The merger and development of equivalence classes by unreinforced conditional selection of comparison stimuli

Three experiments assessed the likelihood that subjects with histories of equivalence class development would respond conditionally on new discriminations in the absence of differential consequences for responses. In the first two experiments, two groups of subjects with different experimental histories, but whose performances showed four equivalence classes, responded on trials without explicit reinforcement involving samples from two of the classes and comparisons from the other two classes, in a two-choice matching-to-sample format. Subjects consistently selected a particular comparison in the presence of a particular sample. Subsequent tests showed the emergence of equivalence relations between stimuli from classes linked by the unreinforced conditional selections. Subsequently, in Experiment II, the subjects' responses in the conditional selection trials were reinforced if the selection was reversed from that made previously. Although reversed selection was maintained, 2 of the 3 subjects continued to perform on equivalence relation trials according to their original unreinforced selections. In the third experiment, these 2 subjects responded on a series of conditional discriminations involving three new pairs of sample stimuli and one new pair of comparison stimuli. No explicit reinforcement followed responses on any trial in this experiment. Subsequent tests for equivalence between sample stimuli revealed the development of two equivalence classes.     

Relations between baseline contingencies and equivalence probe performances

Following the emergence of two three-member equivalence classes (A1B1C1 and A2B2C2), 5 college students were exposed to one or more changes in the reinforcement contingencies controlling baseline conditional discriminations. AC relations were either reversed (i.e., C2 was reinforced and C1 punished when A1 was the sample; C1 was reinforced and C2 punished when A2 was the sample) or arranged randomly (i.e., C2 and C1 were reinforced and punished equally often in the presence of A1 and A2). In a third condition, the original AB and AC relations were reversed. Results showed that although baseline conditional discrimination performances were under the control of reinforcement contingencies, and performances on symmetry trials varied with baseline responding for 3 of 4 subjects when contingencies were reversed, performances on transitivity probes remained consistent with the initial equivalence class. These inconsistencies between probe and baseline performances were striking because conditional discriminations are thought to be the determinants of equivalence class performance. Similarly, the contrast between performances on symmetry and transitivity probes was of theoretical interest because equivalence classes are defined by congruent patterns of responding on probe trials.     

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.     

Equivalence class establishment, expansion, and modification in preschool children

Preschool children were taught four two-choice match-to-sample conditional discriminations with 10 arbitrary visual stimuli. For 6 participants, 2 of the 10 stimuli served as the sample, or conditional, stimuli in all discriminations. For 5 additional participants, the same pair of stimuli served as the discriminative, or comparison, stimuli in all discriminations. Equivalence classes were established with more participants in the latter group, replicating prior research with participants with retardation. Four participants, in whom equivalence classes were established and who were available for further participation, were exposed to new conditional discriminations without trial-by-trial feedback and involving some novel and some familiar stimuli. Consistent conditional responding was observed, and tests for inclusion of the novel stimuli in the original classes showed class expansion. Training to reverse the unreinforced conditional performances produced a reversal of class membership in 3 of 4 participants, an outcome not consistent with other studies. The results are discussed with respect to the interaction of class structure and size.     

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.     

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.     

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.     

Conditional discrimination in mentally retarded adults: the development of generalized skills.

The development of generalized conditional discrimination skills was examined in adults with retardation. Two subjects with histories of failure to acquire arbitrary matching under trial-and-error procedures were successful under procedures that trained one or more prerequisite skills. The successive discrimination between the sample stimuli was established by training the subjects to name the stimuli. The simultaneous discrimination between the comparison stimuli was established using either (a) standard simple discrimination training with reversals or (b) a procedure in which each of the two sample-comparison relations in the conditional discrimination was presented in blocks of trials, with the size of the blocks decreasing gradually until sample presentation was randomized. The amount of prerequisite training required varied across subjects and across successive conditional discriminations. After acquiring either two or three conditional discriminations with component training, both subjects learned new conditional discriminations under trial-and-error procedures. In general, each successive conditional discrimination was acquired more rapidly. Tests showed that conditional responding had become a generalized skill. Symmetry was shown for almost all trained relations. Symmetry trial samples were ultimately named the same as the stimuli to which they were related in training.     

Verbal self-reports of emergent relations in a stimulus equivalence procedure.

During a preliminary training phase, college students were taught to categorize each of their responses accurately in a conditional discrimination task as either correct or incorrect. Next, in the absence of self-reports, subjects acquired conditional discriminations (involving novel stimuli) prerequisite to the formation of two four-member equivalence classes. The self-report procedure was reinstated during probe sessions that tested for untrained relations indicative of equivalence class formation. Interspersed trials involving trained relations provided a positive control, and trials with no class-consistent comparison provided a negative control. Eight of 10 subjects demonstrated equivalence class formation; all accurately reported their performance on trained relations and on trials with no class-consistent comparison. Subjects also reported their performance on most untrained (emergent) relations accurately, but in several instances self-reports indicated failure or uncertainty despite nearly perfect emergent-relations performance. These inconsistencies add to a growing body of literature that suggests there are differences between individual types of emergent relations. We suggest that the present procedure may be helpful in understanding these differences and other equivalence-related effects.     

