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Re: Rich semantics and expressiveness

From: Michael Schneider <m_schnei@gmx.de>
Date: Wed, 21 Feb 2007 20:14:41 +0100
Message-ID: <45DC9A21.9020501@gmx.de>
To: richard@cyganiak.de
CC: semantic-web@w3.org

Hi Richard!

> Hi all,
> 
> A question from someone who is not well-read in the knowledge  
> representation literature. What is meant by statements such as this:
> 
>      "In general, ontologies are more expressive and have richer
>       semantics than relational schemas ..." [1]
> 
> Are there definitions for "expressivity" and "semantic richness"? Is  
> there an objective measurement for these dimensions?

I don't know, if there is common consensus on those two terms, but here 
is an idea, how one could understand them.

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.

Further, I would also say that OWL-DL is /semantically richer/ than 
OWL-Lite, because within an OWL-DL ontology, there can be expressions 
which denote, for instance, complements of given classes, for which 
there are no semantically equivalent means within OWL-Lite.

To make a clearer distinction between both regarded terms, let's regard 
a reduced form of OWL, called "OWL(-)", where no 'allDifferent' axioms 
are allowed. There really will exist more syntactically wellformed 
ontologies for OWL than for OWL(-), so I would regard OWL to be more 
expressive than OWL(-). But because there is a mapping for each 
'allDifferent' axiom to a semantically equivalent set of 'differentFrom' 
axioms, I would /not/ regard OWL to be semantically richer than OWL(-).

Now, let's see how this proposal fits to the case of relational schemes. 
For every given table scheme it is easy to present a semantically 
equivalent class definition in OWL. For instance, if I have a table 
definition for "People", which has attributes for "name" and "age", then 
I could define the following ontology:

   DatatypeProperty(name)
   DatatypeProperty(age)

   Class(People complete
     restriction(name cardinality(1) allValuesFrom(xsd:string))
     restriction(age cardinality(1) allValuesFrom(xsd:int))
   )

On the other hand, I do not have direct support to express, for 
instance, a subclass-relationship within a relational scheme. So I 
really would say that ontologies are semantically richer than relational 
schemes.

Unfortunately, with my pretty rigorous definition of "expressiveness" 
given above, I cannot immediately say that ontologies are more 
"expressive" than relational schemes, because the vocabularies and 
syntaxes of OWL and RDB simply do not match. So a little more laxity on 
the definition of "expressiveness" would be needed, probably in a form, 
where some mapping between the regarded vocabularies and syntaxes is 
allowed.

Well, just an idea for a definition, hopefully clear enough so that it 
can be criticized by everybody else in the list. :)

Cheers,
Michael
Received on Wednesday, 21 February 2007 19:10:49 UTC

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