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.     

Effect of observing response requirements to sample and comparison stimuli on the establishment of reject control (sample/S- relations)

The establishment of sample/S- relations (or reject control) during conditional discrimination training (AB, BC) affects transitivity (AC), equivalence (CA) and reflexivity (AA, BB, CC) test outcomes. The present study parametrically evaluated the effects of different observing patterns to comparison stimuli on the establishment of reject control during baseline conditional relation training. A matching-to-sample with observing requirements (MTS-OR) procedure was implemented during AB and BC conditional discrimination training. During training, the participants were required to observe the sample and incorrect comparison on every trial before responding. In addition, the participants were divided into three groups that differed regarding the percentage of training trials on which they were prevented from observing the correct comparison stimuli: 25%, 50%, and 75%. Once the mastery criteria were achieved during training, transitivity (AC), symmetry (BA, CB), equivalence (CA), and reflexivity (AA, BB, CC) tests were conducted with all comparison stimuli visible from the beginning. The results suggest that the number of errors during transitivity, equivalence, and reflexivity tests progressively increased as participants were prevented from observing the correct comparison on a greater number of trials during training. Symmetry test results, however, were not affected by the experimental manipulation. Moreover, the number of participants showing reject-control patterns during tests slightly increased and the number of participants showing select-control patterns decreased as a function of the number of trials on which the participants were prevented from observing the correct comparison. Thus, we suggest that observing patterns during training is a relevant variable that affects equivalence test outcomes.     

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.     

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.     

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.     

The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.     

Equivalence class formation as a function of preliminary training with pictorial stimuli

The present experiment investigated the effects of preliminary training with pictorial stimuli on the subsequent formation of three 5‐member equivalence classes (A?B?C?D?E) in 84 university students assigned to seven groups of 12. In the Abstract (ABS) group, all stimuli were abstract shapes. In the Picture (PIC) group, the C stimuli were pictures, and the remaining stimuli were the same abstract shapes as in the ABS group. For the remaining five groups, all stimuli were the same abstract shapes as in the ABS group. However, across groups, preliminary training involved either the establishment of conditional relations with simultaneous (SMTS) or delayed (DMTS) matching‐to‐sample with 0 s, 3 s, 6 s, or 9 s between the abstract C stimuli and the meaningful pictures. For the ABS and the PIC groups, 16.7% and 83.3% of participants formed classes, respectively. Preliminary training with SMTS and DMTS with 0 s, 3 s, and 6 s produced a linear increase in the likelihood of equivalence class formation, 41.7%, 50%, and 75%, respectively. Increasing the duration of delay further from 6 s to 9 s produced a substantial decline, 50%. This experiment extends knowledge about how including meaningful pictures enhances equivalence class 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.     

Training intraverbal naming to establish equivalence class performances

The purpose of this three‐experiment study was to evaluate whether performance consistent with the formation of equivalence classes could be established after training adults to tact and intraverbally relate the names of visual stimuli. Fourteen participants were exposed to tact training, listener testing, and intraverbal training (A'B’ and B'C’) prior to matching‐to‐sample (MTS) and intraverbal posttests presented in different sequences across experiments. All participants demonstrated emergent MTS and intraverbal relations consistent with equivalence class formation. More importantly, all participants emitted experimentally defined or self‐generated tacts or intraverbally named the correct sample‐comparison pairs at some point during posttests. These results are consistent with the intraverbal naming account (Horne & Lowe, 1996) in that participants who passed novel relations MTS tests also demonstrated emergence of corresponding intraverbal relations. However, verbal reports and latency data suggest that participants did not necessarily have to use intraverbal naming as a problem solving strategy continuously throughout MTS posttests. These results extended previous research by showing that verbal behavior training of baseline relations (A'B’ and B'C’) is sufficient to establish novel conditional relations consistent with equivalence class formation.     

