Equivalence classes generated by sequence training

In Experiment 1, 3, adult females were taught with verbal instructions and contingencies to select, in sequence, three arbitrary visual stimuli from an array of five stimuli. After four different sequences were taught, match-to-sample tests assessed emergent conditional relations among all stimuli that had been selected in the same order in the sequences. Subjects' performances indicated development of four stimulus classes, three based on ordinal position and one based on nonselection. Next, match-to-sample training established conditional relations between each of four novel figures and one member of each of the ordinal stimulus classes. Tests confirmed that the classes were equivalence classes, each expanded by one new member. In subsequent sequence tests, the new stimuli were selected in a sequence that was consistent with ordinal class membership. Experiment 2 replicated Experiment 1 with 2 different adult females, but the verbal instructions were omitted. Results were similar to Experiment 1, except that extensive review and retesting were required before expansion of the ordinal classes with the novel figures was observed.     

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.     

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.     

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.     

Predicting the extension of equivalence classes from primary generalization gradients: the merger of equivalence classes and perceptual classes.

In Experiment 1, 6 college students were given generalization tests using 25 line lengths as samples with a long line, a short line, and a “neither” option as comparisons. The neither option was to be used if a sample did not go with the other comparisons. Then, four-member equivalence classes were formed. Class 1 included three nonsense words and the short line. Class 2 included three other nonsense words and the long line. After repeating the generalization test for line length, additional tests were conducted using members of the equivalence classes (i.e., nonsense words and lines) as comparisons and intermediate-length lines as samples. All Class 2 comparisons were selected in the presence of the test lines that also evoked the selection of the long line in the generalization test that had been given before equivalence class formation. Class 1 yielded complementary findings. Thus, the preclass primary generalization gradient predicted which test lines acted as members of each equivalence class. Regardless of using comparisons that were nonsense words or lines, the post-class-formation gradients overlapped, showing the substitutability of class members. Experiment 2 assessed the discriminability of the intermediate-length test lines from the Class 1 (shortest) and Class 2 (longest) lines. The test lines that functioned as members of an equivalence class were discriminable from the line that was a member of the same class by training. Thus, these test lines also acted as members of a dimensionally defined class of “long” or “short” lines. Extension of an equivalence class, then, involved its merger with a dimensionally defined class, which converted a close-ended class to an open-ended class. These data suggest a means of predicting class membership in naturally occurring categories.     

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.     

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.     

Establishing stimulus equivalences among retarded adolescents.

Two separate sets of stimuli were established as stimulus classes in a match-to-sample task by using each stimulus as both a sample and choice stimulus for every other member within that set. After classes were established, the subjects were taught to select one member of each class when an associated auditory stimulus was presented. After this training, three of six subjects were able to select the remaining members of each stimulus class in response to the appropriate auditory stimuli without direct training. The other three subjects also demonstrated transfer after additional members of each stimulus class were brought under the control of the auditory stimuli through direct training.     

Naming and categorization in young children: vocal tact training

In three experiments, 2- to 4-year-old children, following pretraining with everyday objects, were presented with arbitrary stimuli of differing shapes. In Experiment 1A, 9 subjects were trained one common tact response, "zag," to three of these and a second tact, "vek," to another three. In category match-to-sample Test 1, 4 subjects sorted accurately when required only to look at the sample before selecting from five comparisons. The remaining 5 subjects succeeded in Test 2, in which they were required to tact the sample before selecting comparisons. Experiment 1B showed, for 2 of these subjects, that tact training with 12 arbitrary stimuli established two six-member classes that were still intact 6 weeks later. In Experiment 2, 3 new subjects participated in a common tact training procedure that ensured that none of the exemplars from the same class were presented together prior to the test for three-member classes. Two subjects passed category Test 1 and the third passed Test 2. Tests showed subjects' listener behavior in response to hearing /zog/ and /vek/ to be in place. These experiments indicate that common naming is effective in establishing arbitrary stimulus classes and that category match-to-sample testing provides a robust measure of categorization.     

