ONT Re: Zeroth Order Theories (ZOT's)
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Example. Partition, Genus & Species (cont.)
Last time we considered in general terms how the forms
of complete partition and contingent partition operate
to maintain mutually disjoint and possibly exhaustive
categories of positions in a universe of discourse.
This time we contemplate another concrete Example of
near minimal complexity, designed to demonstrate how
the forms of partition and subsumption can interact
in structuring a space of feature specifications.
In this Example, we describe a universe of discourse
in terms of the following vocabulary of five features:
L. living_thing
N. non_living
A. animal
V. vegetable
M. mineral
Let us construe these features as being subject to four constraints:
1. Everything is either a living_thing or non_living, but not both.
2. Everything is either animal, vegetable, or mineral,
but no two of these together.
3. A living_thing is either animal or vegetable, but not both,
and everything animal or vegetable is a living_thing.
4. Everything mineral is non_living.
These notions and constructions are expressed in the Log file shown below:
Logical Input File
o-------------------------------------------------o
| |
| ( living_thing , non_living ) |
| |
| (( animal ),( vegetable ),( mineral )) |
| |
| ( living_thing ,( animal ),( vegetable )) |
| |
| ( mineral ( non_living )) |
| |
o-------------------------------------------------o
The cactus expression in this file is the expression
of a "zeroth order theory" (ZOT), one that can be
paraphrased in more ordinary language to say:
Translation
o-------------------------------------------------o
| |
| living_thing =/= non_living |
| |
| par : all -> {animal, vegetable, mineral} |
| |
| par : living_thing -> {animal, vegetable} |
| |
| mineral => non_living |
| |
o-------------------------------------------------o
Here, "par : all -> {p, q, r}" is short for an assertion
that the universe as a whole is partitioned into subsets
that correspond to the features p, q, r.
Also, "par : q -> {r, s}" asserts that "Q partitions into R and S.
It is probably enough just to list the outputs of Model, Tenor, and Sense
when run on the preceding Log file. Using the same format and labeling as
before, we may note that Model has, from 2^5 = 32 possible interpretations,
made 11 evaluations, and found 3 models answering the generic descriptions
that were imposed by the logical input file.
Model Outline
o------------------------o
| living_thing |
| non_living - | 1
| (non_living ) |
| mineral - | 2
| (mineral ) |
| animal |
| vegetable - | 3
| (vegetable ) * | 4 *
| (animal ) |
| vegetable * | 5 *
| (vegetable ) - | 6
| (living_thing ) |
| non_living |
| animal - | 7
| (animal ) |
| vegetable - | 8
| (vegetable ) |
| mineral * | 9 *
| (mineral ) - | 10
| (non_living ) - | 11
o------------------------o
Tenor Outline
o------------------------o
| living_thing |
| (non_living ) |
| (mineral ) |
| animal |
| (vegetable ) * | <1>
| (animal ) |
| vegetable * | <2>
| (living_thing ) |
| non_living |
| (animal ) |
| (vegetable ) |
| mineral * | <3>
o------------------------o
Sense Outline
o------------------------o
| living_thing |
| animal |
| vegetable |
| non_living |
| mineral |
o------------------------o
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