Re: The notion of a "classification criterion" as a class

Hi Bene

Allow me to suggest you are making a basic error in this approach.  
Details below, in-line.

On Apr 15, 2010, at 2:30 PM, Benedicto Rodriguez wrote:

> Hello everyone,
>
> Apologies for cross-posting but I thought the email might be  
> relevant to both mailing lists:ontolog-forum@ontolog.cim3.net and public-owl-dev@w3.org 
> .
>
> I am trying to put together an ontology design pattern (or  
> combination of patterns) with the intent of modeling multiple  
> alternative classification criteria of a domain concept.  At this  
> point, I have to commit my focus to OWL (or more specifically, to an  
> expressivity level within OWL-DL).
>
> In the process I have come across what I think it is an interesting  
> modeling scenario. Let me use a simple example to describe it  
> extracted from [1].  Consider the following set of classes (as a  
> subset of a larger ontology model) in the popular domain of "family  
> relationships" organized according to the following subsumption  
> hierarchy:
>
> :Person
>     |-- :Man
>     |-- :Woman
>     |-- :Parent
>     |-- :Child
>     |-- :Sibling
>
> We could argue that this inheritance structure is not satisfactory  
> because different concepts are represented by classes at the same  
> level.

You could argue that, but to do so would reveal a misunderstanding  
about the nature of class subsumption in OWL (and similar languages).  
Classes in OWL are purely extensional: they are simply *sets* of  
things (in this case, of people).

> That is, the concept of gender, represented by the classes :Man  
> and :Woman, and the concept of kinship relationships, represented by  
> the classes :Parent, :Child and :Sibling.  In that sense, the  
> concepts of gender and kinship could be seen as two different  
> classification criteria for all the subclasses of :Person.

Indeed, they could be so described. However, all these  
subclassifications define subclasses of Person in the *same sense* of  
subclass. The fact that Man is a gender-based subcategory and Child is  
a kinship-based subcategory, while interesting, does not imply that  
the *relationships* between the classes Person and Man, and between  
Person and Child, are intrinsically different. They are not: they are  
both simply subsumption.

Which is why...
>
> The issue that I am trying to solve deals with how to incorporate  
> the representation of these classification criteria concepts into  
> the ontology model.
>
> An initial approach (kind of intuitive to me) would be two represent  
> the two classification criteria as classes (say :PersonByGender  
> and :PersonByKinship) and regroup all the subclasses of :Person  
> accordingly. The result would look like:
>
> :Person
>     |-- :PersonByGender
>     |   |-- :Man
>     |   |-- :Woman
>     |-- :PersonByKinship
>         |-- :Parent
>         |-- :Child
>         |-- :Sibling

.... this is a basic mistake. To see why, ask yourself what could be  
the membership criterion for the category PersonByGender. Remember,  
this has to be a set, determined solely by its members, not by any  
other meta-property that it might be thought to have. But something is  
a PersonByGender exactly when they are a Person (barring, perhaps,  
some medical abnormalities) and also is a PersonByKinship exactly when  
they are a Person. So these classes are all identical, when considered  
as sets. And in OWL-DL, at any rate, one is obliged to treat them as  
sets, by the semantic rules of the language.

>
> However, I see a conceptual problem with this model regarding the  
> subsumption relation between :Person and the classification criteria  
> classes :PersonByGender and :PersonByKinship, given that:
>
> - Who would be the individuals of classes such as :PersonByGender  
> and :PersonByKinship?

Exactly.

> For example, if we consider :John and individual of type :Man, we  
> can say that :John is also of type :Person.  But does it make sense  
> to say that :John is of type :PersonByGender???
>
> - Are these classes :PersonByGender and :PersonByKinship in fact  
> meta-classes?

I have no idea what a meta-class is, in your view. But if they are OWL  
classes, then they are identical to the OWL class Person. So I would  
suggest that this is not a useful design.

