), you instead have to 
> explicitly demand it, by adding a disjointness axiom. But, perhaps, I 
> misunderstood, what you meant here?
>
> Cheers,
> Michael
>
> 
Received on Wednesday, 7 March 2007 22:22:47 GMT

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