Problem Structure And Problem Solving Behavior

One of the most interesting questions in the study of human problem solving is the nature of the Interaction between a problem's intrinsic structure and a problem solver's strategies or behaviors. The present paper suggests the use of techniques developed in research in mechanical problem solving to assist in formulating and illuminating this question. The authors also seek to develop a relationship between artificial intelligence methods and 'structuralist 1 theories of cognition by relating groups of symmetry transformations and 'conservation' operations. One of the most interesting questions in the psychology of problem solving is the nature of the interaction between a problem's intrinsic structure and the strategies or behaviors employed in attempting to solve the problem. Several studies have recently appeared addressing this subject: 1) the learning of mathematical structures such as the Klein group or the cyclic group of order four, Branca & Kllpatrick [13, 2) the study of analogy and transfer in related problem solving situations. 3) the development of mechanical theorem provers both in equation solving, Bundy [4], and in elementary geometry, Gelernter [5] and Goldstein [63. This research, although from diverse points of view, shares a common interest: understanding the effects of problem structure-for instance, a problem's possible subproblem and symmetry decom-positions-on efficient problem solving. This paper suggests techniques that may further aid in formulating and illuminating this question. More ambitiously, the authors seek to develop a relationship between artificial i n t e l l i-gence methods and Piagetian or 'structuralist' theories of cognition. Nilsson [7) has defined the state space representation of a problem as the set of distinguish-able problem configurations or situations together with the permitted moves or steps from one problem situation to another. Thus the state space of a problem consists of an i n i t i a l state, together with all the states that may be reached from the i n i t i a l state by successive legal moves in the problem. One or more of these successor states are classified as goal states. The state space of a problem , represented as a non-directed graph, will be unique only if the problem's description clearly delinlates its initial and goal state(s) and its set of legal moves Egan & Greno [33. Finally, the concept of the state space of a problem can be generalized to the analogous structure for an N-player game, i.e., the game tree …