SUO: Re: Examples! Examples! Examples!
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EEE. Note 26
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Example 1. John Sowa's "Top Level Categories" (cont.)
The axiom !a! that picks out a portion of the
universe of discourse TLC = <|a_1, ..., a_25|>
contains a conjunct of the following form that
specifies a "universal partition" into twelve
mutually exclusive and exhaustive categories:
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| |
| (( Description ),( History ),( Juncture ),( Object ), |
| ( Participation ),( Process ),( Purpose ),( Reason ), |
| ( Schema ),( Script ),( Situation ),( Structure )) |
| |
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As long as we are focusing solely on the points of the TLC model space
that satisfy this partition property, then it is possible to exploit a
huge redundancy in the description of these points, namely, as soon as
we know that a given point x has any one of these 12 features, then we
know right off that it does not have any one of the others.
The component of my Theme One program that does logical modeling
makes good use of this brand of information-theoretic redundancy,
in the settings where it applies, and a good picture of how this
all works out can be seen as we turn to the task of finding all
of the models that the TLC axiom !a! has in the universe of TLC.
One of the ultimate outputs of the program, when run on the TLC axiom !a!,
is the following text, which lists in outline form, the maximal consistent
sets of positive features that are allowed by its propositional constraints.
Table 13. Summary of "Model" Output for the TLC Axiom !a!
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| | |
| 1. | Object |
| | Continuant |
| | Actuality |
| | Independent |
| | Physical |
| 2. | Process |
| | Occurrent |
| | Actuality |
| | Independent |
| | Physical |
| 3. | Schema |
| | Continuant |
| | Form |
| | Independent |
| | Abstract |
| 4. | Script |
| | Occurrent |
| | Form |
| | Independent |
| | Abstract |
| 5. | Juncture |
| | Continuant |
| | Prehension |
| | Relative |
| | Physical |
| 6. | Participation |
| | Occurrent |
| | Prehension |
| | Relative |
| | Physical |
| 7. | Description |
| | Continuant |
| | Proposition |
| | Relative |
| | Abstract |
| 8. | History |
| | Occurrent |
| | Proposition |
| | Relative |
| | Abstract |
| 9. | Structure |
| | Continuant |
| | Nexus |
| | Mediating |
| | Physical |
| 10. | Situation |
| | Occurrent |
| | Nexus |
| | Mediating |
| | Physical |
| 11. | Reason |
| | Continuant |
| | Intention |
| | Mediating |
| | Abstract |
| 12. | Purpose |
| | Occurrent |
| | Intention |
| | Mediating |
| | Abstract |
| | |
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This output summarizes, in terms of positive features alone, all of
the points of TLC = <|a_1, ..., a_25|> that satisfy the TLC axiom !a!,
since the positive features listed here, in the presence of the given
partition constraints, suffice to determine all of the other features.
Jon Awbrey
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