Theme One Program • Jets and Sharks
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Jon Awbrey
Jun 21, 2024, 1:00:29 PM (9 days ago) Jun 21
to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG
Theme One Program • Jets and Sharks 1
• https://inquiryintoinquiry.com/2024/06/20/theme-one-program-jets-and-sharks-1-a/
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 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 “minimal negation operators”
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 minimal negation 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.
Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator
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.
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
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/ )
( 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.
Regards,
Jon
cc: https://www.academia.edu/community/VWYGZo
• https://inquiryintoinquiry.com/2024/06/20/theme-one-program-jets-and-sharks-1-a/
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 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 “minimal negation operators”
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 minimal negation 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.
Minimal Negation Operators
• https://oeis.org/wiki/Minimal_negation_operator
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.
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
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/ )
( 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.
Regards,
Jon
cc: https://www.academia.edu/community/VWYGZo
Jon Awbrey
Jun 23, 2024, 8:24:52 PM (6 days ago) Jun 23
to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG
Theme One Program • Jets and Sharks 2
• https://inquiryintoinquiry.com/2024/06/22/theme-one-program-jets-and-sharks-2-a/
Re: Theme One Program • Jets and Sharks 1
• https://inquiryintoinquiry.com/2024/06/20/theme-one-program-jets-and-sharks-1-a/
Example 5. Jets and Sharks (cont.)
As we saw last time, Theme One reads the text file shown below
and constructs a cactus graph data structure in computer memory.
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.
Resources —
Theme One Program • Overview
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview
Theme One Program • Exposition
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition
Theme One Program • User Guide
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
Regards,
Jon
cc: https://www.academia.edu/community/V319WE
• https://inquiryintoinquiry.com/2024/06/22/theme-one-program-jets-and-sharks-2-a/
Re: Theme One Program • Jets and Sharks 1
• https://inquiryintoinquiry.com/2024/06/20/theme-one-program-jets-and-sharks-1-a/
Example 5. Jets and Sharks (cont.)
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.
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
Our cactus graph incorporates a vocabulary of 41 logical terms, each
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
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.
Resources —
Theme One Program • Overview
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview
Theme One Program • Exposition
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition
Theme One Program • User Guide
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
Regards,
Jon
cc: https://www.academia.edu/community/V319WE
Jon Awbrey
Jun 25, 2024, 2:40:48 PM (5 days ago) Jun 25
to Cybernetic Communications, Laws of Form, Structural Modeling, SysSciWG
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 1 & 2
• 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.)
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).
Exercise 2.1 • Retrieval and Generalization
• 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.
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/ )
( 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.
• https://inquiryintoinquiry.com/2022/09/03/theme-one-program-jets-and-sharks-3/
Re: Theme One Program • Jets and Sharks 1 & 2
• 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.)
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).
Exercise 2.1 • Retrieval and Generalization
• 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.
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/ )
( 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 • Overview
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview
Theme One Program • Exposition
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition
Theme One Program • User Guide
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
Regards,
Jon
cc: https://www.academia.edu/community/LbrKkqTheme One Program • Overview
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Overview
Theme One Program • Exposition
• https://oeis.org/wiki/Theme_One_Program_%E2%80%A2_Exposition
Theme One Program • User Guide
• https://www.academia.edu/5211369/Theme_One_Program_User_Guide
Survey of Theme One Program
• https://inquiryintoinquiry.com/2024/02/26/survey-of-theme-one-program-6/
Regards,
Jon
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