A new approach to the formation of equivalence classes in pigeons

Four pigeons were given simultaneous discrimination training with visual patterns arbitrarily divided into two sets, with the stimuli in one set designated A1, B1, C1, and D1 and those in the other set designated A2, B2, C2, and D2. In sequentially introduced training phases, the pigeons were exposed to a series of reversals to establish AB and then CD equivalences. In subsequent testing sessions, a subset of stimuli from one set served as positive stimuli and those from the other set as negative stimuli on training trials, and transfer of the reinforced relation to other members of the sets was tested with nonreinforced probe trials. The pigeons were trained further on AC and BD equivalences and then were tested for the emergence of untrained AD and BC equivalences. Two of the 4 pigeons exhibited the emergence of one of these untrained equivalences, evidence for the emergence of transitive relations. This finding suggests that the pigeons established three-member functional equivalence classes by incorporating separately trained multiple equivalence relations. Repeated reversal training and probe testing enabled us to explore the formation and expansion of functional equivalence classes in pigeons.     

Contextual control of stimulus generalization and stimulus equivalence in hierarchical categorization

The purpose of this study was to determine whether hierarchical categorization would result from a combination of contextually controlled conditional discrimination training, stimulus generalization, and stimulus equivalence. First, differential selection responses to a specific stimulus feature were brought under contextual control. This contextual control was hierarchical in that stimuli at the top of the hierarchy all evoked one response, whereas those at the bottom each evoked different responses. The evocative functions of these stimuli generalized in predictable ways along a dimension of physical similarity. Then, these functions were indirectly acquired by a set of nonsense syllables that were related via transitivity relations to the originally trained stimuli. These nonsense syllables effectively served as names for the different stimulus classes within each level of the hierarchy.     

Functional equivalence classes in rats: Repeated olfactory discrimination reversals and delayed stimulus probes

The simultaneous matching-to-sample procedures that are widely used to study stimulus equivalence in human participants have generally been unsuccessful in animals. However, functional equivalence classes have been demonstrated in pigeons and sea lions using a concurrent repeated reversal discrimination procedure. In this procedure, responding to one set of stimuli is reinforced but responding to a different set is not and the set associated with reinforcement is changed with multiple reversals during the experiment. The experiments reported here were designed to assess whether functional equivalence classes could be demonstrated in rats using similar techniques. Rats were initially trained with two sets of olfactory stimuli (six odors/set). Following many reversals, probe reversal sessions were conducted in which rats were exposed to a subset of the members of each set and, later in the session, the withheld stimuli were introduced. Responding to these delayed probe trials in accord with the reversed contingencies constituted transfer of function. There was some evidence of transfer in Experiment 1, but the effects were relatively weak and variable. Experiment 2 introduced procedural changes and found strong evidence of transfer of function consistent with the formation of functional equivalence classes. These procedures offer a promising strategy to study symbolic behavior in rodents.     

Stability of functional equivalence and stimulus equivalence: effects of baseline reversals

Functional equivalence and stimulus equivalence classes were established, reversed, and tested for stability with college students. Functional stimulus classes were established using a task in which students were trained to say nonsense words in the presence of arbitrarily assigned sets of symbols. Computer-controlled speech-recognition technology was used to record and analyze students' vocal responses for accuracy. After the establishment of stimulus classes was demonstrated with a transfer-of-function test, the effects of reversing selected baseline simple discriminations were assessed during an additional transfer-of-function test and a follow-up test that occurred several weeks later. With the same students, stimulus equivalence classes were established and demonstrated with computerized matching-to-sample procedures. The effects of reversing selected baseline conditional discriminations also were assessed during a postreversal equivalence test and a follow-up test. Both functional stimulus classes and stimulus equivalence were sensitive to contingency reversals, but the reversals with stimulus equivalence closses affected stimulus class organization whereas reversals with functional stimulus classes did not. Follow-up performances were largely consistent with the original baseline contingencies. The similarities and differences between stimulus equivalence and functional equivalence are related to the specific contingencies that select responding in the presence of the stimuli that form the classes.     