AUDITORY SUCCESSIVE CONDITIONAL DISCRIMINATION AND AUDITORY STIMULUS EQUIVALENCE CLASSES

This paper describes an experimental demonstration of stimulus equivalence classes consisting entirely of auditory stimuli. Stimuli were digitized arbitrary syllables (e.g., “cug,” “vek”) presented via microcomputer. Training and testing were conducted with a two-choice auditory successive conditional discrimination procedure. On each trial, auditory samples and comparisons were presented successively. As each comparison was presented, a response location (a rectangle) appeared on the computer screen. After all stimuli for a trial were presented, subjects selected one of the response locations. Six subjects acquired the conditional discrimination baseline, 4 subjects demonstrated the formation of three-member auditory equivalence classes resulting from sample-S+ relations, and 1 subject demonstrated equivalence classes resulting from sample-S— relations. Four subjects received additional training and subsequently demonstrated expansion of the three-member classes to four members each.     

Stimulus equivalence: testing Sidman's (2000) theory

Sidman's (2000) theory regarding the origin of equivalence relations predicts that a reinforcing stimulus common to distinct equivalence classes must drop out of the equivalence relations. This prediction was tested in the present study by arranging class-specific reinforcers, R1 and R2, following correct responding on the prerequisite conditional discriminations (Ax-Bx, Cx-Bx) for two stimulus classes, A1B1C1 and A2B2C2. A class-common reinforcer, R3, was presented following correct responding on the prerequisite conditional discriminations for a further two stimulus classes, A3B3C3 and A4B4C4. Sidman's theory predicts reinforcer inclusion within Classes 1 and 2 only, given this training arrangement. Experiment 1 tested for the emergence of four equivalence classes and of stimulus-reinforcer and reinforcer-stimulus relations in each class. Four of the 6 subjects demonstrated the reinforcer-based relations in all four equivalence classes, rather than in only those classes with a class-specific reinforcer, as Sidman's theory predicts. One of the remaining 2 subjects showed the reinforcer-based relations in three of the four classes. Experiment 2 extended these findings to document the emergence of interclass matching relations based on the common reinforcer R3, in 5 of 6 subjects, such that a Class 3 sample occasioned the selection of a Class 4 sample when the Class 3 comparison was absent, and similarly, a Class 4 sample occasioned the selection of a Class 3 comparison when the Class 4 comparison was absent. These interclass relations emerged despite the simultaneous maintenance of Class 3 and 4 baseline conditional discriminations, so that the Class 3 and 4 stimuli and reinforcer simultaneously were, and were not, part of a single larger equivalence class. These data are irreconcilable with Sidman's theory, and question the utility of the application of the equivalence relation in describing derived stimulus relations.     

Transfer of a conditional ordering response through conditional equivalence classes

Eight adult humans were taught conditional discriminations in a matching-to-sample format that led to the formation of two four-member equivalence classes. When subjects were taught to select one comparison stimulus from each class in a set order, they then ordered all other members of the equivalence classes without explicit training. When the ordering response itself was brought under conditional control, conditional sequencing also transferred to all other members of the two equivalence classes. When the conditional discriminations in the matching-to-sample task were brought under higher order conditional control, the eight stimulus members were arranged into four conditional equivalence classes. Both ordering and conditional ordering transferred to all members of the four conditional equivalence classes; for some subjects this occurred without a typical test for equivalence. One hundred twenty untrained sequences emerged from eight trained sequences for all subjects. Transfer of functions through equivalence classes may contribute to a behavior-analytic approach to semantics and generative grammar.     

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.     

Expansion of Sidman's theory: The inclusion of prompt stimuli in equivalence classes

Stimulus equivalence is defined as the ability to relate stimuli in novel ways after training in which not all of the stimuli had been directly linked to one another. Sidman (2000) suggested all elements of conditional discrimination training contingencies that result in equivalence potentially become class members. Research has demonstrated the inclusion of samples, comparisons, responses, and reinforcers in equivalence classes. Given the evidence that all elements of a conditional discrimination become part of the class, the purpose of this study was to determine if class-specific prompts would also enter into their relevant equivalence classes. Experiment 1 investigated the inclusion of prompts in an equivalence class using abstract stimuli with neurotypical students enrolled in higher education courses. Experiment 2 systematically replicated Experiment 1 using meaningful stimuli and individuals diagnosed with autism spectrum disorder. The results of both experiments demonstrated that class-specific prompts became part of equivalence classes with the other positive elements of the contingency. The results are discussed in terms of class expansion and the potential impact on equivalence-based instruction.     

Reversal of baseline relations and stimulus equivalence: I. Adults

Following the emergence of two four-member equivalence classes (A1B1C1D1 and A2B2C2D2), 5 students were exposed to a series of phases including a baseline conditional discrimination reversal (i.e., choosing D2 was reinforced and D1 punished given Sample A1; choosing D1 was reinforced and D2 punished given Sample A2), the delayed introduction of CD/DC transitivity/equivalence probes, DE conditional discrimination training, a second baseline conditional discrimination reversal (i.e., choosing C2 was reinforced given B1, etc.), and a return to original baseline reinforcement contingencies. Results showed that baseline and symmetry probe performances were extremely sensitive to baseline modifications. In contrast, patterns on transitivity/equivalence probes remained predominantly consistent with the originally established equivalence classes, although there were exceptions on some E probe relations for 2 subjects. The dissociation between baseline and symmetry versus transitivity/equivalence patterns may have important implications because it is not easily accounted for by current models of equivalence phenomena.     

