[topicmapmail] Hierarchy PSIs

[Murray Altheim]

tpassin@comcast.net wrote:
> Bernard Vatant wrote -
[...]
> Bernard, that is very astute of you!  You are suggesting, are 
> you not, that there should be one "master" strict hierarchy 
> association type (designated by a PSI)?  I could support such 
> a thing.  I think it would be desirable to provide a partial-
> ordering-only association type as well.  Would you agree?  
> Any suggestions for a name for a virtual hierarchy association type?

Tom,

I certainly believe Bernard is more qualified to answer this
than I (his mathematical chops are better than mine), but I
think you may be misinterpreting "partial", which isn't the
converse of "strict". In creating an 'ur-hierarchy', I believe
one must also create definitions for sets, collections,
classes, and the like, and define membership in terms of
intentionality or extensionality. Absent this people will
generally misinterpret the various things available to them,
e.g., conflating sets and collections.

But I think we are onto something. Since I believe we've all
referenced Sowa, one look at Figure 2.14 (p.95 of KR) shows
a generalization hierarchy, and that PartialOrdering may be
the place we want to start. I'll try to reproduce a bit of
that diagram here:

                  Tautologies
          ________/  |  \________________
         /           |   \               \
        /            |    \               \
    Antisymmetry     |     \          Symmetry
        \            |      \             /
         \    Transitivity  Reflexivity  /
          \        /    \      |        /
           \      /      \     |       /
            \    /        \    |      /
          PartialOrdering  Equivalence
            /      \
           /        \
        Trees      Lattices ______________
          \        /     |        \       \
           \      /      |         \       \
       LinearOrdering  Theories  Types  Collections
         /    \                          /    \
        /      \                        /      \
    Sequences  Numbers                Sets    Mereology
                                              /   |   \
                                             /    |    \
                                      Discrete  Lumpy  Continuous


This all has to do not with truth values but with theories, which
are (to my understanding) the basis of ontological commitments.
Maybe Bernard can shed some more light, and I'll probably tag John
on maybe lending a hand too.

Murray

......................................................................
Murray Altheim                    http://kmi.open.ac.uk/people/murray/
Knowledge Media Institute
The Open University, Milton Keynes, Bucks, MK7 6AA, UK               .

     "The US Government has expanded its recall of beef after the
      discovery of its first case of "mad cow" disease. Officials
      had said the meat from the infected cow, slaughtered on
      9 December in Washington State, went to Oregon, California,
      Nevada and Washington. They have now determined that meat
      from the same facility, killed on the same day, went to
      Alaska, Hawaii, Montana, Idaho and the territory of Guam."
      http://news.bbc.co.uk/1/hi/world/americas/3352911.stm

    One cow distributed across nine states and territories. Maybe
    if we were buying meat raised and slaughtered locally, and not
    feeding meat to herbivores (to increase profit, not quality)
    this might not have happened.