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This paper proposes a taxonomy of information-processing tasks. Information conserving, reducing, and creating operations are viewed as different methods of processing. The main concern of this paper is information reduction which, it is suggested, represents a kind of thinking in which the solution is in some way implicit in the problem, but in which the input information must be reflected in a reduced or condensed output. A number of tasks within the areas of concept identification and utilization are shown to have this character. If the tasks require complete representation of the stimulus in the response (condensation) the amount of information reduced is directly related to difficulty both during learning and in utilization of previously learned rules. If the tasks allow Ss to ignore information in the stimulus (gating) the direct relation between reduction and difficulty is found during learning but may not occur after the rule is learned.

A mathematical model for stimulus generalization and discrimination is described in terms of simple set-theoretic concepts. An index of similarity is defined in terms of the model but is related to measurements in generalization experiments. The mathematical operators for acquisition and extinction, discussed in an earlier paper [1], are derived from the set-theoretic model presented here. The model is finally applied to the analysis of experiments on stimulus discrimination.

This paper reports an attempt to apply a simple association learning model to the analysis of the influence of response and training variables on paired-associate learning. The issues under investigation are old ones but have not been resolved satisfactorily in the past. With the aid of the elementary learning model, the problems are posed clearly and, the data willing, adequately resolved by the use of a few simple and intuitively compelling assumptions about learning. The first problem that led to this investigation concerns the relationship betvven the number of response alternatives (N) and error rate in pairedassociate learning. Experimental results (Noble, 1955; Riley, 1952) are in agreement in showing that the number of errors subjects make before reaching some criterion of learning is greater the larger the number of response alternatives. There is little agreement, however, as to the interpretation of this fact. Two possible factors could be involved. First, the effectiveness of a reinforced trial in increasing performance (i.e., the learning rate constant) may be influenced by N; and second, N may influence the probability of being correct by sheer guessing on items that are yet unlearned. It is a reasonably safe assumption that N has the second effect on chance guessing. Previous data are unclear on whether N also influences the first factor, the