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Re: Rich semantics and expressiveness

From: Vaughan Pratt <pratt@cs.stanford.edu>
Date: Thu, 22 Feb 2007 10:10:47 -0800
Message-ID: <45DDDCA7.7050706@cs.stanford.edu>
To: semantic-web@w3.org

On Wed, 2007-02-21 at 20:14 +0100, Michael Schneider wrote:
> As an example, I would say that OWL-DL is /more expressive/ than 
> OWL-Lite, because the set of OWL-DL ontologies is a real superset of the 
> set of all OWL-Lite ontologies, where I regard an ontology as a set of 
> syntactically wellformed OWL-axioms. For instance, you can have an 
> OWL-DL ontology containing an axiom like
>    Class(C equivalentClass(complementOf(D))
> but such an ontology would not be allowed in OWL-Lite. So, by "more 
> expressive" I mean that there are more syntactical expressions possible.

Who uses "expressive" with this meaning?  Certainly not the annual 
EXPRESS series of conferences on expressiveness in concurrency, the 14th 
of which will be in Lisbon in September.  For them, just because 
language L has two syntactically different ways of expressing a concept 
that L' has only one expression for doesn't make L more expressive than L'.

On the other hand if you make expressiveness a semantic notion then you 
run into the problem of the semantics for "complementOf(D)".  For D = 
"registered Democrats," are Santa's elves and the states of bliss in 
complementOf(D)? How do OWL-DL users typically use complementOf, and 
what do they think it means?

Relative complement is not so problematic, e.g. dogs that aren't 
Dalmatians, or voters that aren't registered Democrats.  It's also ok to 
have dogs that aren't registered Democrats or voters that aren't 
Dalmatians provided the ontology admits the intersection of dogs and 
voters as a class (a competent type-checking ontology might object to 
this class on the ground that dogs don't vote, as a way of catching more 
errors).  Absolute complement  however seems neither terribly useful nor 
terribly tractable from either a theory or implementation standpoint, 
and so doesn't seem like a strong selling point for OWL-DL over OWL-Lite.

Vaughan Pratt
Received on Thursday, 22 February 2007 18:10:56 UTC

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