Solution Strategies, Transfer, and Computational Resources II: Move Pattern Strategy     Perceptual Predicates      The figure below provides a list of the perceptual predicates used in this Tower of Hanoi Problem. Notice that the column on the left is labeled functional and that on the right is labeled basic. Basic perceptual predicates are assumed to be part of the problem independent perceptual predicates possessed by the problem solver.      In contrast, functional predicates are assumed to be perceptual predicates that have been developed as a result of understanding and solving a particular problem - they are problem dependent. For example, the functional predicate in the third row is ABOVE(X,Y).  This predicate is defined as true if 'a disk X that is on the peg of disk Y and X is a larger disk than disk Y.      The functional predicate in row 4, FREE(A,X), has a relatively complex definition involving a universal quantifier. It is true 'if for all disk Y, Y is on A implies Y is larger than disk X.'      Now one could define hundreds of predicates over the problem solving context. For example, one could define a predicate that is true 'if the first and third pegs are both empty or if one peg holds an even number of disks at the same time as the other holds an odd number of disks and the middle peg is empty.' This appears to be a totally arbitrary predicate. However, one could probably imagine some problem solving context where it could have functional significance.      There is a sense in which the problem solver sees the situation in terms of the problem. This is an important observation that is often overlooked. Recall the observations that we made in discussing the nature of human chess expertise. Again, the experts "see" the chess board differently. Similarly, there is evidence that a radiologist "sees" the radiological images differently than you and I. Adapted from Simon, Herbert A. "The functional equivalence of problem solving skills." Cognitive Psychology, 1975, 7, 268-288. The next part of this section on learning considers the learning of concepts from the game of baseball. It will be very obvious in this context that the basic observational language must be mapped to the functional language of plans in order to understand the game.   Move Pattern Strategy      The figure below depicts the Production Systems that realize the Move Pattern Strategy. Note that there are two coupled sets of production rules. The lower set represents the perceptual system. This system tests the predicate NEXT SMALLEST and is invoked by P4. T1 tests to determine if the problem is solved, if not then T2 returns the value of the next smallest disk that is clear.       The smallest disk is always moved on odd-numbered moves. The Move Pattern Production system keeps track of this by setting the variable PARITY appropriately. P2 applies when this variable has the value ODD. Its action is to move the smallest disk to the next peg that is in the cycle which is returned by the function NEXT(P(I)), and then to set PARITY to EVEN.      If the variable NEXT-SMALLEST has a value then that disk is moved and the variable deleted. Finally, when the memory holds EVEN and no value for NEXT-SMALLEST, P4 is invoked. P4 invokes the Production System for Perceptual Tests which returns the number of that disk which is next smallest and clear. Adapted from Simon, Herbert A. "The functional equivalence of problem solving skills." Cognitive Psychology, 1975, 7, 268-288.       In this strategy the only information that must be retained in memory is the parity of the move and the value of the disk that can be moved on even moves. Embedded in the move actions are variables, I or J which hold the value of a peg number and functions P(I) which returns the number of the peg that Disk I occupies and O(P(I) ,P(J))) which returns the value of the peg which is occupied by neither Disk I nor Disk J.     Thus, very little memory is required since the perceptual component is responsible for relaying the required information about the current state of the problem. Note that this system identifies the disk that satisfies the preconditions for the move. However, the receipt and use of this perceptual information must be coordinated with the overall strategy. This is the task of the upper or controlling production system      Note that this strategy transfers to problems involving any number of disks and can be adapted for any choice of starting and final destinations of the stack of disks. It does not transfer to problems involving state pairs drawn from other states in the state space.

	Solution Strategies, Transfer, and Computational Resources I
	Solution Strategies, Transfer, and Computational Resources III: Goal Recursion Strategy	Tower of Hanoi Topics
© Charles F. Schmidt	Transfer to K Pegs and N Disks?