The development of functional and equivalence classes in high-functioning autistic children: the role of naming.

The development of functional and equivalence classes was studied in four high-functioning, preschool-aged autistic children. Initially, all subjects failed to demonstrate match-to-sample relations indicative of stimulus equivalence among two three-member classes of visual stimuli. Then, 2 subjects showed emergence of those relations after they were taught to assign the same name to all members in each class. Next, subjects were taught names for new stimuli outside the match-to-sample format. On subsequent match-to-sample tests, 2 subjects demonstrated untrained conditional relations among the stimuli given a common name. New, unnamed stimuli were then related via match-to-sample training to stimuli from sets of named stimuli. Tests for emergent conditional relations between the new unnamed stimuli and the named stimuli yielded positive results for 1 subject and somewhat mixed results for 3 subjects. Finally, without naming, 2 subjects developed stimulus equivalence among two new three-member classes of visual stimuli. These data suggest that naming may remediate failures to develop untrained conditional relations, some of which are indicative of stimulus equivalence.     

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.     

Equivalence relations, contextual control, and naming

This paper reports two experiments that investigated the role of verbal behavior in the emergence and generalization of contextually controlled equivalence classes. During both experiments, participants were trained with two different combinations of the same easily nameable, yet formally unrelated, pictorial stimuli. Match-to-sample baselines for eight four-member classes were established under the contextual control of two colors. In the presence of one color, conditional relations were established between stimuli whose normative names rhymed. In the presence of the other color, conditional relations were established between stimuli whose normative names did not rhyme. Although, during Experiment 1, all participants demonstrated equivalence classes involving rhyming stimuli, none demonstrated the formation of nonrhyme equivalence classes. To investigate this finding, Experiment 2 evaluated whether participants would demonstrate both rhyme and nonrhyme equivalence classes given more extensive exposure to the experimental contingencies. All participants demonstrated contextually controlled rhyme and nonrhyme equivalence classes, although rhyme classes were demonstrated with greater facility than nonrhyme classes. Results indicate that visual stimuli are named, that verbal bases for stimulus classification can affect the emergence of contextually controlled equivalence classes, and that untrained contextually controlled conditional discriminations involving novel stimuli can emerge on the basis of participants' verbal behavior.     

Six-member stimulus classes generated by conditional-discrimination procedures

In conditional-discrimination procedures with three sets of stimuli, A, B, and C, three stimuli per set (A1A2A3, B1B2B3, and C1C2C3), subjects (children and adults) learned to select Set-B and Set-C comparisons conditionally upon Set-A samples (A1B1, A1C1, A2B2, A2C2, A3B3, A3C3). If the conditional-discrimination procedures also generated equivalence relations, three 3-member stimulus classes would be demonstrable, A1B1C1, A2B2C2, and A3B3C3. In addition to these three sets, the present experiments used three other sets of stimuli--D, E, and F. The subjects learned to select Set-E and Set-F comparisons conditionally upon Set-D samples (D1E1, D1F1, D2E2, D2F2, D3E3, D3F3). This established a second group of three 3-member stimulus classes, D1E1F1, D2E2F2, and D3E3F3. In all, two groups of three 3-member classes were established by teaching subjects 12 conditional discriminations. The two groups of 3-member classes were then combined (successfully for 5 of 8 subjects) into a single group of three 6-member classes by teaching the subjects three more conditional relations (E1C1, E2C2, and E3C3). With three other children, enlarging the classes one member at a time also produced 6-member classes. As a consequence of class formation, 60 untrained conditional relations emerged from 15 that had been explicitly taught. Six of the subjects also proved capable of naming the stimuli consistently in accord with their class membership, but two subjects demonstrated class formation even in the absence of consistent naming.     

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.     

