[topicmapmail] Getty Art and Architecture Thesaurus On Line

[Nagarjuna G.]

On Sun, Aug 31, 2003 at 12:20:07PM -0400, Thomas B. Passin wrote:
> [Kal Ahmed
> > Is instanceOf really a transitive relation ? I don't believe it is.
> >
> > Kal instanceOf Homo Sapiens
> >
> > Homo Sapiens instanceOf Species
> >
> > Kal instanceOf Species ?
> >
> > Subclass/superclass *is* transitive, but not instanceOf. Unless you mean
> > something different to a class-instance relationship by 'instanceOf'
> >
> 
> I do not think that this illustrates anything about transitivity.  Rather,
> this is the class/instance conundrum.  Is an "instance" of a class supposed
> to be a class or an individual?  If it is supposed to be an individual, you
> would not say "Homo Sapiens instanceOf Species".  If it is allowed to be a
> class, how do you know how to distinguish an instance as a class form an
> instance as an individual?
> 
> This has been discussed before, in this and other lists, but I confess that
> I am still not clear on how to deal with the issue except to rule that an
> "instance" by definition means an individual member of some class.  I gather
> that this is not altogether satisfactory because sometimes one does want the
> individual to be a class - although this is getting into the dangerous
> waters of the class of all classes

I dont think the matter is only regarding distinguishing between
class-subclass relation from class-instance relation.  subclassOf and
instanceOf are semantically different.  I do think we should maintain
this distinction.  Eg., Mammal, Primates, Homo sapiens are
Classes/Types, where as this particular cat, and Socrates are
individuals/tokens.  Transitivity will not create a problem if we are
representating this domain with instanceOf relation.  Problems arise
because of the kind illustrated by Kal: `Homo sapiens instanceOf
species'.  Why?  Because `species' is the name of a taxonomic
*category* and not a name of an individual.  This example states an
orthogonal fact.  The problem in my opinion arose because we mixed
categories with classes and individuals.  Categories may also be
classes, but it is clearly a metalevel description, for their
instances are always classes and never individuals.  Transitivity will
not be a problem if we dont do this mixing.

The big question to ask is: are these distinctions between,
categories, classes, and individuals maintainable?  I personally think
we should maintain.  

A suggestion: We can avoid these invalid inferences if we mark them
properly as topicTypes of a special kind, constraint being their
instances/members are never individuals.  The other possibility is to
represent these categories like `species' as attributes of topicTypes,
and not as topicTypes.  If we treat them as attributes the inference
problems due to transitivity may never arise, since attribution is
orthogonal to membership.

Nagarjuna
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