[topicmapmail] Getty Art and Architecture Thesaurus On Line

[Murray Altheim]

Thomas B. Passin wrote:
> [Murray Altheim]
> 
>>I think in this instance the answer comes from Peirce: class-instance
>>is a dyadic relation, and what we need is Thirdness, triadic relations.
>>I.e., class-instance relations should [usually] be stated within a
>>specific context. Something can be considered an instance of a class
>>in one context, but may be used as a class in another. In Topic Maps
>>one could scope the associations.
>>
>>So in the example provided, "Homo sapiens" is an instance of the
>>class of "species" (and would appear as such in a Topic Map describing
>>the zoological taxonomy),
>
> The terminology used by rdfs and OWL is sometimes very useful.  I'm thinking
> here of domain/range.  Say the relationship between "species" and "Homo
> sapiens" is class-subclass.  Then you could say
> 
> subclassOf domain Class
> subclassOf range Class
> "Homo sapiens" subclassOf species
>
> No ambiguity here. you could also invent a relationship instanceClass, say,
> to indicate that you want to consider a class to be an instance of another
> class, and you would give that relationship the same domain and range as
> subclassOf.  In fact, it is not clear to me why the two would be different
> relationships.

Except that to my understanding of RDF/OWL, what you've written, is that
the statements are incorrect. "domain" is not a subclass of "Class", nor
is "range" is not a subclass of "Class". Neither is "Homo sapiens" a
subclass of a species, rather an instance of a species. Perhaps I'm not
understanding what you're saying correctly, as this seems fairly straight-
forwardly wrong. Could you clarify?

> With an instance that is supposed to be an actual individual thing, not a
> class, you could make up a new relationship, say individualInstanceOf.  Then
> you could have something like this -
> 
> individualInstanceOf domain Class
> individualInstanceOf range IndividualThing
> 
> My point here is that I think of these two usages of "instance" as different
> relationships, since they have different ranges.  [...]

Actually, better definitions can be found in either Cyc, SUO, or the
recently-announced ISO 15926 definitions. See

  http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lifecycle_integration_schema.html

particularly

  Class
  http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lexical/class.html

  Class of Class
  http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lexical/class_of_class.html

  Class of Class of Individual
  http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lexical/class_of_class_of_individual.html

  Class of Individual
  http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lexical/class_of_individual.html

  Possible Individual
  http://www.tc184-sc4.org/wg3ndocs/wg3n1328/lifecycle_integration_schema/lexical/possible_individual.html

Now, there are many ways to skin a cat. I'm not particularly fond of this
scheme, but it apparently works for the audience of ISO 15926.

 > Of course, it is hard to
> be certain without a good definition of "Class" and "Instance", which we do
> not have.  In OWL, a class is not just a set of individuals.  Instead, a
> class somehow is associated with a collection of individuals, but is
> distinct from that set.  Apparently this bit of trickery has made OWL
> mathematically tractable.
>
> Notice that this approach is different from saying that a class is a set of
> individuals that is ussed for the purposes of classification, which is
> another definition that is sometimes used (not is OWL).

The problem is not that there isn't an available definition of a class-
instance relationship, it's that there are a number of competing ones,
such as classes built upon their membership (extensive) or by their
characteristics (intensive).

> Maybe we should define what a class is, for the purposes of being more
> precise about themeaning of superclass-subclass and instanceOf.

I think a more appropriate thing than *us* doing it, is to simply use
PSIs pointing to the various existing definitions as developed within
each of the various competing schools of thought on the subject. For
example, I don't agree with much of *any* of this, so I don't use any of
these definitions. As I said, I tend to agree with Peirce and think that
knowledge representation only has validity as a form of communication
of non-Platonic concepts within a specific, given interpretation. You
need thirdness, context.

I don't believe you can create static, universal class definitions. John
Sowa has stated [1][2] that he thinks that through careful analysis the
human community could eventually "discover" these Platonic ideals. Well,
that to me is religiousity in a nutshell. So for myself, I should say
that you don't have to believe me either. You just choose the school
of thought you like to believe in (since this is ultimately an act of
faith, not science) and use PSI identifiers to provide your audience
with the definitions you like. Very egalitarian approach, I think. Nobody
has to be right or wrong.

Murray

[1] http://www.infoloom.com/pipermail/topicmapmail/2003q2/004805.html
[2] http://suo.ieee.org/email/msg09656.html
...........................................................................
Murray Altheim                         http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK                    .

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