Simple discrimination training with differential responses to establish functional and equivalence classes with preschool children

The present study assessed whether simple discrimination training with differential responses would produce functional and equivalence classes with preschool children. In Experiment 1, we exposed 10 children to simple successive discrimination training in which they had to press different buttons (selection‐based responses). Response 1 (R1) was reinforced only in the presence of A1, B1, or C1, and Response 2 (R2) was reinforced only in the presence of A2, B2, or C2. We assessed the formation of functional classes by training new selection responses in the presence of one member of each class (A1‐R3, A2‐R4) and testing to see if these responses would occur in the presence of other members. Eight children responded consistently with functional class formation. Four of these eight children also responded consistently with the formation of equivalence classes. Experiment 2 investigated whether differential motor responses (i.e., gestures) would improve equivalence class yields. Three of six children showed both functional and equivalence class formation. In general, the results indicate that the simple discrimination procedure with differential responses yielded functional and equivalence class formation.     

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.     

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.     

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.     

Compound stimuli in emergent stimulus relations: Extending the scope of stimulus equivalence

Three experiments were conducted to investigate stimulus relations that might emerge when college students are taught relations between compound sample stimuli and unitary comparison stimuli using match-to-sample procedures. In Experiment 1, subjects were taught nine AB-C stimulus relations, then tested for the emergence of 18 AC-B and BC-A relations. All subjects showed the emergence of all tested relations. Twelve subjects participated in Experiment 2. Six subjects were taught nine AB-C relations and were then tested for symmetrical (C-AB) relations. Six subjects were taught nine AB-C and three C-D relations and were then tested for nine AB-D (transitive) relations. Five of 6 subjects demonstrated the emergence of symmetrical relations, and 6 subjects showed the emergence of transitivity. In Experiment 3, 5 college students were taught nine AB-C and three C-D relations and were then tested for nine equivalence (D-AB) relations and 18 AD-B and BD-A relations. Three subjects demonstrated all tested relations. One subject demonstrated the AD-B and BD-A relations but not the D-AB relations. One subject did not respond systematically during testing. The results of these experiments extend stimulus equivalence research to more complex cases.     

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.     

Typicality effects in contingency-shaped generalized equivalence classes

Two experiments were conducted using match-to-sample methodologies in an effort to model lexical classes, which include both arbitrary and perceptual relations between class members. Training in both experiments used a one-to-many mapping procedure with nonsense syllables as samples and eight sets of abstract stimuli as comparisons. These abstract stimuli differed along a number of dimensions, four of which were critical to the experimenter-defined class membership. Stimuli in some comparison sets included only one of the class-defining features, but stimuli in other sets included two, three, or all four of the critical features. After mastery of the baseline training, three types of probe tests were conducted: symmetry, transitivity/equivalence, and novel probe tests in which the training nonsense syllables served as samples, and comparisons were novel abstract stimuli that included one or more of the class-defining features. Symmetry and transitivity/equivalence probe tests showed that the stimuli used in training became members of equivalence classes. The novel stimuli also became class members on the basis of inclusion of any of the critical features. Thus these probe tests revealed the formation of open-ended generalized equivalence classes. In addition, typicality effects were observed such that comparison sets with more critical features were learned with fewer errors, responded to more rapidly, and judged to be better exemplars of the class. Contingency-shaped stimulus classes established through a match-to-sample procedure thus show several important behavioral similarities to natural lexical categories.     

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.     

Reorganization of equivalence classes: effects of preliminary training and meaningful stimuli

In Condition 1, adults learned the baseline relations for the three equivalence classes A1‐B1‐C1‐D1‐E1, A2‐B2‐C2‐D2‐E2, and A3‐B3‐C3‐D3‐E3. Classes contained abstract shapes in the ABS and four preliminary training groups. Each class in the PIC group contained one picture and four abstract shapes. Before class formation for four other groups, preliminary training involved establishing identity (CC) or arbitrary (CX) relations either with or without a delay. Without preliminary training, classes formed with low and high likelihoods in the ABS and PIC groups, respectively. Preliminary training with no delay produced modest increases in class formation, while preliminary training with delay produced large increases in class formation. Condition 2 replicated Condition 1 but with training of reassigned BC and CD relations that linked C from one class to B and D from another class: B1‐C2, B2‐C3, B3‐C1, C2‐D1, C3‐D2, and C1‐D3. Subsequent tests assessed the emergence of the reorganized classes A1‐B1 ‐C2 ‐D1‐E1, A2‐B2‐ C3 ‐D2‐E2, and A3‐B3‐ C1 ‐D3‐E3. All preliminary training procedures increased likelihood of forming the reorganized classes to the level seen in the PIC group. Greater gains were produced by preliminary training with no delays than with delays. Test performances also showed how preliminary training influenced baseline acquisition speed and participant‐defined 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.     

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.