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.     

On the effectiveness of including meaningful pictures in the formation of equivalence classes

In three experiments, 165 adult participants were trained on 12 baseline conditional discriminations and tested for the formation of three 5-member equivalence classes (A➔B➔C➔D➔E). All experiments included two reference groups; the abstract (ABS) group was trained with all abstract stimuli and the picture (PIC) group with C-stimuli as meaningful pictorial stimuli but A, B, D, and E stimuli as abstract shapes. In Experiment 1, the color of the meaningful stimuli was manipulated. In the ABS, PIC, and black-and-white groups, 33.3%, 80%, and 93.3% formed equivalence classes, respectively. In Experiment 2, participants were exposed to a test block with and without trials that included C stimuli. For the groups with and without C trials in the test, 93.3% and 86.7% formed equivalence classes, respectively, compared to 20% in the ABS group. In Experiment 3, the number of meaningful pictures and their location in stimulus classes were manipulated. One group was trained with 3 pictures (C1/B2/D3, the 3-PIC) while the other groups had 2 pictures (C1/B2 and C1/D3, the 2-PIC). In the second test block for the ABS and PIC groups, 6.7% and 86% of the participants formed equivalence classes, respectively. For the 3-PIC and the 2-PIC groups, 66.7% and 50% of the participants formed equivalence classes, respectively. Results suggest that the effects of meaningful stimuli in equivalence classes (a) cannot be attributed to the use of colorful stimuli in previous studies, (b) occur during training and are not dependent on the presence of meaningful stimuli at test, and (c) are sensitive to stimulus location.     

Establishing Functional Classes In A Chimpanzee (Pan troglodytes) With A Two-item Sequential-Responding Procedure

A 9-year-old female chimpanzee was trained on a two-item sequential-responding task. Attempts were made with successive-reversal training to establish functional classes. In Experiment 1, the subject was exposed to between-session successive-reversal training in which one of two pairs of stimuli was reversed, and transfer of reversal responding to the other pair was tested with nonreinforcement probe trials. She did not show transfer during the course of reversals. Stimulus control established in the original training was maintained on nonreinforcement probe trials. In Experiment 2, within-session reversals were introduced. She showed transfer from the initially reversed pair to the other. The results were consistent with Vaughan's (1988) results with pigeons on successive discriminations, which indicated the formation of functional classes. In Experiment 3, crossover and wild-card tests were conducted to clarify the stimulus control of sequential responding. The results suggested that the sequential responding was controlled only by the first stimulus of each pair. To establish control by both first and second stimuli, trial-unique stimuli or wild cards were substituted for one of the items of the lists in Experiment 4. Further transfer tests, in which stimuli for the two new pairs appeared, were also given to the subject. She successfully responded to these two merged lists and reversed the order as the result of reversal training.     

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.     

A transfer of functions through derived arbitrary and nonarbitrary stimulus relations

During Experiments 1 and 2, subjects were trained in a series of related conditional discriminations in a matching-to-sample format (A1-B1, A1-C1 and A2-B2, A2-C2). A low-rate performance was then explicitly trained in the presence of B1, and a high-rate performance was explicitly trained in the presence of B2. The two types of schedule performance transferred to the C stimuli for all subjects in both experiments, in the absence of explicit reinforcement through equivalence (i.e., C1 = low rate and C2 = high rate). In Experiment 2, it was also shown that these discriminative functions transferred from the C1-C2 stimuli to two novel stimuli that were physically similar to the C stimuli (SC1 and SC2, respectively). For both these experiments, subjects demonstrated the predicted equivalence responding during matching-to-sample equivalence tests. In Experiments 3 and 4, the conditional discrimination training from the first two experiments was modified in that two further conditional discrimination tasks were trained (C1-D1 and C2-D2). However, for these tasks the D stimuli served only as positive comparisons, and ND1 and ND2 stimuli served as negative comparisons (i.e., C1 × ND1 and C2 × ND2). Subsequent to training, the negatively related stimuli (ND1 and ND2) did not become discriminative for the schedule performances explicitly trained in the presence of B1 and B2, respectively. Instead, the ND1 stimulus became discriminative for the schedule performance trained in the presence of B2, and ND2 became discriminative for the schedule performance trained in the presence of B1. All subjects from Experiment 4 showed that the novel stimulus SND1, which was physically similar to ND1, became discriminative for the same response pattern as that controlled by ND1. Similarly, SND2, which was physically similar to ND2, became discriminative for the same response pattern as that controlled by ND2. Subjects from both Experiments 3 and 4 also produced equivalence responding on matching-to-sample equivalence tests that corresponded perfectly to the derived performances shown on the transfer of discriminative control tests.