[topicmapmail] Undue Violence to Collections vs. Classes?

[Murray Altheim]

I think most of us who were involved in the development of XTM 1.0
would agree that our specification of the PSIs for class-instance
and superclass-subclass were relatively underspecified, perhaps
even by design. Leaving some measure of generality allows for a
variety of interpretations, which can be seen in both positive and
negative light. Ambiguity has both its pros and cons.

Over the past few years my own work has leaned heavily on both of
these PSIs (and their role PSIs), and I've often felt that perhaps
I was stepping out onto rather shakey territory. Now that I'm actually
beginning to use these PSIs in inferencing, I'm seeing that I either
need to "stretch the truth" of their definitions or begin using a
different set.

Most of this comes about due to the lack of definition of "class",
or perhaps a poor choice of words in XTM. People often believe they
understand the definition of the term "set" or "class", but of
course this is more complicated than the naive understanding. I've
been looking for the past few months at mereology and more recently
mereotopology, and they back at Cyc, and realizing that the thing
I've/we've been calling classes are in many cases actually collections.
For example, the two most common relations in Cyc are #$isa and
#$genls, the class-instance and superclass-subclass relations. But
no, actually not. In Cyc, they're actually collection-instance and
supercollection-subcollection. It doesn't sound as nice, but it's
more accurate.

This has rather subtle but profound impacts on taxonomy design,
as the differences between collections and extensional and
intensional sets are not ignoreable. I don't claim to be the expert
on logic that I would like to be, so rather than create new PSIs I
thought I'd throw this open for a bit of discussion with the group...

For a background on this, there's Sowa's chapter [KR], plus the
documentation on the Cyc site [CYC]. As Sowa notes, Lenat and
Guha (developers of Cyc) have admitted that they freely intermix
the usage of collection, set and category. This is either a good
thing or a bad thing, I don't know how to judge. The question is
really whether our similar choice in XTM's PSI language should be
left to stand, be changed, or at least be commented upon.

Murray

________________
[KR] Chapter 2.6 "Sets, Collections, Types and Categories" in
     "Knowledge Representation", John F. Sowa, pp.97-109.
[CYC] on #$isa and #$genls:
   http://www.cyc.com/cycdoc/vocab/fundamental-vocab.html#isa
   http://www.cyc.com/cycdoc/vocab/fundamental-vocab.html#genls
and a tutorial on "Sets and Individuals in Cyc":
   http://www.cyc.com/cycdoc/course/collections-module.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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