SUO: *Date 14 Apr 2002 -- Modulated Logic
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| Conches and kettledrums,
| cymbals, tabors, and trumpets
| were sounded at once
| and the din of tumult arose.
|
| Sanjaya -- Bhagavad Gita, 1.13.
|
|'The Bhagavad-Gita: Krishna’s Counsel in Time of War'.
| B.S. Miller (trans.), Bantam Books, New York, NY, 1986.
Modulated Logic
The Themes Out Of One School Of Model Theory
Do Yet Play On That Nonpareil Ontology Field.
Here Is The Programme As It Extends This Day:
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Model Theory
1. Introduction
1.1. What Is Model Theory?
01. http://suo.ieee.org/ontology/msg03985.html
02. http://suo.ieee.org/ontology/msg03986.html
03. http://suo.ieee.org/ontology/msg03987.html
1.2. Model Theory for Sentential Logic
04. http://suo.ieee.org/ontology/msg03988.html
05. http://suo.ieee.org/ontology/msg03989.html
06. http://suo.ieee.org/ontology/msg03991.html
07. http://suo.ieee.org/ontology/msg03992.html
08. http://suo.ieee.org/ontology/msg03993.html
09. http://suo.ieee.org/ontology/msg03994.html
10. http://suo.ieee.org/ontology/msg03995.html
11. http://suo.ieee.org/ontology/msg03996.html
12. http://suo.ieee.org/ontology/msg03997.html
13. http://suo.ieee.org/ontology/msg03999.html
14. http://suo.ieee.org/ontology/msg04000.html
15. http://suo.ieee.org/ontology/msg04001.html
16. http://suo.ieee.org/ontology/msg04002.html
17. http://suo.ieee.org/ontology/msg04003.html
18. http://suo.ieee.org/ontology/msg04004.html
1.3. Languages, Models, and Satisfaction
19. http://suo.ieee.org/ontology/msg04005.html
20. http://suo.ieee.org/ontology/msg04006.html
21. http://suo.ieee.org/ontology/msg04007.html
22. http://suo.ieee.org/ontology/msg04008.html
23. http://suo.ieee.org/ontology/msg04009.html
24. http://suo.ieee.org/ontology/msg04010.html
All of the above material is excerpted from:
| C.C. Chang and H.J. Keisler, 'Model Theory',
| North-Holland, Amsterdam, Netherlands, 1973.
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We have just broached the sections on predicate logic,
and the presentation there might be worth your review
as giving a dutiful treatment to the standard banners.
There are a couple features of the authors' presentation
that perhaps deserve comment. They expend what may seem
like an inordinate amount of attention on the subject of
sentential logic (Section 1.2), a topic that would often
be shrugged off with the usual rap on truth tables. Why?
Two reasons why this makes such good sense come to mind:
1. The authors are working, like bricklayers, if you will,
laying down the "minimal modules" of their subject matter
one incremental "course" at a time, and meanwhile availing
themselves of the opportunity to demonstrate a number of the
most fundamental methods of the larger subject in rudimentary
and much less overwhelming, but still utterly essential forms.
2. One could actually do a lot more at this level of logic
than most people suspect -- for instance, almost all of
the "latticework" that we have struggled to build up in
in work on ontology so far is quite easily incorporated
within the more patent fenestrations of an architecture
"degree zero", as I have often stated or exhibited here.
Some of the wisdom of this course of action will become evident when and if
we make it to the section on "Quantifier Elimination" (Section 1.5), which
demonstrates one of the techniques that is frequently exploited in all of
the "industrial strength" mathematical theorem provers even to this day.
This all brings me back to my heuristic device from the other day:
| Watch your P's and Q's and R's. Mnemonically unpacked:
| Discern and tease apart from their warly entanglements
| Propositional, Quantificational, Relational attributes
| along their natural filaments, laminations, striations.
In the light of several recent discussions, that once again
pit "efficiency" and "expressiveness" versus one another in
the sort of contest that the dyadic spectator no doubt sees
as being inescapable, I can add along these lines one point:
There is one moderating factor that is routinely overlooked
on this field of battle, to wit, the "expressive efficiency"
of the syntax selected, and that, I aver, need not be fixed.
In this regard, I am less worried than others are about the
proven limitations of "order one predicate calculus" (OOPC).
It is an information channel, and every information channel
has its limits, no matter how well we "legis/negotiate" the
"rules of the road" at the Chunnel Crossover, and so end up
with a Drive By Chuting A Rapid Rap Of Viscous Etudes, else
a Demolition Derby.
The Pragmatic Question,
Is, As Ever, How Much
Can We Get For Our
Quantum Of Logic?
Jon Awbrey
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