Theme One Program • Jets and Sharks

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Jon Awbrey

Aug 25, 2022, 6:12:13 PM8/25/22
to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Theme One Program • Jets and Sharks 1
http://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/

All,

It is easy to spend a long time on the rudiments of learning and logic
before getting down to practical applications — but I think we've
circled square one long enough to expand our scope and see what
the category of programs envisioned in Theme One can do with
more substantial examples and exercises.

During the development of the Theme One program I tested successive
implementations of its Reasoning Module or Logical Modeler on
appropriate examples of logical problems current in the literature
of the day. The PDP Handbook of McClelland and Rumelhart set one
of the wittiest gems ever to whet one's app‑titude so I could hardly
help but take it on. The following text is a light revision of the
way I set it up in the program's User Guide.

Example 5. Jets and Sharks
==========================

The propositional calculus based on the minimal negation operator
( https://oeis.org/wiki/Minimal_negation_operator ) can be interpreted
in a way resembling the logic of activation states and competition
constraints in one class of neural network models. One way to do this
is to interpret the blank or unmarked state as the resting state of
a neural pool, the bound or marked state as its activated state, and
to represent a mutually inhibitory pool of neurons A, B, C by the
proposition (A , B , C). The manner of representation may be
illustrated by transcribing a well-known example from the parallel
distributed processing literature (McClelland and Rumelhart 1988)
and working through a couple of the associated exercises as
translated into logical graphs.

Displayed below is the text expression of a traversal string which
Theme One parses into a cactus graph data structure in computer memory.
The cactus graph represents a single logical formula in propositional
calculus and this proposition embodies all the logical constraints
defining the Jets and Sharks data base.

Display. Theme One Guide • Jets and Sharks • Log File
https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280a2-jets-and-sharks-e280a2-log-file.png&h=828

To be continued …

References
==========

• McClelland, J.L. (2015), Explorations in Parallel Distributed Processing :
A Handbook of Models, Programs, and Exercises, 2nd ed. (draft), Stanford
Parallel Distributed Processing Lab ( https://web.stanford.edu/group/pdplab/ ).
Online ( https://web.stanford.edu/group/pdplab/pdphandbook/ ),
Section 2.3 ( https://web.stanford.edu/group/pdplab/pdphandbook/handbookch3#x7-320002.3 ),
Figure 2.1 ( https://web.stanford.edu/group/pdplab/pdphandbook/jetsandsharkstable.png ).

• McClelland, J.L., and Rumelhart, D.E. (1988), Explorations in Parallel Distributed
Processing : A Handbook of Models, Programs, and Exercises, MIT Press, Cambridge, MA.
“Figure 1. Characteristics of a number of individuals belonging to two gangs, the
Jets and the Sharks”, p. 39, from McClelland (1981).

• McClelland, J.L. (1981), “Retrieving General and Specific Knowledge
From Stored Knowledge of Specifics”, Proceedings of the Third Annual
Conference of the Cognitive Science Society, Berkeley, CA.

Resources
=========

• Theme One Program • User Guide

• Example. Jets and Sharks
https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280a2-jets-and-sharks.odt
https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280a2-jets-and-sharks.pdf

Regards,

Jon
Theme One Guide • Jets and Sharks • Log File.png

Jon Awbrey

Aug 31, 2022, 12:12:28 PM8/31/22
to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Theme One Program • Jets and Sharks 2
http://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks-2/

Re: Theme One Program • Jets and Sharks 1
https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/

Example 5. Jets and Sharks (cont.)

All,

As we saw last time, Theme One reads the text file shown below and
constructs a cactus graph data structure in computer memory. The
cactus graph represents a single logical formula in propositional
calculus and that proposition embodies the logical constraints
defining the Jets and Sharks data base.

Our cactus graph incorporates a vocabulary of 41 logical terms, each of which
represents a boolean variable, so the proposition in question, call it “q”,
is a boolean function of the form q : B⁴¹ → B. Given 2⁴¹ = 2,199,023,255,552
we know a truth table for q takes over two trillion rows and a venn diagram
for q takes the same number of cells. Topping it off, there are 2^(2⁴¹)
boolean functions of the form f : B⁴¹ → B and q is just one of them.

Measures of strategy are clearly needed to negotiate patches of cacti like those.

To be continued …

Regards,

Jon
Theme One Guide • Jets and Sharks • Log File.png

Jon Awbrey

Sep 3, 2022, 4:20:18 PM9/3/22
to Cybernetic Communications, Laws of Form, Ontolog Forum, Structural Modeling, SysSciWG
Cf: Theme One Program • Jets and Sharks 3
https://inquiryintoinquiry.com/2022/09/03/theme-one-program-jets-and-sharks-3/

Re: Theme One Program • Jets and Sharks
https://inquiryintoinquiry.com/2022/08/25/theme-one-program-jets-and-sharks-1/
https://inquiryintoinquiry.com/2022/08/30/theme-one-program-jets-and-sharks-2/

Example 5. Jets and Sharks (cont.)

All,

Given a representation of the Jets and Sharks universe in
computer memory, we naturally want to see if that memory
serves to supply the facts a well-constructed data base
should.

In their PDP Handbook presentation of the Jets and Sharks example,
McClelland and Rumelhart suggest several exercises for the reader
to explore the performance of their neural pool memory model on
the tasks of retrieval and generalization (Exercise 2.1).
( https://web.stanford.edu/group/pdplab/pdphandbook/handbookch3#x7-330001 )

Using cactus graphs or minimal negations to implement pools of
mutually inhibitory neurons lends itself to neural architectures
on a substantially different foundation from the garden variety
connectionist models. At a high level of abstraction, however,
there is enough homology between the two orders to compare their
performance on many of the same tasks. With that in mind, I tried
Theme One on a number of examples like the ones suggested by
McClelland and Rumelhart.

What follows is a brief discussion of two examples as given in the
original User Guide. Next time I'll fill in more details about the
examples and discuss their bearing on the larger issues at hand.

With a query on the name “ken” we obtain the following output,
giving all the features associated with Ken.

Jets and Sharks • Query 1
https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280a2-jets-and-sharks-e280a2-query-1.png

With a query on the two features “college” and “sharks” we obtain
the following outline of all features satisfying those constraints.

Jets and Sharks • Query 2
https://inquiryintoinquiry.files.wordpress.com/2022/08/theme-one-guide-e280a2-jets-and-sharks-e280a2-query-2.png

From this we discover all college Sharks are 30‑something and married.
Further, we have a complete listing of their names broken down by occupation.
Theme One Guide • Jets and Sharks • Query 1.png
Theme One Guide • Jets and Sharks • Query 2.png