Re: Rich semantics and expressiveness

Hi Michael,

In my experience relational schema often has more implicit data than OWL ontologies. With implicit I mean that a lot is left out because the user or the application software is supposed to be able to fill the gaps.
The way we implement OWL does not allow such gaps.

Does this implicity/explicity play a role in your opinion?

Regards,
Hans

----- Original Message -----
From: Michael Schneider <m_schnei@gmx.de>
Date: Wednesday, February 21, 2007 8:14 pm
Subject: Re: Rich semantics and expressiveness

> 
> 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 21:41:00 UTC