RE: OEP] Constrained hierarchies and meta-classes

At 10:37 +0200 9-06-2004, Bernard Vatant wrote:
>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
>individuals.
>
>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 ...

Let me reformulate your case:

1) documentalists maintain heading hierarchies (I assume they are a 
sort of "topic")
2) documentalists manipulate folders (I assume folders are locations 
of books or documents)
3) documentalists declare some relation between folders ("subFolderOf")
4) ???categories are defined wrt to the subFolder relation???
5) ???a category is a subClassOf Folder???

I am lost. Maybe you could provide an excerpt of a folder set, and an 
excerpt of a heading hierarchy, so that our intuition gets closer to 
the point.

>... 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?

As usual, I do not care much about what representation primitives 
should be used, until I do understand the intended meaning of the 
experts. OK, documentalist use informal structures, but before 
deciding on what formal structure we can suggest, we need to know 
what they want ro talk about, and for what purpose.


>  > 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.

Perfect. Then let's understand what's the intended meaning and use of 
each pattern, schema, etc., and then let's find if any reusable 
relation already exists, what characteristics should be encoded, etc.
Once we have understood that, we can easily choose the appropriate 
logical form to be used to encode the ontology.
I interpret "representing at best the legacy" as a good encoding of 
the intended meaning/use, not as a (possibly awkward) encoding of the 
original structure.
If we are able to understand the semantics of the legacy, we can even 
reproduce the original format or syntax, but being aware of the 
underlying semantics.

>  > 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.
>
>Indeed
>
>>  >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).

Give me some example to judge on awkwardness ...

>  > 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 ...

A mereology as an ontology of part is any theory that includes part 
relations in its signature, and provides axioms for that relation wrt 
a specified domain. There is a lot of curious or fancy stuff out 
there, but let's try to stay focused ...

Ciao
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 Friday, 25 June 2004 10:16:10 UTC