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.     

On the limits of the matching concept in monkeys (Cebus apella).

Two cebus monkeys, with many years of experience matching a variety of static visual stimuli (forms and colors) within a standard matching-to-sample paradigm, were trained to press a left lever when a pair of displayed static stimuli were the same and to press a right lever when they were different. After learning the same/different task, the monkeys were tested for transfer to dynamic visual stimuli (flashing versus steady green disks), with which they had no previous experience. Both failed to transfer to the dynamic stimuli. A third monkey, also with massive past experience matching static visual stimuli, was tested for transfer to the dynamic stimuli within our standard matching paradigm, and it, too, failed. All 3 subjects were unable to reach a moderate acquisition criterion despite as many as 52 sessions of training with the dynamic stimuli. These results provide further evidence that, in monkeys, the matching (or identity) concept has a very limited reach; they consequently do not support the view held by some theorists that an abstract matching concept based on physical similarity is a general endowment of animals.     

Functional classes and equivalence relations

Three adult subjects were taught a set of two-choice simultaneous discriminations, with three positive and three negative stimuli; all possible combinations of positive and negative stimuli yielded nine different pairs. The discriminations were repeatedly reversed and rereversed, the former positive stimuli becoming negative and the former negative stimuli becoming positive. With all subjects, a reversal of the contingencies for one pair of stimuli became sufficient to change their responses to all of the other pairs. The reversals had produced functional stimulus classes. Then, all subjects showed conditional discriminations emerging between members of a functional class; given a sample from one class and comparisons from both classes, they selected the comparison that was in the same class as the sample. Next, 2 of the subjects showed that the within-class conditional relations possessed the symmetric and transitive properties of equivalence relations; after having been taught to relate new stimuli to existing class members, the subjects then matched other class members to the new stimuli. Subsequent tests of two-choice discriminations showed that the conditional discriminations had transferred functional class membership to the new stimuli. The 3rd subject, who did not show equivalence relations among functional class members, was also found to have lost the within-class conditional relations after the equivalence tests.     

Transfer of matching-to-figure samples in the pigeon

Three pigeons were trained on a modified six-key matching-to-sample procedure. The third peck on the figure-sample key (which presented a bird, hand, face, beetle, rabbit, fish, flower, or red hue, as the sample) lighted only one comparison key. Every three additional pecks on the sample lighted another comparison key, up to a maximum of five keys. Pecks on keys of matching figures produced grain. Pecks on nonmatching keys (mismatches) turned off all lights on the comparison keys and repeated the trial. Three figures were used during acquisition. The birds learned to peck each sample until the matching comparison stimulus appeared on one of three comparison stimulus keys, and then to peck that key. Later, five novel stimuli, employed as both sample and comparison stimuli, and two additional matching keys were added. Each bird showed matching transfer to the novel samples. The data suggest that the birds may have learned the concept of figure matching rather than a series of two-component chains or discrete five-key discriminations.     

CONDITIONAL DISCRIMINATION VS. MATCHING TO SAMPLE: AN EXPANSION OF THE TESTING PARADIGM

A subject's performance under a conditional-discrimination procedure defines conditional relations between stimuli: “If A1, then B1; if A2, then B2.” The procedure may also generate matching to sample. If so, the stimuli will be related not only by conditionality, but by equivalence: A1 and B1 will become equivalent members of one stimulus class, A2 and B2 of another. One paradigm for testing whether a conditional-discrimination procedure has generated equivalence relations uses three sets of stimuli, A, B, and C, three stimuli per set. Subjects learn to select Set-B and Set-C comparisons conditionally upon Set-A samples. Having been explicitly taught six sample-comparison relations, A1B1, A1C1, A2B2, A2C2, A3B3, and A3C3, subjects prove immediately capable of matching the B- and C-stimuli; six new relations emerge (B1C1, B2C2, B3C3, C1B1, C2B2, C3B3). The 12 stimulus relations, six taught and six emergent, define the existence of three three-member stimulus classes, A1B1C1, A2B2C2, and A3B3C3. This paradigm was expanded by introducing three more stimuli (Set D), and teaching eight children not only the AB and AC relations but DC relations also—selecting Set-C comparisons conditionally upon Set-D samples. Six of the children proved immediately capable of matching the B- and D-stimuli to each other. By selecting appropriate Set-B comparisons conditionally upon Set-D samples, and Set-D comparisons conditionally upon Set-B samples, they demonstrated the existence of three four-member stimulus classes, A1B1C1D1, A2B2C2D2, and A3B3C3D3. These larger classes were confirmed by the subjects' success with the prerequisite lower-level conditional relations; they were also able to select Set-D comparisons conditionally upon samples from Sets A and C, and to do the BC and CB matching that defined the original three-member classes. Adding the three DC relations therefore generated 12 more, three each in BD, DB, AD, and CD. Enlarging each class by one member brought about a disproportionate increase in the number of emergent relations. Ancillary oral naming tests suggested that the subject's application of the same name to each stimulus was neither necessary nor sufficient to establish classes of equivalent stimuli.     