Transfer of contextual stimulus function via equivalence class development

In a conditional discrimination, 6 college students arranged six Cyrillic letters into groups of three based upon which of two additional Cyrillic letters (contextual stimuli) was present. All subjects demonstrated symmetry and transitivity within each class of equivalent stimuli. In a second conditional discrimination, two more Cyrillic letters were related to each contextual stimulus. Testing of symmetrical and transitive relations between the original contextual stimulus and the two new ones confirmed the development of two three-member classes of contextual stimuli. Subsequent tests demonstrated that the new contextual stimuli controlled the previously trained sample-comparison relations for all subjects.     

Contextual control by function and form of transfer of functions

This study investigated conditions leading to contextual control by stimulus topography over transfer of functions. Three 4-member stimulus equivalence classes, each consisting of four (A, B, C, D) topographically distinct visual stimuli, were established for 5 college students. Across classes, designated A stimuli were open-ended linear figures, B stimuli were circular, C stimuli three-sided, and D stimuli four-sided. Three different computer tasks then were trained with the B stimuli. Differential reinforcement and punishment procedures were then used to establish control over function transfer by the topography of the class members. For Task 1, function transfer, responding to C and D stimuli as subjects had to B stimuli, was reinforced. For Task 2, function transfer was reinforced for C stimuli but punished for D stimuli. For Task 3, function transfer was punished for both C and D stimuli. New equivalence classes were then established and tests for generalized contextual control were presented. All 5 subjects showed generalized contextual control of transfer of functions by stimulus topography. Implications of contextual control over function transfer in natural settings are discussed.     

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.     

Effects of preliminary class membership on subsequent stimulus equivalence class formation

The present study examined the effects of including stimuli previously trained as members of functional classes or equivalence classes on subsequent equivalence class formation, and isolated the effects of preliminary training from those of the acquired function stimuli. Fifty-six adults were assigned to 1 of 5 conditions. The control group (CONT) received no preliminary training prior to the terminal phase. Participants in the other 4 groups learned two 3-member functional classes and two 3-member equivalence classes during the preliminary phase. The terminal equivalence phase trained two 5-member classes (A → B → C → D → E) comprising abstract forms; the C stimuli in the terminal phase were (a) from the preliminary functional classes for 1 group (ACQ-F), (b) from the preliminary equivalence classes for the second experimental group (ACQ-E), (c) pictures of everyday objects for the picture control group (PIC), and (d) novel, unfamiliar stimuli for the preliminary training control group (PRE-CONT). Class formation yields were 100% in the PIC condition and 11% in the CONT condition; however, low yields in the PRE-CONT, ACQ-F, and ACQ-E conditions were unexpected, suggesting that procedural variables in preliminary training account for more of the subsequent effects on class formation than the stimulus control properties of the acquired function stimuli.     

Effects of a meaningful, a discriminative, and a meaningless stimulus on equivalence class formation

Thirty college students attempted to form three 3-node 5-member equivalence classes under the simultaneous protocol. After concurrent training of AB, BC, CD, and DE relations, all probes used to assess the emergence of symmetrical, transitive, and equivalence relations were presented for two test blocks. When the A-E stimuli were all abstract shapes, none of 10 participants formed classes. When the A, B, D, and E stimuli were abstract shapes and the C stimuli were meaningful pictures, 8 of 10 participants formed classes. This high yield may reflect the expansion of existing classes that consist of the associates of the meaningful stimuli, rather than the formation of the ABCDE classes, per se. When the A-E stimuli were abstract shapes and the C stimuli became S(D)s prior to class formation, 5 out of 10 participants formed classes. Thus, the discriminative functions served by the meaningful stimuli can account for some of the enhancement of class formation produced by the inclusion of a meaningful stimulus as a class member. A sorting task, which provided a secondary measure of class formation, indicated the formation of all three classes when the emergent relations probes indicated the same outcome. In contrast, the sorting test indicated "partial" class formation when the emergent relations test indicated no class formation. Finally, the effects of nodal distance on the relatedness of stimuli in the equivalence classes were not influenced by the functions served by the C stimuli in the equivalence classes.     