The transfer of contextual control over equivalence classes through equivalence classes: a possible model of social stereotyping.

In Experiment 1, subjects acquired conditional equivalence classes controlled by three male and three female names as contextual stimuli. When equivalence relations were tested using new names not used in training (three male and three female), contextual control remained intact. Thus, generalized control of the composition of conditional equivalence classes by characteristically gender-identified names was shown. A basic analysis of this finding was tested in Experiment 2. Contextual equivalence classes were established using as contextual stimuli nonrepresentational visual figures that were members of additional pretrained three-member equivalence classes. When other stimuli in the pretrained equivalence classes were used as contextual stimuli, the conditional equivalence classes remained intact. Control subjects showed that this effect depended on the equivalence relations established in pretraining. The results show that contextual control over equivalence classes can transfer through equivalence classes. The implications of this phenomenon for social stereotyping are discussed.     

Equivalence classes with requirements for short response latencies

Five adult humans were tested for emergent conditional discriminations under rapid-responding contingencies. During four-comparison matching-to-sample baseline training (AB and AC), limited-hold contingencies for responding to samples and comparisons were gradually restricted to the shortest duration consistent with at least 95% accuracy and no more than 5% failures to respond. The final limited-hold values were 0.4-0.5 s for samples and 1.2-1.3 s for comparisons; mean response latencies were 0.15-0.28 s for samples and 0.59-0.73 s for comparisons; inter-trial intervals were 0.4 s. With these fast-responding requirements, test blocks presented 72 probe trials interspersed among 72 baseline trials, all without programmed differential consequences. Four equivalence test blocks (BC and CB probes, which tested simultaneously for both symmetry and transitivity) were followed by four symmetry (BA and CA probes) test blocks. Three subjects' results documented emergent performances indicative of equivalence classes despite fast-responding requirements that severely limited the time available for mediating vocal or subvocal responses. For these three subjects, mean latencies were slightly shorter in baseline trials than in probes, and shorter on symmetry than on equivalence probes. These differences, however, were usually less than the differences among mean latencies on the different types of trials within the baseline and probed performances.     

Relations among equivalence, naming, and conflicting baseline control

Three studies were conducted with different groups of 6 students each to explore the effects of training class-inconsistent relations and naming on demonstrations of emergent arbitrary stimulus relations. In all studies, two three-member equivalence classes of Greek symbols (A1B1C1 and A2B2C2) emerged as a result of training in conditional discriminations. Two new symbols were introduced (X and Y), and additional conditional discriminations were trained, whereby X was designated as the positive discriminative stimulus (S+) and Y was designated as the negative discriminative stimulus (S-) for A1 and B2. Conversely, Y was designated as the S+ and X as the S- for B1 and A2. This introduced conflicting sources of control within and between classes. In Study 1, subjects were not provided with names for the stimuli. In Study 2, the experimenter provided common names for the stimuli within each class. In Study 3, the subjects were required to use the common names during conditional discrimination training and test-trial blocks. In all experiments, equivalence responding with respect to the original classes was disrupted for some subjects subsequent to learning the new relations. Furthermore, in Studies 2 and 3, there were frequent examples of noncorrespondence between observed (listener or speaker) naming patterns and derived relations. These results support the view that demonstrations of equivalence are subject to control from a variety of sources rather than being fundamentally dependent on naming.     

Nodality effects during equivalence class formation: An extension to sight-word reading and concept development

Three students with moderate disabilities were taught to read and match-to-sample sight words comprising stimulus sets based upon the four food groups. We taught students conditional discriminations within four four-member sets using a single-sample/four-comparison procedure. Students were taught A-B, B-C, and C-D conditional discriminations for each of the four potential stimulus classes. Subsequent probes tested for relations based upon symmetry and one-node and two-node transitivity. The performances for all students indicated that symmetric relations emerged before one-node transitive relations, and that one-node transitive relations emerged before two-node transitive relations. These results are consistent with a pattern of responding, referred to as a "nodality effect," in which relations with fewer nodes are demonstrated prior to the demonstration of relations with a greater number of nodes. These results extend this area of research to sight-word reading for students with moderate disabilities.     