What I think you might find more useful (though it cannot be  
encompassed in OWL-DL) would be to classify the properties, a  
restriction on which defines the classes in question. Thus, if we were  
to say that Man is the restriction of hasGender to Male, for example,  
and that Parent is a hasValue restriction in the hasChild property,  
then it would be these properties which characterize the various  
classification  criteria with which your began. But this is just a  
suggestion.

Pat Hayes

> (If I could use an analogy with object-oriented design, it is as if  
> these two classes could be seen as abstract or deferred classes).
>
> This type of modeling scenario can be found in many concepts from  
> various domains (essentially any concept whose individuals/instances  
> could be grouped according to multiple different classification  
> criteria). Below is another popular example in the OWL literature  
> modified to fit into the same scenario and illustrate the problem [2]:
>
> :Wine
>     |-- :WineByColor
>     |   |-- :WhiteWine
>     |   |-- :RedWine
>     |   |-- (etc.)
>     |-- :WineByGrape
>          |-- :PinotGrigioWine
>          |-- :MerlotWine
>          |-- :CabernetSauvignonWine
>          |-- (etc.)
>
> In this case the classification criteria of :Wine are wines based on  
> their color and wines based on their type of grape.  Like in the  
> example of :Person, the classification criteria classes :WineByColor  
> and :WineByGrape seem intuitive choices to group the rest of all  
> subclasses of :Wine.

I believe that is the same mistake.

> However, the subsumption relation between :Wine <-  :WineByColor  
> and :Wine <- :WineByGrape seems problematic.  Who would be the  
> individuals of classes such as :WineByColor or :WineByGrape?
>
> In general terms, the subsumption relation between a :DomainConcept  
> and a :ClassificationCriterion for that concept seems a bit  
> controversial.  For example, It does not seem to fit into one of the  
> 4 kinds of is-a relations defined by Johansson[3] plus  I think it  
> would violate the constraints of the OntoClean evaluation as well.   
> (Even though, for the most part I understand the theory behind the  
> OntoClean method and I think it is very useful, I personally find it  
> a bit difficult to apply coming from a software developer background).
>
> In summary, after this lengthy introduction, below are the questions  
> that I am trying to answer:
>
> - Are subsumption relations such as :Person <- :PersonByGender  
> or :Wine <- :WineByGrape acceptable?

Well yes, but only in a trivial sense. I suspect that for the purposes  
you have in mind, the answer is no.

>
> - Can classes such as :PersonByGender or :WineByGrape be “correctly”  
> represented in the ontology model?  That is, classes that correspond  
> to a “classification criterion” and that may not have individuals  
> (or extensional representation) in the real world.

If they have no individuals then they are the empty class, which is  
also probably not what you want.

>
> - Are there some guidelines or good-practices on how to represent  
> concepts that correspond to a “classification criterion” of the  
> domain concept that is being modeled?

No.

>
> Thanks a lot for any comments you may have!
>
> (For the record, I'll mention that this work is part of my PhD  
> research.  One aspect of the overall idea is trying to adapt faceted  
> classification design guidelines to ontology design.  The notion of  
> “facet” and “classification criterion” seem to be fairly similar.  
> Identifying a reasonable representation of a “classification  
> criterion” in an ontology can help to bridge the gap between these  
> two design methodologies and that’s the reason for the examples  
> above.  Finally, I would like to present if possible, the overall  
> outcome as an ontology design pattern or combination of them).
>
> Regards,
> Bene Rodriguez-Castro
>
> Postgraduate Student | Intelligence, Agents and Multimedia Group |  
> School of Electronics and Computer Science | University of  
> Southampton | Southampton SO17 1BJ | United Kingdom | Phone: +44 23  
> 8059 4059 | Email: b.rodriguez@ecs.soton.ac.uk
>
> ----
> [1] http://protege.cim3.net/file/pub/ontologies/generations/generations.owl
> [2] http://protege.cim3.net/file/pub/ontologies/wine/wine.owl
> [3] Ingvar Johansson. Four kinds of is_a relations: genus- 
> subsumption, determinable-subsumption, specification, and  
> specialization. In WSPI 2006: Contributions to the Third  
> International Workshop on Philosophy and Informatics, Saarbrucken,  
> 2006.
>

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