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RE: OEP] Constrained hierarchies and meta-classes

From: Bernard Vatant <bernard.vatant@mondeca.com>
Date: Wed, 9 Jun 2004 10:37:42 +0200
To: "Aldo Gangemi" <a.gangemi@istc.cnr.it>, "SWBPD" <public-swbp-wg@w3.org>
Message-ID: <GOEIKOOAMJONEFCANOKCGEKEEEAA.bernard.vatant@mondeca.com>

Hi Aldo

Thanks for your input. Comments below.

> >Region subdivisionOf  Country
> >City   subdivisionOf  Region
> >
> >It's clear that this relation is neither a subClassOf, nor a partOf relation
> I don't see the need for these metaclasses. A class can be the domain
> or range of a relation without any postulated metaclass needed. We
> can say that Country is a subclassOf Geographical Unit.

> For example (in OWL abstract syntax):
> Class(Country partial
>   GeographicalUnit)
> Class(Region partial
>   GeographicalUnit
>   (restriction(subdivisionOf someValuesFrom Country)))
> Class(City partial
>   GeographicalUnit
>   (restriction(subdivisionOf someValuesFrom Region)))

I've been through that path. It assumes that the generic hierarchy (between classes) can
be defined by restrictions put on the hierarchy used at instance level. So there is no
point in wanting to express this generic hierarchy by a direct relation using classes as

OTOH, in some contexts, modeling habits have led to different vocabularies for the generic
hierarchy and instance hierarchy. For example, in documentation management, documentalists
can be constrained to map their folder hierarchy on a so-called "taxonomy" (hierarchy of
"headings" or "categories"). And it's not obvious to port the above type of modeling in
this domain:

- A Folder is an instance of a generic Category, itself a subclass of Folder
- The Category hierarchy is defined by restrictions on the Folder-SubFolder relation ...

... This is technically correct, but quite difficult (not to say almost impossible) to
explain to documentalists, very unfamiliar with the class-instance paradigm, let alone
property restrictions :(
There again, do we want to push what we consider is "right" modeling, or represent at best
the legacy?

> therefore ...
> >I have three questions about it :
> >
> >1. What generic kind of relation is subdivisionOf? What are the
> >modeling current
> >practices?
> I use "geographic part" relations, like your "subdivisionOf" for part
> applied to political or functional geographic objects. My rationale
> is that political mereology has different characteristics from
> physical mereology, like part when applied to rocks.
> Then, the relationship between Strasbourg and Alsace is simply an
> instance of the "subdivisionOf" relation.

Agreed, but the distinction between administrative vs geographical mereology is an
orthogonal issue.

> >2. How to express it in SW languages?
> See above

Seen :))

> >3. How to express that the hierarchy defined by the partOf relation
> >is "conformant" to, or
> >"inherited from" the hierarchy declared by the subdivisionOf relation,
> If you refer to partial orders, you should decide on which relation
> creates that order, and then you can start evaluating morphisms
> between different orders.

Exactly. It's all about morphisms. Not necessarily restricted to partial orders, though.
It can be extended to any generic pattern or organization scheme using different relation
types, like e.g. a publication schema organizing its different parts (Introduction, (
Chapter, Paragraph* )*, Table of Contents, Bibliography ...) using both "subdivision" and
"succession" relations.

> But I don't think your example needs that .
> Conformity in your example applies between individuals (Strasbourg,
> etc.), and classes (City, etc.), in the sense that asserting triples
> on individuals should not violate the restrictions given on the
> classes.


> >without having to
> >declare each specific restriction it entails, e.g:
> >
> >Any City is part of some Region
> >Any Region is part of some Country
> >...
> Why not? this is the standard way to do it.

Standard, indeed, but a bit awkward if you have a lot of classes, like in the above
example of Folders and Categories (which is actually the original use case I was
struggling with).

> The problem (if any) is
> about *your* intended meaning of part or subdivision: what
> individuals are in the universe of those relations? are those
> relations transitive?, etc.

Browsing literature about mereology, it seems that it often confuse, like NL does, generic
relations like "Region is part of Country" or "Head is part of Body" and specific ones
like "Alsace is part of France" or "My head is part of my body". Not sure of what the
individuals are in the generic example ... seems to me they assert relation between
concepts, not unlike a "Broader-Narrower" in a thesaurus, rather than implicit
restrictions on instances of implicit classes.
There again, we are close to the "classes as values" issue ...


Bernard Vatant
Senior Consultant
Knowledge Engineering
Mondeca - www.mondeca.com
Received on Wednesday, 9 June 2004 04:38:06 UTC

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