An Extended Theory of Human Problem Solving

An Extended Theory of Human Problem Solving Pat Langley (langley@csli.stanford.edu) Seth Rogers (srogers@csli.stanford.edu) Computational Learning Laboratory Center for the Study of Language and Information Stanford University, Stanford, CA 94305 USA Abstract Human problem solving has long been a central topic in cognitive science. We review the established theory in this area and note some phenomena it does not ad- dress. In response, we present an extended framework, cast within a theory of the cognitive architecture, that provides one account of these phenomena and that we illustrate using the familiar Tower of Hanoi puzzle. We conclude by discussing other extensions to the standard theory and directions for future research. Introductory Remarks Research on human problem solving has a venerable his- tory that played a central role in the creation of cognitive science. Early studies of problem-solving behavior on puzzles and other novel tasks led to many insights about representation, performance, and learning that now un- derpin the field. Moreover, computational models devel- oped from these studies remain some of the most detailed and precise accounts of human cognition. However, the past decade has seen considerably less attention paid to this important topic, presumably be- cause many researchers believe that it is sufficiently well understood. In contrast, we maintain that the standard theory of problem solving, although basically accurate, is still incomplete, and we need additional work, at the level of both theoretical principles and specific computa- tional models, to extend our understanding of this com- plex cognitive activity. In this paper, we review traditional accounts of prob- lem solving and note some important omissions that re- quire further effort. After this, we present an extended framework that we have embedded in Icarus, a compu- tational theory of the human cognitive architecture. We then illustrate our points using a classic task, the Tower of Hanoi. In closing, we discuss other variations on the traditional theory and topics for future research. The Standard Problem Solving Theory dynamics, as well as addressing the observed behavioral differences between domain experts and novices. The theory makes a number of claims about hu- man cognition. The most basic is that problem solv- ing involves the mental inspection and manipulation of list structures. Newell and Simon (1976) later refined this into their physical symbol system hypothesis, which states that symbolic processing is a necessary and suffi- cient condition for intelligent behavior. Another central claim, termed the problem space hypothesis, is that prob- lem solving involves search through a space of candidate states generated by operators. A more detailed aspect of the theory is that, in many cases, problem solvers utilize means-ends analysis (Newell & Simon, 1972). This class of search methods involves a combination of selecting differences between the desired and current states, selecting operators that will reduce the chosen differences, and either applying the operators or creating subproblems to transform the current states into ones in which they can apply. This requires one to chain backward from aspects of the goal state to find relevant operators and determine useful sub- goals. However, with experience this novice strategy is replaced in experts with forward chaining that leads di- rectly to the goal (Larkin et al., 1980). Nevertheless, closer analyses of human behavior on novel tasks have suggested that this story is incomplete and that the actual situation is more complicated. Here we make some additional observations that are not ad- dressed by the standard theory. • Problem solving occurs in a physical context. Puz- zles like the Tower of Hanoi are typically presented in some physical form, with solutions relying on manual actions and tests for legal moves requiring visual inspection. This physical setting simplifies the task by providing an external memory, but it also introduces irrelevant features. • Problem solving abstracts away from physical de- tails, yet must return to them to implement the solu- tion. For instance, when solving the Tower of Hanoi, humans appear to search through an abstract prob- lem space that describes states in terms of disk-peg configurations and operators as transitions between them. They ignore the details of grasping and mov- ing required to demonstrate the solution, but they can execute these actions when necessary. The standard theory of problem solving, initially out- lined by Newell, Shaw, and Simon (1958), focuses on how humans respond when they are confronted with un- familiar tasks. Early work focused on abstract problems like proving theorems in propositional logic and solving the Tower of Hanoi puzzle. Later research adapted the framework to explain cognition in semantically rich do- mains like solving word problems in physics and thermo-