[Inquiry] Re: Examples! Examples! Examples!

[Jon Awbrey]

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EEE.  Note 28

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Example 1.  John Sowa's "Top Level Categories" (cont.)

I derived my first description of the TLC space, expressed in terms of
the axiom !a!, purely from looking at the lattice picture, Figure 2.6
in the text of 'KR' or Figure 1 at either of the following webloci:

http://www.jfsowa.com/ontology/toplevel.htm
http://users.bestweb.net/~sowa/ontology/toplevel.htm

Had I woken up in the other hemisphere of my brain on the day in question,
I might have begun by reading the text first and looking at the pictures
second, in which case I could have derived the proposition !b! (beta)
that is displayed in Table 16, from the discussion surrounding the
matrix table, Figure 2.7 in the text or Figure 2 on either of
the above webpages.

Table 16.  TLC in Cactus Language:  Proposition !b!
o-----------------------------------------------------------o
|                                                           |
|   (( Object        , Independent Physical Continuant ))   |
|   (( Process       , Independent Physical Occurrent  ))   |
|   (( Schema        , Independent Abstract Continuant ))   |
|   (( Script        , Independent Abstract Occurrent  ))   |
|   (( Juncture      , Relative    Physical Continuant ))   |
|   (( Participation , Relative    Physical Occurrent  ))   |
|   (( Description   , Relative    Abstract Continuant ))   |
|   (( History       , Relative    Abstract Occurrent  ))   |
|   (( Structure     , Mediating   Physical Continuant ))   |
|   (( Situation     , Mediating   Physical Occurrent  ))   |
|   (( Reason        , Mediating   Abstract Continuant ))   |
|   (( Purpose       , Mediating   Abstract Occurrent  ))   |
|                                                           |
|   (( Actuality     , Independent Physical ))              |
|   (( Form          , Independent Abstract ))              |
|   (( Prehension    , Relative    Physical ))              |
|   (( Proposition   , Relative    Abstract ))              |
|   (( Nexus         , Mediating   Physical ))              |
|   (( Intention     , Mediating   Abstract ))              |
|                                                           |
o-----------------------------------------------------------o

Each of the clauses in proposition !b! has the form of a propositional
equation, that is, a logical equivalence, between a single feature and
a conjunction of several features.  A clause of this form is naturally
comprehended as a "definition" of its lead feature in terms of a class
of more primitive stock features.

But it does not seem to me, just at first glance, that proposition !a!
and proposition !b! can be equivalent, inasmuch as !a! demands that
everything in the quotient universe of discourse be partitioned
into just one of 12 categories, while !b! only defines a set
of 18 features in terms of a stock of 7 others.

So let let next examine the relation between !a! and !b!.

Reference:

| John F. Sowa,
|'Knowledge Representation:
| Logical, Philosophical, and Computational Foundations',
| Brooks/Cole, Pacific Grove, CA, 2000.

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