Theme One Program • Jets and Sharks 2

Re: Theme One Program • Jets and Sharks • (1)

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.

$\text{Jets and Sharks} \stackrel{_\bullet}{} \text{Log File}$

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 $q : \mathbb{B}^{41} \to \mathbb{B}.$  Given $2^{41} = 2,199,023,255,552$ 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 $2^{2^{41}}$ boolean functions of the form $f : \mathbb{B}^{41} \to \mathbb{B}$ and $q$ is just one of them.

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

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 LabOnline, Section 2.3, Figure 2.1.
• 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.

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