Re: Rich semantics and expressiveness

Michael, 
thanks for your definitions, they certainly helped me, a lurker here.

With respect to comparing expressivity of different languages, perhaps
one could change your "expressivity" definition to something like this:

        Between two languages with the same semantic richness, the more
        expressive language can express some concepts in fewer terms
        (e.g. one allDifferent vs. many times differentFrom).

I'd say that a more semantically rich language should always be
considered as more expressive, or that comparing expressivity of
languages with different semantic richness is of limited use.

Then there are corner cases where languages can be differently
semantically rich in different directions, and likewise differently
expressive, i.e. incomparable.

Regards,
Jacek



On Wed, 2007-02-21 at 20:14 +0100, Michael Schneider wrote:
> 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 Thursday, 22 February 2007 09:58:25 UTC