A precursor to the relational evaluation procedure: searching for the contextual cues that control equivalence responding.

The precursor to the relational evaluation procedure (pREP) is a go/no-go successive discrimination procedure for examining stimulus equivalence. Previous research has shown that it does not readily produce equivalence responding unless some matching-to-sample (MTS) procedures are incorporated into the experimental sequence. Two experiments attempted to identify contextual cues that would generate equivalence responding on the pREP. Experiment 1 examined the effects of using abstract symbols or various verbal labels as response options on the pREP. Only the words same and different, when used as response options, reliably produced equivalence responding across 4 subjects. Experiment 2 examined different pretraining preparations designed to attach the functions of the words same and different to abstract symbols that could then be used as response options on the pREP. The most effective pretraining procedure involved multiple-exemplar training during which subjects were trained to respond to abstract symbols in the presence of pairs of stimuli that were either formally the same or different. The abstract symbols were subsequently used as response options with the pREP, and all subjects reliably demonstrated equivalence responding. The findings suggest that the relations of same and different may be fundamental to equivalence responding. These findings are discussed in terms of what they suggest about the nature of the equivalence phenomenon specifically and derived relational responding more generally.     

The transfer of Crel contextual control (same,opposite, less than,more than) through equivalence relations

According to Relational Frame Theory (RFT) C_rel denotes a contextual stimulus that controls a particular type of relational response (sameness, opposition, comparative, temporal, hierarchical etc.) in a given situation. Previous studies suggest that contextual functions may be indirectly acquired via transfer of function. The present study investigated the transfer of C_rel contextual control through equivalence relations. Experiment 1 evaluated the transfer of C_rel contextual functions for relational responses based on sameness and opposition. Experiment 2 extended these findings by evaluating transfer of function using comparative C_rel stimuli. Both experiments followed a similar sequence of phases. First, abstract forms were established as C_rel stimuli via multiple exemplar training (Phase 1). The contextual cues were then applied to establish arbitrary relations among nonsense words and to test derived relations (Phase 2). After that, equivalence relations involving the original C_rel stimuli and other abstract forms were trained and tested (Phase 3). Transfer of function was evaluated by replacing the directly established C_rel stimuli with their equivalent stimuli in the former experimental tasks (Phases 1 and 2). Results from both experiments suggest that C_rel contextual control may be extended via equivalence relations, allowing other arbitrarily related stimuli to indirectly acquire C_rel functions and regulate behavior by evoking appropriate relational responses in the presence of both previously known and novel stimuli.     

Observing behavior and atypically restricted stimulus control

Restricted stimulus control refers to discrimination learning with atypical limitations in the range of controlling stimuli or stimulus features. In the study reported here, 4 normally capable individuals and 10 individuals with intellectual disabilities (ID) performed two-sample delayed matching to sample. Sample-stimulus observing was recorded with an eye-tracking apparatus. High accuracy scores indicated stimulus control by both sample stimuli for the 4 nondisabled participants and 4 participants with ID, and eye tracking data showed reliable observing of all stimuli. Intermediate accuracy scores indicated restricted stimulus control for the remaining 6 participants. Their eye-tracking data showed that errors were related to failures to observe sample stimuli and relatively brief observing durations. Five of these participants were then given interventions designed to improve observing behavior. For 4 participants, the interventions resulted initially in elimination of observing failures, increased observing durations, and increased accuracy. For 2 of these participants, contingencies sufficient to maintain adequate observing were not always sufficient to maintain high accuracy; subsequent procedure modifications restored it, however. For the 5th participant, initial improvements in observing were not accompanied by improved accuracy, an apparent instance of observing without attending; accuracy improved only after an additional intervention that imposed contingencies on observing behavior. Thus, interventions that control observing behavior seem necessary but may not always be sufficient for the remediation of restricted stimulus control.