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.     

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.     

A transfer of self-discrimination response functions through equivalence relations

The present study tested the idea that human self-discrimination response functions may transfer through equivalence relations. Four subjects were trained in six symbolic matching-to-sample tasks (if see A1, choose B1; A1-C1, A2-B2, A2-C2, A3-B3, A3-C3) and were then tested for the formation of three equivalence relations (B1-C1, B2-C2, B3-C3). Two of the B stimuli (B1 and B2) were then used to train two different self-discrimination responses using either detailed instructions (Subjects 1 to 3) or minimal instructions (Subject 4) on two complex schedules of reinforcement (i.e., subjects were trained to pick the B1 stimulus if they had not emitted a response, and to pick the B2 stimulus if they had emitted one or more responses on the previous schedule). All 4 subjects showed the predicted transfer of self-discrimination response functions through equivalence relations (i.e., no response on the schedule, pick C1; one or more responses on the schedule, pick C2). Subjects also demonstrated this transfer when they were required to discriminate their schedule performance before exposure to the schedule (i.e., “what I intend to do”). Four control subjects were also used in the study. Two of these (Subjects 5 and 6) were not exposed to any form of matching-to-sample training and testing (nonequivalence controls). The 2 remaining subjects (7 and 8) were exposed to matching-to-sample training and testing that incorporated stimuli not used during the transfer test; C1 and C2 were replaced by N1 and N2 during the matching-to-sample training and testing, but C1 and C2 were used for the transfer tests (equivalence controls). All 4 subjects failed to produce the self-discrimination transfer performances observed with the experimental subjects.     

Development of conditional and equivalence relations without differential consequences

Two experiments were conducted to establish conditional stimulus relations without differential consequences and to test for the emergence of other relations. In Experiment 1, 3 adults responded to match-to-sample displays in which sample-comparison pairs were constant while the second comparison presented with each pair changed periodically across trials. No differential consequences followed any comparison selections. All subjects learned conditional relations between constant samples and comparisons, but results of tests for transitivity in those relations were equivocal. In Experiment 2, 4 children were given unreinforced training and testing similar to that provided to the adults in Experiment 1, with procedural refinements. One child learned conditional relations and demonstrated emergent relations that confirmed the development of two four-member equivalence classes. Another child learned the conditional relations but did not demonstrate any emergent relations reliably. A 3rd child, after reinforced training on two conditional relations, learned four new conditional relations without differential consequences and demonstrated symmetry but not equivalence in the trained relations. The 4th child did not learn the conditional relations. These findings emphasize the importance of careful construction of tests for stimulus equivalence and suggest a need for critical analyses of the apparent emergence of untrained stimulus relations on unreinforced tests that has been observed in several stimulus equivalence studies.     

Transfer of specific contextual functions to novel conditional discriminations

Three adolescents and 4 children participated in studies designed to examine contextually controlled conditional discrimination performance. In Study 1, participants selected Comparison B1 in the presence one stimulus (A1) and Comparison B2 in the presence of another stimulus (A2) using a matching-to-sample procedure. Next, contextual stimuli X1 or X2 were presented, such that in the presence of X1, selection of B1 given A1 and selection of B2 given A2 were reinforced; and in the presence of X2, selection of B2 given A1 and selection of B1 given A2 were reinforced. Then, new conditional discriminations were taught with Stimuli E and F. When the contextual Stimuli X1 and X2 were presented, participants selected the same comparisons as previously established in the EF relations in the presence of X1, but the opposite comparison as in the EF relations in the presence of X2. The results then were replicated with new Stimuli G and H. In Study 2, a new conditional discrimination, CD, was taught. Then, four combinations of two-element samples--C1 and D1, C2 and D2, C1 and D2, or C2 and D1--were presented with X1 and X2 as comparisons. Five of 6 participants selected X1 in the presence of C1 and D1 or C2 and D2, and selected X2 in the presence of C1 and D2 or C2 and D1. Finally, in Study 3, two new discriminations IJ and JK were taught. Then, the transitive IK relations were tested with X1 and X2 as contextual stimuli. The 4 participants selected K1 in the presence of I1 and K2 in the presence of I2 when the contextual stimulus was X1--demonstrating class formation--and selected the other comparisons when the contextual stimulus was X2. These results suggest that the contextual control functions of X1 and X2 transferred even to relations that had not been directly taught. These results extend those demonstrating generalized contextual control by showing transfer of functions of the contextual stimuli in transitivity tests and when the former contextual stimuli were presented as comparisons.     

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.     

Testing response-stimulus equivalence relations using differential responses as a sample

This study tested the notion that an equivalence relation may include a response when differential responses are paired with stimuli presented during training. Eight normal adults learned three kinds of computer mouse movements as differential response topographies (R1, R2, and R3). Next, in matching-to-sample training, one of the response topographies was used to select a comparison stimulus B (B1, B2, or B3) conditionally upon presentation of sample stimulus A (A1, A2, or A3), and to select stimulus D (D1, D2, or D3) conditionally upon presentation of stimulus C (C1, C2, or C3). After two sample-comparison-response relations (ABR and CDR) were established, 18 sample-comparison relations were tested (BA, DC, RA, RB, RC, RD, AC, CA, AD, DA, BC, CB, BD, DB, AA, BB, CC, and DD). In the RA, RB, RC, and RD tests, the differential responses (R1, R2, and R3) were used as sample stimuli. All subjects made class-consistent comparison selections in the tests. This study provides evidence that responses may become members of an equivalence class.     

