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.     

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.     

Equivalence classification by California sea lions using class-specific reinforcers

The ability to group dissimilar stimuli into categories on the basis of common stimulus relations (stimulus equivalence) or common functional relations (functional equivalence) has been convincingly demonstrated in verbally competent subjects. However, there are investigations with verbally limited humans and with nonhuman animals that suggest that the formation and use of classification schemes based on equivalence does not depend on linguistic skills. The present investigation documented the ability of two California sea lions to classify stimuli into functional classes using a simple discrimination reversal procedure. Following the formation of functional classes in this context, the second experiment showed transfer of the relations that emerged between class members to a matching-to-sample procedure. The third experiment demonstrated that the functional classes could be expanded through traditionally defined equivalence relations. In these three experiments, appropriate within-class responding produced class-specific food reinforcers. Experiment 3 addressed the role of these reinforcers in equivalence classification and showed that the class-specific reinforcers were sufficient to relate new stimuli to the functional classes. These findings show that sea lions can form equivalence classes in simple and conditional discrimination procedures, and that class-specific reinforcers can become equivalence class members.     

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.     

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.     

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.     

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.     

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.     

A test of the discrimination account in equivalence class formation

An equivalence class is typically established when a subject is taught a set of interrelated conditional discriminations with physically unrelated stimuli and additional, untaught, conditional discriminations are then demonstrated. Interestingly, and perhaps counter-intuitively, the relations among the stimuli within such a class are not necessarily equal. Rather, some members of the class are differentially related to other class members. There are two opposing theories of why relations among stimuli are unequal: nodal and discrimination accounts. The former suggests that delayed emergence is due to nodal distance (i.e. the number of intervening stimuli) while the latter suggests that delayed emergence is an artifact of the training procedure itself. The current paper reports on the first empirical study that directly compares these theories. Forty participants were given training designed to establish two 5-member equivalence classes. Participants’ response speed supported the nodal account, thus suggesting that unequal relations among equivalence class members is not an artifact of the training procedure.     

Conditional discrimination and equivalence relations: Control by negative stimuli

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

Development and crossmodal transfer of contextual control of emergent stimulus relations

Six normally capable adults first learned three conditional relations in each of two prospective equivalence classes via match-to-sample training with figures as conditional (sample) and discriminative (comparison) stimuli. Then one trained conditional relation in each prospective class was brought under the control of contextual stimuli, two dictated nonsense syllables. Test performances indicated the emergence of untrained conditional relations, and therefore two equivalence classes, that were conditional on the contextual stimuli. These tests involved untrained combinations of contextual stimuli and stimuli in conditional relations, suggesting that the contextual stimuli functioned independently to control conditional relations rather than forming compound stimuli with samples and comparisons in training. Next, two novel figures were made equivalent to each of the original dictated contextual stimuli by match-to-sample training and testing. On subsequent tests, all subjects demonstrated transfer of conditional control of untrained conditional relations from the original auditory contextual stimuli to equivalent visual stimuli. These outcomes further supported the conclusion that the contextual stimuli exerted true conditional control over conditional relations in the equivalence classes and were not merely elements of compound stimuli.     

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.     

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.     

Formation of new stimulus equivalence classes by exclusion

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

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.     

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.     

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.     

REVERSAL OF BASELINE RELATIONS AND STIMULUS EQUIVALENCE: II. CHILDREN

In a systematic replication of a study using college-student subjects (Pilgrim & Galizio, 1990), 5- to 7-year-old children learned two conditional discriminations (i.e., A1B1, A2B2, A1C1, and A2C2) in a two-choice arbitrary match-to-sample task and showed the emergence of two three-member equivalence classes (A1B1C1 and A2B2C2). Baseline conditional discrimination performances were quickly controlled by reversals of the AC reinforcement contingencies (i.e., choosing Comparison Stimulus C2 was reinforced given Sample A1, and choosing C1 was reinforced given Sample A2) when the reversals were introduced in restricted baselines. On reflexivity, symmetry, and transitivity/equivalence probes following the reversal, there was some limited indication of equivalence-class reorganization (i.e., A1B1C2 and A2B2C1) in keeping with the concurrently performed baseline relations for 2 of 5 subjects, but the predominant pattern across probe trials was one of inconsistent conditional control. These findings suggest that, given similar challenges, equivalence-class performances may be more easily disrupted in young children than in adults.     

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.