Cf: Theme One Program • Jets and Sharks 1
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
) 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
To be continued …
• 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.
• Theme One Program • User Guide
• Example. Jets and Sharks