Conditional discrimination and equivalence relations: A theoretical analysis of control by negative stimuli

A detailed analysis is presented of the ways in which control by the negative stimulus in two-comparison conditional discriminations may be expected to affect the outcome of tests for the properties of equivalence relations. Control by the negative stimulus should produce the following results: (a) no observable effect on symmetry tests; (b) reflexivity test results should look like “oddity” rather than “identity”; and (c) transitivity tests that involve an odd number of nodes should yield results that are 100% opposite to tests that involve an even number of nodes. The analysis also considers the effects of variation in the type of comparison-stimulus control between and within baseline conditional discriminations. Methods are suggested for experimentally regulating the type of control, and for verifying the predictions that the analysis generates. If suggested experiments continue to support the analysis, investigators who use two-comparison conditional discriminations to study equivalence relations will either have to control explicitly whether the positive or the negative comparison governs their subjects' choices, or they will have to abandon two comparisons and use three or more comparisons instead.     

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.     

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.     

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.     

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.     

Training sequence effects on emergent conditional discriminations: Replication and extension to selection-based training

We examined the replicability and generality of a previously reported training sequence effect on emergent conditional discriminations in the intraverbal naming task. In Experiment 1, a tact–intraverbal (TI) group learned first to vocally label 6 visual patterns and then to intraverbally relate pairs of verbal labels, whereas an intraverbal–tact (IT) group received the same training in the opposite sequence. Emergent conditional discriminations among pattern stimuli were assessed in match-to-sample (MTS) format. Experiment 2 was identical, except vocal tact and intraverbal training were replaced with selection-based training in which the verbal labels were text stimuli. Compared to the IT sequence, the TI sequence resulted in greater mean accuracy at test (Experiment 1), higher yields (Experiment 2), and shorter reaction times (Experiment 2). Experiment 2 data suggested the TI group's performance might be less dependent on intact intraverbal relations relative to the IT group, but related to participants' reports of visualization during intraverbal training. The results suggest the sequence effect is replicable and occurs in experimental preparations commonly used to study derived stimulus relations. They also provide novel support for the hypothesis that participant behavior during training alters sources of stimulus control available at test.     

Baseline training sequence affects speed of emergent conditional discriminations

We examined the effects of baseline training sequence on the emergence of conditional discriminations in an intraverbal naming task. Thirty‐two college students were randomly assigned to two groups. The tact‐intraverbal (TI) group first learned to vocally tact eight visual stimuli using a unique verbal label for each stimulus, and then to intraverbally relate four pairs of verbal labels. The intraverbal‐tact (IT) group received the same training but in the opposite sequence. Both groups then received a match‐to‐sample test involving the visual stimuli alone. On average, the TI group had significantly shorter reaction times than the IT group throughout all four test blocks, even when controlling for intraverbal retention, which was lower in the IT group. Accuracy on the MTS test did not differ significantly between groups when controlling for intraverbal retention. However, MTS accuracy and intraverbal retention were strongly correlated in the IT group but uncorrelated in the TI group. We suggest the effect of training sequence reflects different sources of stimulus control available to subjects in different groups when confronted with the novel MTS trials.     

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.     

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.     

Stimulus equivalence and arbitrarily applicable relational responding.

Subjects' responses to nonarbitrary stimulus relations of sameness, oppositeness, or difference were brought under contextual control. In the presence of the SAME context, selecting the same comparison as the sample was reinforced. In the presence of the OPPOSITE context, selecting a comparison as far from the sample as possible on the physical dimension defined by the set of comparisons was reinforced. Given the DIFFERENT context, selecting any comparison other than the sample was reinforced. Subjects were then exposed to arbitrary matching-to-sample training in the presence of these same contextual cues. Some subjects received training using the SAME and OPPOSITE contexts, others received SAME and DIFFERENT, and others received SAME, OPPOSITE, and DIFFERENT. The stimulus networks established allowed testing for a wide variety of derived relations. In two experiments it was shown that derived performances were consistent with relational responding brought to bear by the contextual cues. In contexts relevant to the relation of sameness, stimulus equivalence emerged. Other kinds of relational networks emerged in the other contexts. Arbitrarily applicable relational responding may give rise to a very wide variety of derived stimulus relations. The kinds of performances seen in stimulus equivalence do not appear to be unique.     

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.     

Emergent equivalence relations between interoceptive (drug) and exteroceptive (visual) stimuli.

Conditional "if-then" relations between drug (interoceptive) stimuli and visual (exteroceptive) stimuli were taught to 4 normal humans. Interoceptive stimuli were the effects produced by 0.32 mg/70 kg triazolam (a prototypical benzodiazepine) and placebo (lactose-filled capsules); exteroceptive stimuli were black symbols on white flash cards. Following the training of the prerequisite conditional relations, tests of emergent relations were conducted between exteroceptive stimuli and between interoceptive and exteroceptive stimuli. Equivalence relations emerged immediately without explicit training for all 4 subjects. Accuracy of responding during the interoceptive-exteroceptive equivalence tests and subjects' self-reports showed consistent discrimination between the drug effects of triazolam and placebo. Finally, a generalization test assessed whether a novel visual stimulus presented in the context of the placebo (i.e., no drug) would generalize to visual stimuli belonging to the placebo stimulus class. All 3 subjects who completed this test reliably chose the visual stimuli belonging to the placebo class and not the visual stimuli belonging to the triazolam stimulus class. The development of equivalence relations between interoceptive and exteroceptive stimuli demonstrates that private and public stimulus events can emerge as members of the same equivalence class. Theoretical and clinical implications are discussed.