Generalization of cross-modal stimulus equivalence classes: operant processes as components in human category formation.

This study employed a stimulus-class rating procedure to explore whether stimulus equivalence and stimulus generalization can combine to promote the formation of open-ended categories incorporating cross-modal stimuli. A pretest of simple auditory discrimination indicated that subjects (college students) could discriminate among a range of tones used in the main study. Before beginning the main study, 10 subjects learned to use a rating procedure for categorizing sets of stimuli as class consistent or class inconsistent. After completing conditional discrimination training with new stimuli (shapes and tones), the subjects demonstrated the formation of cross-modal equivalence classes. Subsequently, the class-inclusion rating procedure was reinstituted, this time with cross-modal sets of stimuli drawn from the equivalence classes. On some occasions, the tones of the equivalence classes were replaced by novel tones. The probability that these novel sets would be rated as class consistent was generally a function of the auditory distance between the novel tone and the tone that was explicitly included in the equivalence class. These data extend prior work on generalization of equivalence classes, and support the role of operant processes in human category formation.     

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.     

Conditional discrimination and equivalence relations: Control by negative stimuli

Three adult subjects were taught the following two-sample, two-comparison conditional discriminations (each sample is shown with its positive and negative comparison, in that order): A1-B1B2, A2-B2B1; B1-C1C2, B2-C2C1; and C1-D1D2, C2-D2D1. A teaching procedure was designed to encourage control by negative comparisons. Subjects were then tested for emergent performances that would indicate whether the baseline conditional discriminations were reflexive, symmetric, and transitive. The tests documented the emergence of two classes of equivalent stimuli: A1, B2, C1, D2 and A2, B1, C2, D1. These were the classes to be expected if the negative comparisons were the controlling comparisons in the baseline conditional discriminations. The negative comparisons, however, were not the comparisons that subjects were recorded as having chosen in the baseline conditional discriminations. Differential test results confirmed predictions arising from a stimulus-control analysis: In reflexivity tests (AA, BB, CC, DD), subjects chose comparisons that differed from the sample; one-node transitivity (AC, BD) and "equivalence" (CA, DB) tests also yielded results that were the opposite of those to be expected from control by positive comparisons; symmetry tests (BA, CB, DC), two-node transitivity (AD) tests, and two-node "equivalence" (DA) tests yielded results that were to be expected from control by either positive or negative comparisons.     

Compound stimuli in emergent stimulus relations: Extending the scope of stimulus equivalence

Three experiments were conducted to investigate stimulus relations that might emerge when college students are taught relations between compound sample stimuli and unitary comparison stimuli using match-to-sample procedures. In Experiment 1, subjects were taught nine AB-C stimulus relations, then tested for the emergence of 18 AC-B and BC-A relations. All subjects showed the emergence of all tested relations. Twelve subjects participated in Experiment 2. Six subjects were taught nine AB-C relations and were then tested for symmetrical (C-AB) relations. Six subjects were taught nine AB-C and three C-D relations and were then tested for nine AB-D (transitive) relations. Five of 6 subjects demonstrated the emergence of symmetrical relations, and 6 subjects showed the emergence of transitivity. In Experiment 3, 5 college students were taught nine AB-C and three C-D relations and were then tested for nine equivalence (D-AB) relations and 18 AD-B and BD-A relations. Three subjects demonstrated all tested relations. One subject demonstrated the AD-B and BD-A relations but not the D-AB relations. One subject did not respond systematically during testing. The results of these experiments extend stimulus equivalence research to more complex cases.     

