| Abstract |
A model of human information processing during concept formation has been constructed, using a list processing, digital computer program. The program's input consists of descriptions of objects in terms of dimensions and values. The universe of objects is divided into two or more sets. The program attempts to form a decision rule, based upon the descriptions of the objects, which can be used to assign any previously presented or new object to its correct set. The program is a model for human information processing, rather than an artificial intelligence system. It contains features which limit the number of objects in internal memory and the number of dimensions which may be involved in an answer. Using this program, simulations have been performed of a number of psychological experiments in concept learning. Comparison of these simulations with the data obtained from human subjects will be discussed. What is a concept? Ordinary usage is not precise. The English "the concept of force", "the concept of massive retaliation," and the "concept of dogs" are all permissible. Church has offered a definition which has been accepted, implicitly, by psychologists who perform "concept learning" experiments. Church's argument is that any given symbol (or name) can be attached to the members of a set of objects. For any arbitrary object there exists a rule concerning the description of the object, a rule which can be used to decide whether or not the object is a member of the set of objects to which the name applies. The decision rule is the concept of the name, the set of objects is the denotation of the name. In a typical concept learning experiment the subject is confronted with a series of stimuli which are given a particular name and another series of stimuli which are either given another particular name, or a series of different names. Thus the first set might be called "dogs" and the second either "not-dogs" or "cats, wolves, sheep, etc." Thus some routines are necessary to classify the instances to correspond to the names assigned by the experimenter. These are our ordering routines. Sometimes the various stimuli given one name have certain common characteristics, e.g. all the positive instances may have three triangles. At other times there are no common stimulus elements, but there are common relationships, e.g. all the positive instances may have the same size of upper figure as lower figure, although the figures may be large, medium or small sized in each row. A machine routine may be required to describe relations between basic stimulus elements. So we must have description routines in a simulation. Finally, different types of stimulus sets may be organized differently in terms of different types of logical connectives. Sometimes the concept involves the joint presence of two or more characteristics. Such concepts are referred to as conjunctive concepts (e.g. large red figure). Other concepts involve the presence of different subsets of characteristics. These are disjunctive concepts, e.g. red or large figures. Different ways of defining the form of an answer are provided by a set of solution routines. The program must be capable of simulating a variety of conditions under which experiments have been performed. As illustrations of some of the variations, or manipulations, which must be simulated the following may be mentioned. The number and complexity of the stimuli may vary from study to study. The speed of presentation of new stimuli can be altered. The instances may be left in view or the subject may be forced to rely on his memory. Different concept learning problems can be compared along such dimensions as: logical complexity of the correct answer, number of relevant vs. number of irrelevant dimensions, order of presentation of problems of different types, and presentation of information by positive or negative instances. The subject may make a variety of responses during the experiment. Subjects may describe, verbally, their intermediate and final hypotheses concerning the characteristics of the concept. These responses may give us clues as to the nature of the individual's information processing procedures. As such, they constitute accessory measures used in our simulation studies. The time taken to develop an answer under various experimental conditions is also a useful response measure. The errors that subjects make in subsequent identifications of stimulus names can be analyzed. The more objective records are to be preferred, and our major goal is to predict these by computer simulation. In order to develop a theoretical explanation of concept learning we have accepted the "black box" analogy. We have attempted to write a computer program which, when given as input coded representations of the stimuli, will give as output coded responses that can be used to predict the responses of a human subject. Accurate prediction of the responses, not the development of a good hypothesis developer, nor, solely, the reproduction of previously obtained protocols, is our goal. We are not concerned with the processes specific to the task of categorizing geometric patterns. These are used as stimuli because they are convenient and because they represent stimuli which can be described in terms of previously discriminated stimuli. Hopefully we shall be able to make conclusions about concept learning processes irrespective of the particular form of the stimuli. Reports of our psychological experimental work have been, and are being, made in separate publications. This paper will be concerned with the programming details of our concept learning model. This model has been completed, debugged, and used to simulate several experiments. After describing the model we shall indicate the result of some simulations and discuss the modifications of the model which have been indicated. The concept learning program is a list processing language program written for the IBM 709-7090 data processing systems. The original programs were written in Information Processing Language V (IPL-V), the interpreter list processing language developed by Newell, Simon, and Shaw (cf. Green). Partly for local administrative reasons, we are in the process of converting our programs to LISP, a list processing language developed by McCarthy. We do not have sufficient experience with LISP to compare the two languages for our type of problem. As the basic logic of the LISP and IPL-V programs are the same no distinction will be made between them. |
