The three-term series problem

There are three apparently conflicting theories about the process by which an individual solves three-term series problems, i.e. problems such as ‘A is better than B, B is better than C, who is best?’ An information-processing analysis is presented which reveals that the IMAGE model of De Soto, Handel and London (1965) can easily be reconciled with the LINGUISTIC model of Clark (1969). However, an examination of some slight inconsistencies among the empirical findings reveals that such a reconciliation may be misleading. It is suggested instead that there is likely to be a change of approach during an experimental session. The individual initially may utilize a procedure analogous to the IMAGE model, modified to incorporate one of the principles of Hunter's (1957) OPERATIONAL model. Subsequently, as the result of practice, he may develop a procedure more analogous to the LINGUISTIC model.     

Graphics for three-term contingencies

A source of confusion in the general readership regarding the relationship of operant to S-R psychology is traced to the use of graphics in the behavioral literature. A case is made for supplementing traditional linear notation systems with triangular graphics to illustrate three-term contingencies. Constructing discriminative stimuli in this fashion makes the distinction between operant and S-R formulations more conspicuous and reveals more comprehensive relationships for an extended radical behaviorism.     

Cognitive processes in the solution of three-term series problems.

This study investigated the nature of strategies used in solving the three-term series problem. Three presentation modes (auditory, visual/sequential, and visual/simultaneous) were crossed with two question positions (before-premises and after-premises), for a total of six methods of problem presentation. Both high-spatial/imagal and low-spatial/imagal problems were employed, the assumption being that better performance on high-spatial/imagal problems reflected the use of a spatial/imagal strategy, while equal performance on both types of problems indicated the use of an alternative, perhaps verbal, strategy. It was hypothesized that different presentations would lead to differences in memory demands, input/processing interference, and mathemagenic behaviors, and thus to different problem-solving strategies. Response data and subjective reports confirmed this prediction. Results were discussed in terms of the Clark-Huttenlocher controversy (H. H. Clark, Linguistic processes in deductive reasoning, in Psychological Review, 1969, 76, 387--404; J. Huttenlocher, Constructing spatial images: A strategy in reasoning, Psychological Review, 1968, 75, 550--560).     

Why children have difficulty reasoning with three-term series problems

This study examined a number of hypotheses as to why children have difficulty in solving three-term series problems. No support was found for the hypothesis that their difficulties arise because of their inability to understand transitive relations. In addition, the problems were present throughout the task, so that poor memory for the premises was ruled out as a contributory factor in reasoning difficulty. The children's performance was found to improve, however, when they were provided with an aid to reduce the demands of the task on working memory, although this advantage was not maintained in a later test without a memory aid. There was also evidence that, overall, the children had greater difficulty in solving problems that imposed a higher load on working memory.     

Necessity and contingency

The paper considers the question of when the operator L of necessity in modal logic can be expressed in terms of the operator meaning it is non-contingent that.This paper was presented by title at the 1986 Annual Conference of the Australasian Association of Logic in Auckland, 9–12 July, 1986.     

The contingency of composition

There is widespread disagreement as to what the facts are concerning just when a collection of objects composes some further object; but there is widespread agreement that, whatever those facts are, they are necessary. I am unhappy to simply assume this, and in this paper I ask whether there is reason to think that the facts concerning when composition occurs hold necessarily. I consider various reasons to think so, but find fault with each of them. I examine the theory of composition as identity, but argue that the version of this doctrine that entails universalism is unwarranted. I consider the claim that the a priority of such facts leads to their necessity, but give a defence of substantial contingent a priori truths. I ask whether the contingency of such facts would lead to unwelcome possibilities, but argue that it does not. Next, I argue against the thought that the Lewis–Sider argument against restricted composition might give us reason to accept the necessity of universalism. Lastly, I respond to two objections from the 2006 BSPC. I conclude in favour of the contingency of the facts concerning when some things compose some thing.

Equivalence relations and the reinforcement contingency

Where do equivalence relations come from? One possible answer is that they arise directly from the reinforcement contingency. That is to say, a reinforcement contingency produces two types of outcome: (a) 2‐, 3‐, 4‐, 5‐, or n‐term units of analysis that are known, respectively, as operant reinforcement, simple discrimination, conditional discrimination, second‐order conditional discrimination, and so on; and (b) equivalence relations that consist of ordered pairs of all positive elements that participate in the contingency. This conception of the origin of equivalence relations leads to a number of new and verifiable ways of conceptualizing equivalence relations and, more generally, the stimulus control of operant behavior. The theory is also capable of experimental disproof.     

