Re: Rich semantics and expressiveness

Thanks for the clear explanation Michael. What you say is very  
convincing for the OWL family of languages. I'm not so sure about  
comparisons between data models that are less similar. For example,  
SQL schemas may contain integrity constraints that use arbitrary SQL  
expressions, like calculations. These constraints cannot be expressed  
in OWL. Isn't SQL semantically richer then? So I'm still unsure how  
to evaluate statements like the one cited in my original mail.

Richard


On 21 Feb 2007, at 20:14, 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 14:42:16 UTC