Acquired equivalence between stimuli trained in the same context

The role of context was examined in human acquired equivalence. Participants were trained on two conditional discriminations. In the first conditional discrimination, if sample A1 was presented, choice of comparison B1, but not B2, was correct, and if sample A2 was presented, choice of comparison B2, but not B1, was correct. In the second conditional discrimination, if sample X1 was presented, choice of comparison Y1, but not Y2, was correct, and if sample X2 was presented, choice of comparison Y2, but not Y1, was correct. In each conditional discrimination, one of the conditional relations was trained in context 1 (e.g., A1 → B1 and X1 → Y1) and the other was trained in context 2 (i.e., A2 → B2 and X2 → Y2). On test trials, when conditional stimuli from the two conditional discriminations were interchanged (e.g., sample A1 was presented with comparisons Y1 and Y2) and were presented in a neutral context, positive transfer resulted. That is, in the absence of the training context, stimuli that shared a common context on different trials in training came to be treated as equivalent.     

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.     

The effect of logarithmic transformation on estimating the parameters of the generalized matching law

This study examined stimulus class membership established via stimulus-reinforcer relations. Mentally retarded subjects learned conditional discriminations with four two-member sets of visual stimuli (A, B, C, and D). On arbitrary-matching trials, they selected comparison stimuli B1 and B2 conditionally upon samples A1 and A2, respectively, and C1 and C2 conditionally upon B1 and B2, respectively. On identity-matching trials, they selected all stimuli as comparisons conditionally upon identical stimuli as samples. Throughout training, correct selections of A1, B1, C1, and D1 were followed by one reinforcer, R1, and those of A2, B2, C2, and D2 were followed by another, R2. Subsequent tests documented the formation of two four-member stimulus classes, A1-B1-C1-D1 and A2-B2-C2-D2. The class membership of the A, B, and C stimuli could have been based on equivalence relations that resulted from the arbitrary-matching training. D1 and D2 had never appeared on arbitrary-matching trials, however. Their class membership must have been based on relations with R1 and R2, respectively. Results thus confirm a previous finding that stimulus classes can be expanded via stimulus-reinforcer relations. They also define more precisely the potential nature of those classes and the conditions under which class membership can be established.     

Naming in conditional discrimination and stimulus equivalence.

Using a matching-to-sample procedure, McIntire, Cleary, and Thompson (1987) taught monkeys the conditional relations A1-R1-A1-R1, A2-R2-A2-R2, A1-R1-B1-R1, A2-R2-B2-R2, B1-R1-C1-R1, and B2-R2-C2-R2, where the first and third terms in each relation refer to the sample and comparison stimuli, respectively, and the second and last terms refer to the emission of a distinctive pattern of responding. The subjects were then tested for the emergent relations A-C, C-A, B-A, C-B, and B-B, with the differential response produced by a given stimulus during training also emitted on test trials (e.g., A1-R1-C1-R1). The performances of both subjects were as accurate on the tested relations as they had been on the trained relations. The new relations were characterized as demonstrations of stimulus equivalence. However, the conditional discrimination literature shows that such training procedures generate control of comparison selection by the differential response patterns. Therefore, no emergent relations were demonstrated because all of the trained response-stimulus relations were preserved on test trials. This paper suggests that these procedures do not provide an appropriate analogy for the kind of emergent stimulus-stimulus relations exhibited by human subjects in equivalence studies and outlines a paradigm for assessing the relative influence of stimulus-stimulus and response-stimulus relations.     

Acquisition of arbitrary conditional discriminations by young normally developing children

Three experiments investigated conditions designed to facilitate acquisition of arbitrary conditional discriminations in 3- to 6-year-old normally developing children. In Experiment 1, 6 subjects failed to master the arbitrary match-to-sample task under conditions of differential reinforcement alone, but 7 subjects did so when instructions or instructions and sample naming were added. In Experiment 2, sample naming introduced in a blocked-trial arrangement resulted in acquisition, but only when the sample name was a nonsense syllable provided by the experimenter (5 of 7 subjects) and not when the sample name was generated by the subject (0 of 5 subjects). Experiment 3 demonstrated the effectiveness of a training sequence involving thematically related stimuli as an intermediate step facilitating the transition from identity to novel arbitrary relations. The difficulties in mastering arbitrary conditional discriminations shown here imply that further analyses with young children will be particularly important in efforts to investigate the development of theoretically important stimulus relations.     

