Production systems and cognitive modelling

Now to get onto some psychology at last: some more detailed reading on production systems and modelling.

• Learning and Problem Solving 3, Open University Course D303, Block 4, Units 26--28, pp 83--118. This shows production systems at work modelling two different tasks, and discusses some of the issues in designing a good model.

• Boden, Computer models of Mind, 154--168 and 210--213. Pages 210--213 deal with the same topic as pp 112--117 of the OU book: modelling childrens' performance on the task of seriation (picking bricks and putting them in order of size) and how their cognitive development improves performance. The task was explained by Piaget in terms of sudden progressions from one stage of development to another. Boden's description of the production system model is less detailed than the OU book's, but she's stronger on discussing its fit with Piaget's analysis.

  Note when reading her productions that you work from the bottom up, not the top down!

  Pages 154--168 continue from the topic of GPS as a model to production systems. Page 164 lists what Newell and Simon take to be the architectural features of the mind.

You may find the OU book heavy going if you work straight through from page 83. Unfortunately, it starts by discussing models of cryptarithmetic-solving, and they are not particularly simple.

Possibly this order will help:

• Pages 112--117 OU: seriation.

  See what Young was trying to do with his model. Try dry-running the simple rules in figure 25 page 115.

  The notation for rules is different from before. The condition and action are separated by arrows. In the condition, there are tests of the form goal=seriate or goal=add first block. These test the top goal on the goal stack, which is a part of STM. In terms of the next paragraph, these look at the top message on the spike, never anything lower down. There are also tests of the form ``task just started'' or ``holding block in hand''. These test perceptions of the outside world.

  In the action, there are things like push(goal = add first block). This put the symbols add first block onto the goal stack. Think of the goal stack as a spike, initially empty, onto which you can push bits of paper. push(goal = add first block) pushes a piece of paper with goal = add first block onto the spike. As mentioned above, the tests goal = X always look at the message at the top: anything lower down is invisible until it's uncovered.

  There are also actions of the form pop goal stack. These take the top (and only the top) piece of paper off the spike, uncovering what's underneath.

  This notion of a stack is described on p 105 of the OU book. Using goals stored on a stack to control rules is a bit like what Bagger did. The difference is that Bagger only ever noted one goal (the current goal). Here, we can store a whole stack of them.

  Question: is this psychologically realistic? How deep can the stack be?

• Pages 210--213 of Boden.

  Read the comparison between this model and Piaget's explanation.

• OU, pages 83--94.

  Skim the computational details, except in section 2.4. Pick out the issues relevant to psychological modelling. Note the comment about ``cheats'' on p 92. Ignore comments about SOLO (it's a bit like Prolog, if you know Prolog). For STRIPS, read GPS: in the points he's making, there's little difference between them.

• OU, pages 95--102.

  Read in detail. Note the concepts of production memory, working memory (i.e. STM), how rules are activated, conflict resolution.

• OU, pages 103--111.

  Note the three different strategies. In general, you can make many different sets of production rules to model any one behaviour. How do you know which best fits the mind....?

• OU, seriation again.

  Now go back and dry-run the different sets of rules. See how well they model a child as it develops.

• Boden, pages 154--168.

  The issue of modelling.