Re: OEP] Constrained hierarchies and meta-classes

Hi Bernard, interesting case of overcommitment ...

At 0:00 +0200 9-06-2004, Bernard Vatant wrote:
>I have been struggling for a while to find out a generic 
>representation of situations of
>which the following one is an example. Seems close to the "Classes 
>as Values" issue, but
>quite different.
>
>Suppose I have the three following classes and instances
>
>Country :  France
>Region  :  Alsace
>City	  :  Strasbourg
>
>The instances Strasbourg, Alsace and France are bound by a partitive 
>(administrative or
>geographical) relationship
>
>Strasbourg	 partOf	Alsace
>Alsace	 partOf	France
>
>The classes themselves are instances of a meta-class "Geographical 
>Unit", being both Range
>and Domain of another hierarchical relation like "isSubdivisionOf" 
>(whatever, something to
>make it distinct from the partOf relation at instance level)
>
>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)))

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.

>2. How to express it in SW languages?

See above

>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. 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. 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.

Have a good time
Aldo

-- 
Aldo Gangemi
Research Scientist
Laboratory for Applied Ontology
Institute for Cognitive Sciences and Technology
National Research Council (ISTC-CNR)
Via Nomentana 56, 00161, Roma, Italy
Tel: +390644161535
Fax: +3906824737
a.gangemi@istc.cnr.it

Received on Tuesday, 8 June 2004 19:31:28 UTC