Reorganization of equivalence classes: effects of preliminary training and meaningful stimuli

In Condition 1, adults learned the baseline relations for the three equivalence classes A1‐B1‐C1‐D1‐E1, A2‐B2‐C2‐D2‐E2, and A3‐B3‐C3‐D3‐E3. Classes contained abstract shapes in the ABS and four preliminary training groups. Each class in the PIC group contained one picture and four abstract shapes. Before class formation for four other groups, preliminary training involved establishing identity (CC) or arbitrary (CX) relations either with or without a delay. Without preliminary training, classes formed with low and high likelihoods in the ABS and PIC groups, respectively. Preliminary training with no delay produced modest increases in class formation, while preliminary training with delay produced large increases in class formation. Condition 2 replicated Condition 1 but with training of reassigned BC and CD relations that linked C from one class to B and D from another class: B1‐C2, B2‐C3, B3‐C1, C2‐D1, C3‐D2, and C1‐D3. Subsequent tests assessed the emergence of the reorganized classes A1‐B1 ‐C2 ‐D1‐E1, A2‐B2‐ C3 ‐D2‐E2, and A3‐B3‐ C1 ‐D3‐E3. All preliminary training procedures increased likelihood of forming the reorganized classes to the level seen in the PIC group. Greater gains were produced by preliminary training with no delays than with delays. Test performances also showed how preliminary training influenced baseline acquisition speed and participant‐defined relations.     

The transfer of respondent eliciting and extinction functions through stimulus equivalence classes

Two studies investigated the transfer of respondent elicitation through equivalence classes. In Experiment 1, match-to-sample procedures were used to teach 8 subjects two four-member equivalence classes. One member of one class was then paired with electric shock, and one member of the other class was presented without shock. All remaining stimuli were then presented. Using skin conductance as the measure of conditioning, transfer of conditioning was demonstrated in 6 of the 8 subjects. In Experiment 2, similar procedures were used to replicate the results of Experiment 1 and investigate the transfer of extinction. Following equivalence training and conditioning to all members of one class, one member was then presented in extinction. When the remaining stimuli from this class were then presented, they failed to elicit skin conductance. In the final phase of the experiment, the stimulus that was previously presented in extinction was reconditioned. Test trials with other members of the class revealed that they regained elicitation function. These results demonstrate that both respondent elicitation and extinction can transfer through stimulus classes. The clinical and applied significance of the results is discussed.     

The relation between stimulus function and equivalence class formation

Fifty participants were exposed to a simple discrimination-training procedure during which six S+ functions were established for six arbitrary stimuli, and S- functions were established for a further six stimuli. Following this training, each participant was exposed to one of five conditions. In the S+ condition, participants were exposed to a stimulus equivalence training and testing procedure using only the six S+ stimuli as samples and comparisons. In the S+/S- condition, participants were exposed to the same training and testing sequence as in the S+ condition, the difference being that three S+ and three S- stimuli were used as sample and comparison stimuli, with each set of three corresponding to the trained equivalence relations. In the S+/S- mixed condition, the S+ and S- stimuli were assigned to their roles as samples and comparisons in a quasi-random order. In the S- condition, all six S- stimuli were used. The no-function condition served as a control condition and employed stimuli for which no stimulus-control functions had been established. The results showed that, on average, participants required more testing trials to form equivalence relations when the stimuli involved were functionally similar rather than functionally different. Moreover, participants required more test trials to form equivalence relations when novel arbitrary stimuli, rather than functionally distinct stimuli, were used as samples and comparisons. The speed of acquisition of stimulus equivalence was also related to the number of functionally similar stimuli established before training. These findings indicate a variety of ways in which the emergence of equivalence relations is affected by the functional classes in which the relevant stimuli participate.     

A discrimination analysis of training-structure effects on stimulus equivalence outcomes.

