Problemspace Theory

• For any given problem there are a large number of alternative paths from an initial state to a goal state; the total set of such states, as generated by the legal operators, is called the basic problem space.

• People's problem-solving behaviour can be viewed as the production of knowledge states by the application of mental operators, moving from an initial knowledge state to a goal knowledge state.

• Mental operators encode legal moves that can be made and restrictions that explicitly disallow a move if certain conditions hold.

The initial state and goal state in the Tower of Hanoi problem.

• People use their knowledge and various heuristic methods (like means-end analysis) to search through the problem space and to find a path from the initial state to the goal state.

• All of these processes occur within the Iimits of a particular cognitive system; that is, there may be working-memory limitations and limitations on the speed with which information can be stored and retrieved from long-term memory.

through similar knowledge states in their heads. They begin at an initial knowledge state and search through a space of alternative mental states until they reach a goal knowledge state. Moves from one knowledge state to the next are achieved by the application of mental operators. As a given problem may have a large number of alternative paths, people use strategies (or heuristic methods) to move from the initial state to the goal state, efficiently. Search may also be reduced by breaking the initial goal into subgoals which, when achieved, lead to the goals; for instance, if your goal is "to get to the shop before it closes" you might generate the three subgoals of "find a map", "plan the shortest route", and "find a mode of transport faster than walking" to achieve the goal. All in all, the knowledge a person brings to the problem is critical; the person's conception of a problem (i.e., how they represent the initial state) and the knowledge they bring to it (the operators and strategies available to them) critically determine the observed problem-solving behaviour. Problem-space theory is summarised in Panel 14.1 (see Newell, 1990; Newell & Simon, 1972; Simon, 1978):

This theory pins down in explicit representational terms the various hypothetical knowledge states and processes that are used to solve many different problems. It also makes predictions about what makes a problem difficult; for example, the size of the search space is clearly important to problem-solving success and the interaction between it and the method people use to search this space. Newell and Simon's theory has been implemented in computer programs that usually take the form of production systems (see Chapter 1). In these models, the various knowledge states are held in a working memory, and long-term memory consists of a set of productions that encode the operators that modify these states in working memory. Their now-famous model was called the General Problem Solver (GPS; see Newell, Shaw, & Simon, 1958, 1960) which has grown and been developed into the Soar cognitive architecture in the 1990s (Newell, 1990; Polk & Newell, 1995). Let us consider a typical problem to which the theory has been applied. Problem-space theory and the Tower of Hanoi

Problem-space theory and the Tower of Hanoi

In the "Tower of Hanoi" problem, subjects are presented with three vertical pegs in a row, the first of which has a number of disks piled on it in order of size; that is, the largest disk is at the bottom, the next largest on top of it and so on to the smallest at the top (see Figure 14.5). The goal of the problem is to have all the

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