Stimulus generalization and the response-reinforcement contingency

Generalization gradients along a line-tilt continuum were obtained from groups of pigeons that had been trained to peck a key on different schedules of reinforcement. In Exp. I, gradients following training on a differential-reinforcement-of-low-rate (DRL) schedule proved to be much flatter than gradients following the usual 1-min variable interval (VI) training. In Exp. II, the value of the VI schedule itself was parametrically studied; Ss trained on long VI schedules (e.g., 4-min) produced much flatter gradients than Ss trained on short VI schedules (30-sec; 1-min). The results were interpreted mainly in terms of the relative control exerted by internal, proprioceptive cues on the different reinforcement schedules. Several implications of the results for other problems in the field of stimulus generalization are discussed.     

Spatial contingency and the McCollough effect

On the basis of a conditioning analysis of the orientation-contingent color aftereffect (McCollough effect, ME), orientation stimuli become associated with simultaneously presented chromatic stimuli. This account suggests that decreasing the contingency between the grid orientation and color should decrease the strength of the aftereffect. Results of previous research indicate that decreasing the temporal contingency (by presenting homogeneous chromatic stimuli between presentations of chromatic grids) does not decrease the ME. However, it has been suggested that the appropriate contingency-degradation procedure would involve decreasing spatial (rather than temporal) contingency. That is, the illusion should be attenuated by extending the color beyond the confines of the grid. Contrary to this hypothesis, the results of the present experiments provide no evidence that decreasing the spatial contingency between grid and color decreases the ME; rather, the aftereffect is increased by such a manipulation.     

Neural events in the reinforcement contingency

When neural events are analyzed as stimuli and responses, functional relations among them and among overt stimuli and responses can be unveiled. The integration of neuroscience and the experimental analysis of behavior is beginning to provide empirical evidence of involvement of neural events in the three-term contingency relating discriminative stimuli, responses, and consequences. This paper is aimed at highlighting exemplar instances in the development of this issue. It has long been known that the electrical stimulation of certain cerebral areas can have a reinforcing function. Extraordinary technological advances in recent years show that neural activity can be selected by consequences. For example, the activity of in vitro isolated neurons that receive dopamine as a reinforcer functions as a cellular analogue of operant conditioning. The in vivo activity of populations of neurons of rats and monkeys can be recorded on an instant-to-instant basis and can then be used to move mechanical arms or track a target as a function of consequences. Neural stimulation acts as a discriminative stimulus for operant responses that are in turn maintained by neural consequences. Together with investigations on the molecular basis of classical conditioning, those studies are examples of possibilities that are being created for the study of behavior-environment interactions within the organism. More important, they show that, as an element in the three-term contingency, neural activity follows the same laws as other events.     

Stimulus control and the response-reinforcement contingency

Pigeons were trained under a schedule in which reinforcement was made available at varying periods of time after a prior reinforcement. The first key peck after a reinforcer was available began a timer and a second key peck, which exceeded a specified minimal time interval, produced the reinforcer. It was shown that a contingency which contains a minimal interresponse time does not necessarily weaken stimulus control by an exteroceptive stimulus.     

Strategy changes in human contingency judgments as a function of contingency tables.

Judgment strategies of 169 undergraduate students on problems to judge the contingency between two binary events were identified by the method of rule-based analysis to clarify whether or not the strategies the subjects used would be affected by the concrete nature of the contingency table. Problems were constructed along two factors: total cell frequency and width of range of objective contingencies. Although the factor of total cell frequency had no effect on subjects' strategies, the number of subjects who changed strategies corresponding with problem instances increased when the objective contingencies were set closer to zero or when problems became more difficult. These results are discussed in the context of previous studies of this issue in the literature.     

Revisiting the relation between contingency awareness and attention: Evaluative conditioning relies on a contingency focus

Although evaluative conditioning has occasionally been demonstrated in the absence of contingency awareness, many recent studies imply that its acquisition depends on the availability of attentional resources during conditioning. In previous experiments attention has typically been manipulated in a general way rather than looking at the particular focus of attention. The present study investigated the role of a focus on the CS–US contingency. Two separate distraction tasks were designed that either diverted attention from the stimuli or directed it to the stimuli while drawing attention away from the contingency between the stimuli. Both types of distraction were shown to eliminate evaluative conditioning. Significant evaluative conditioning was observed in a third group of participants who were required to attend the contingencies. A mediation analysis showed that the observed discrepancy in evaluative conditioning effects between groups was mediated by contingency awareness. The results imply that attention in terms of a stimulus focus is not sufficient for evaluative conditioning to occur. Rather, attention to the contingencies between stimuli appears to be crucial in evaluative conditioning, because it is supposed to foster the acquisition of contingency awareness.