Experiments designed to establish stimulus equivalence classes frequently produce differential outcomes that may be attributable to training structure, defined as the order and arrangement of baseline conditional discrimination training trials. Several possible explanations for these differences have been suggested. Here we develop a hypothesis based on an analysis of the simple simultaneous and successive discriminations embedded in conditional discrimination training and testing within each of the training structures that are typically used in stimulus equivalence experiments. Our analysis shows that only the comparison-as-node (many-to-one) structure presents all the simple discriminations in training that are subsequently required for consistently positive outcomes on all tests for the properties of equivalence. The sample-as-node (one-to-many) training structure does not present all the simple discriminations required for positive outcomes on either the symmetry or combined transitivity and symmetry (equivalence) tests. The linear-series training structure presents all the simple discriminations required for consistently positive outcomes on tests for symmetry, but not for symmetry and transitivity combined (equivalence) or transitivity alone. Further, the difference in the number of simple discriminations presented in comparison-as-node training versus the other training structures is larger when the intended class size is greater than three or the number of classes is larger than two. We discuss the relevance of this analysis to interpretations of stimulus equivalence research, as well as some methodological and theoretical implications.     

Protocol analysis of the correspondence of verbal behavior and equivalence class formation.

In two equivalence experiments, a "think aloud" procedure modeled after Ericsson and Simon's (1980) protocol analysis was implemented to examine subjects' covert verbal responses during matching to sample. The purpose was to identify variables that might explain individual differences in equivalence class formation. The results from Experiment 1 suggested that subjects who formed equivalence classes described the relations among stimuli, whereas those not showing equivalence described sample and comparison stimuli as unitary compounds. Because Experiment 1 only demonstrated a correlation between describing stimulus compounds and the absence of equivalence classes, a second study was conducted. In Experiment 2, equivalence class formation was brought under experimental control through pretraining manipulations that facilitated responding either to stimulus compounds or to relations among stimuli. The results demonstrated that a history of describing stimulus compounds, when compared with describing the relations among the stimuli, interfered with the emergence of stimulus equivalence. These findings clarify individual differences in stimulus equivalence. They also demonstrate the utility of analyzing verbal reports to identify possible variables that can be manipulated experimentally.     

Transfer of baseline reject control to transitivity trials and its effect on equivalence class formation

This study explored the role of baseline reject control on transitivity responding. In Experiment 1, participants learned to respond to a baseline of arbitrary AB and AC conditional relations, and then they were exposed to transitivity‐like BC and CB trials in which the correct comparison stimulus was replaced by a novel stimulus (D). Five of 10 participants selected stimulus D, but only 1 showed expansion of the baseline stimulus classes to include the D stimuli. In Experiment 2, the emergence of symmetry and transitivity from baseline relations was assessed before participants were exposed to the transitivity‐like trials. Six of 8 participants who showed emergence of equivalence relations selected the D stimuli on transitivity‐like trials and provided evidence that baseline classes expanded to include these stimuli. In Experiment 3, these 6 participants selected novel stimuli (E) in additional transitivity‐like trials, and all showed that the E stimuli had become members of the previously established classes, which now comprised 5 members. A route for the emergence of transitivity by way of the transfer of baseline between‐classes reject control is discussed.     

Formation of new stimulus equivalence classes by exclusion

This study presents three experiments that aimed to show the formation of stimulus equivalence relations among stimuli that had been previously related only by exclusion. In Experiment 1, participants were trained on baseline conditional discriminations to establish two 3‐member equivalence classes. Then, they were exposed to exclusion trials, without feedback, in which undefined stimuli had to be matched by rejecting the defined baseline stimuli. Finally, participants responded to test trials evaluating the emergence of symmetry and transitivity among the undefined stimuli from the exclusion trials. For half of the participants, the stimuli related by exclusion were introduced as S‐ stimuli in the baseline trials, whereas for the other half they were not. Further, half of the participants were assessed for emergent relations with stimuli from all the classes, whereas the other half was assessed for emergent relations with only the stimuli related by exclusion. In Experiment 2, the S‐ comparisons in the emergent relations test trials with stimuli only related by exclusion were stimuli from a null class. In Experiment 3, the number of exclusion trials was doubled. Across experiments, most participants showed emergence of equivalence relations among the stimuli related by exclusion. Some conditions of stimulus control associated with exclusion learning and the emergence of equivalence relations are discussed.