Effect of delay-interval stimuli on delayed symbolic matching to sample in the pigeon

In Experiment 1, food-deprived pigeons received delayed symbolic matching to sample training in a darkened Skinner box. Trials began with the illumination of the grain feeder lamp (no food sample), or illumination of this lamp, accompanied by the raising of the feeder tray (food sample). After a delay of a few seconds, the two side response keys were illuminated, one with red and one with green light, with positions counterbalanced over trials. Pecking the red (green) comparison produced grain reinforcement if the trial had started with food (no food); pecking red after a no-food sample or green after a food sample was not reinforced. Once matching performance was stable, four stimuli were presented during the delay interval, and their effects on matching accuracy were evaluated. Both illumination of the houselight and the center key with white geometric forms decreased matching accuracy, whereas presentation of a tone and vibration of the test chamber did not. In Experiment 2, pecking the red center key was reinforced with food according to a variable interval schedule. The effects of occasional brief presentations of the four stimuli used in the first experiment on ongoing pecking were assessed. The houselight and form disturbed key pecking, but the tone and vibration did not. Thus, stimuli that interfered with delayed matching also interfered with simple operant behavior. Implications of these results for theories of remembering are discussed.     

The formation of a generalized categorization repertoire: effect of training with multiple domains,samples, and comparisons

The present experiment explored the effects of three variables on the spontaneous categorization of stimuli in perceptually distinct and novel domains. Each of six stimulus domains was created by morphing two images that were the domain endpoints. The endpoints of the domains were male and female faces, two abstract drawings, a car and a truck, two banded-elevation satellite land images, a tree and a cat, and two false-color satellite images. The stimulus variants at each end of a domain defined two potential perceptual classes. Training was conducted in a matching-to-sample format and used stimuli from one or two domains, one or three variants per class as samples, and one or three variants per class as comparisons. The spontaneous categorization of stimuli in the untrained stimulus domains showed the emergence of a generalized categorization repertoire. The proportion of spontaneously categorized stimuli in the new domains was positively related to the number of domains and samples used in training, and was inversely related to the number of comparisons used in training. Differential reaction times demonstrated the discriminability of the stimuli in the emergent classes. This study is among the first to provide an empirical basis for a behavior-analytic model of the development of generalized categorization repertoires in natural settings.     

Addressing the “Replication Crisis”: Using Original Studies to Design Replication Studies with Appropriate Statistical Power

Psychology is undergoing a replication crisis. The discussion surrounding this crisis has centered on mistrust of previous findings. Researchers planning replication studies often use the original study sample effect size as the basis for sample size planning. However, this strategy ignores uncertainty and publication bias in estimated effect sizes, resulting in overly optimistic calculations. A psychologist who intends to obtain power of .80 in the replication study, and performs calculations accordingly, may have an actual power lower than .80. We performed simulations to reveal the magnitude of the difference between actual and intended power based on common sample size planning strategies and assessed the performance of methods that aim to correct for effect size uncertainty and/or bias. Our results imply that even if original studies reflect actual phenomena and were conducted in the absence of questionable research practices, popular approaches to designing replication studies may result in a low success rate, especially if the original study is underpowered. Methods correcting for bias and/or uncertainty generally had higher actual power, but were not a panacea for an underpowered original study. Thus, it becomes imperative that 1) original studies are adequately powered and 2) replication studies are designed with methods that are more likely to yield the intended level of power.     

Neural correlates of a default response in a delayed go/no-go task

Working memory, the ability to temporarily retain task-relevant information across a delay, is frequently investigated using delayed matching-to-sample (DMTS) or delayed Go/No-Go tasks (DGNG). In DMTS tasks, sample cues instruct the animal which type of response has to be executed at the end of a delay. Typically, performance decreases with increasing delay duration, indicating that working memory fades across a delay. However, no such performance decrease has been found when the sample cues exist of present vs. absent stimuli, suggesting that pigeons do not rely on working memory, but seem to respond by default in those trials. We trained 3 pigeons in a DGNG task and found a similar default response pattern: The diverging slopes of the retention functions on correct Go and No-Go trials suggested that pigeons by default omitted their response following No-Go stimuli, but actively retained task-relevant information across the delay for successful responses on Go trials. We conducted single-cell recordings in the avian nidopallium caudolaterale, a structure comparable to the mammalian prefrontal cortex. On Go trials, many neurons displayed sustained elevated activity during the delay preceding the response, replicating previous findings and suggesting that task-relevant information was neurally represented and maintained across the delay. However, the same units did not show enhanced delay activity preceding correct response suppressions in No-Go trials. This activation-inactivation pattern presumably constitutes a neural correlate of the default response strategy observed in the DGNG task.     

The development of derived stimulus relations through training in arbitrary-matching sequences

Five-year-old children were taught three-stage sequences of arbitrary matching: A-C, B-C, A-D; A-C, B-D, B-C; or A-C, A-D, B-C. Each stage refers to a sample-comparison relation between stimuli. Unreinforced test probes revealed untrained arbitrary matches (B-D, A-D, and B-D, respectively), derivable by substitution of stimuli with a common sample or comparison function. Additional probes revealed further untrained sample-comparison relations derivable by substitution and identity, including the commuted relations D-B, D-A, and D-B, respectively. These processes may have relevance to conceptual and verbal behavior.