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.     

New knowledge derived from learned knowledge: functional-anatomic correlates of stimulus equivalence

Forming new knowledge based on knowledge established through prior learning is a central feature of higher cognition that is captured in research on stimulus equivalence (SE). Numerous SE investigations show that reinforcing behavior under control of distinct sets of arbitrary conditional relations gives rise to stimulus control by new, derived relations. This investigation examined whether frontal-subcortical and frontal-parietal networks known to support reinforced conditional relations also support derived conditional relations. Twelve adult subjects completed matching-to-sample (MTS) training with correct/wrong feedback to establish four trained conditional relations within two distinct, three-member stimulus classes: (1) A1-->B1, B1-->C1 and (2) A2-->B2, B2-->C2. Afterwards, functional neuroimaging was performed when MTS trials were presented involving matching two identical circles (a sensorimotor control condition), trained relations (A-->B, B-->C), and derived relations: symmetry (B-->A, C-->B), transitivity (A-->C), and equivalence (C-->A). Conditional responding to trained and derived relations was similarly correlated with bilateral activation in the targeted networks. Comparing trained to derived relations, however, highlighted greater activation in several prefrontal regions, the caudate, thalamus, and putamen, which may represent the effects of extended training or feedback present during imaging. Each derived relation also evidenced a unique activation pattern. Collectively, the findings extend the role of frontal-subcortical and frontal-parietal networks to derived conditional relations and suggest that regional involvement varies with the type of derived conditional relation.     

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.     

Resurgence of derived stimulus relations.

Resurgence has been shown in human and nonhuman operant behavior, but not in derived relational responses. The present study examined this issue. Twenty-three undergraduates were trained to make conditional discriminations in a three-choice matching-to-sample paradigm. The training resulted in three equivalence classes, each consisting of four arbitrarily configured visual stimuli. The same 12 stimuli were then reorganized, and the conditional discrimination training was repeated such that three new classes were possible. In a subsequent test of derived relations, most subjects showed response patterns that were consistent with the altered conditional discriminations. Subjects were then exposed to conditional discrimination trials under extinction. Most subjects continued to respond consistently with the most recently reinforced conditional discrimination trials. During the next phase, subjects were exposed to symmetry and equivalence trials. Responses consistent with the most recent training produced feedback saying that the responses were incorrect, whereas other responses produced no feedback. Most subjects showed a resurgence of responding that was consistent with their earlier training. Finally, subjects were exposed to conditional discrimination trials carried out in extinction. Most subjects continued to show a resurgence of responding that was consistent with their early training.     

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.     

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.     

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.     

OBSERVATIONAL LEARNING AND THE EMERGENCE OF SYMMETRY RELATIONS IN TEACHING SPANISH VOCABULARY WORDS TO TYPICALLY DEVELOPING CHILDREN

One 9‐year‐old child was taught conditional discriminations between dictated names in Spanish and their corresponding pictures across three stimulus sets while her 10‐year‐old brother observed. Posttests revealed the emergence of symmetry relations in the form of oral naming skills by both children.     

Social Categorization and Stimulus Equivalence

Northern Irish Protestant subjects, Northern Irish Catholic subjects, and English Protestant subjects were taught a series of conditional discriminations using a matching-to-sample procedure. In the presence of Northern Irish Catholic names, subjects were trained to select three-letter nonsense syllables, and in the presence of the nonsense syllables subjects were trained to select Northern Irish Protestant symbols. Subjects were then tested to determine whether the Protestant symbols and Catholic names had become related through symmetry and transitivity. A generalization test was employed to allow for a preliminary investigation of the transfer of experimentally generated equivalence responding to untrained, socially loaded names. Preliminary findings suggest that prior social learning might interfere with equivalence responding. The relevance of these results to the theoretical interpretation of the equivalence phenomenon and to social attitude measurement in general is discussed.