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.     

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.     

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.     

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.     

Nodality effects during equivalence class formation: An extension to sight-word reading and concept development

Three students with moderate disabilities were taught to read and match-to-sample sight words comprising stimulus sets based upon the four food groups. We taught students conditional discriminations within four four-member sets using a single-sample/four-comparison procedure. Students were taught A-B, B-C, and C-D conditional discriminations for each of the four potential stimulus classes. Subsequent probes tested for relations based upon symmetry and one-node and two-node transitivity. The performances for all students indicated that symmetric relations emerged before one-node transitive relations, and that one-node transitive relations emerged before two-node transitive relations. These results are consistent with a pattern of responding, referred to as a "nodality effect," in which relations with fewer nodes are demonstrated prior to the demonstration of relations with a greater number of nodes. These results extend this area of research to sight-word reading for students with moderate disabilities.     

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.     

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.     

Reversal of baseline relations and stimulus equivalence: I. Adults

Following the emergence of two four-member equivalence classes (A1B1C1D1 and A2B2C2D2), 5 students were exposed to a series of phases including a baseline conditional discrimination reversal (i.e., choosing D2 was reinforced and D1 punished given Sample A1; choosing D1 was reinforced and D2 punished given Sample A2), the delayed introduction of CD/DC transitivity/equivalence probes, DE conditional discrimination training, a second baseline conditional discrimination reversal (i.e., choosing C2 was reinforced given B1, etc.), and a return to original baseline reinforcement contingencies. Results showed that baseline and symmetry probe performances were extremely sensitive to baseline modifications. In contrast, patterns on transitivity/equivalence probes remained predominantly consistent with the originally established equivalence classes, although there were exceptions on some E probe relations for 2 subjects. The dissociation between baseline and symmetry versus transitivity/equivalence patterns may have important implications because it is not easily accounted for by current models of equivalence phenomena.     

Establishing auditory stimulus control over an eight-member equivalence class via conditional discrimination procedures

Two eight-member equivalence classes of visual stimuli were established during three phases of a training program. In Phase 1, two training arrangements were compared. In one, 3 subjects were taught on different trials to select from a single pair of comparison stimuli (A1, A2) in response to eight sample stimuli that were trained in pairs (B1, B2; C1, C2; D1, D2; E1, E2). In the second arrangement, subjects were taught to select from four pairs of comparisons (B1, B2; C1, C2; D3, D2; E2, E2) in response to two samples (A1, A2). Training with the single pair of comparison stimuli resulted in the development of equivalence relations (B1C1, B2C2, D1B1, D2B2, B1E1, B2E2, C1D1, C2D2, C1E1, C2E2, D1E1, D2E2, and their reciprocals) between the sample stimuli without direct training of these relations. In the other training arrangement, these relations among the comparison stimuli developed in the performance of 1 subject only. In Phase 2, three new pairs of stimuli (F1, F2; G1, G2; H1, H2) were substituted for three of the original pairs (B1, B2; C1, C2; D1, D2) and the training arrangements for the groups were reversed. Following training, the performances that showed equivalence relations on the probes in the first phase also showed equivalence relations in the second phase. If such relations did not develop in the first phase, they did not do so in the second phase. In Phase 3, relations between stimuli across the two previous phases (e.g., B1F1, B2F2, B1G1, B2H2, C1F1, etc.) were investigated. The 4 subjects whose performances showed the development of these relations were taught to select one stimulus from each class (E1 and E2) in response to a verbal label (I1 and I2) and then were tested to see if the verbal label controlled responding to the remaining members of the class (e.g., I1A1, I2A2, I1B1, I2B2, etc.). For 3 subjects, this generalized control occurred; for the 4th, generalization occurred only after verbal training with a second pair of visual stimuli (F1 and F2). In retests several months later, these auditory-visual relations were found to be intact or, if not, were recovered without direct training.     

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.     

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.     

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.     

On the role of covarying functions in stimulus class formation and transfer of function

This experiment investigated whether directly trained covarying functions are necessary for stimulus class formation and transfer of function in humans. Initial class training was designed to establish two respondent-based stimulus classes by pairing two visual stimuli with shock and two other visual stimuli with no shock. Next, two operant discrimination functions were trained to one stimulus of each putative class. The no-shock group received the same training and testing in all phases, except no stimuli were ever paired with shock. The data indicated that skin conductance response conditioning did not occur for the shock groups or for the no-shock group. Tests showed transfer of the established discriminative functions, however, only for the shock groups, indicating the formation of two stimulus classes only for those participants who received respondent class training. The results suggest that transfer of function does not depend on first covarying the stimulus class functions.     

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.     

Stimulus equivalence and arbitrarily applicable relational responding.

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

Contextual control of stimulus generalization and stimulus equivalence in hierarchical categorization

The purpose of this study was to determine whether hierarchical categorization would result from a combination of contextually controlled conditional discrimination training, stimulus generalization, and stimulus equivalence. First, differential selection responses to a specific stimulus feature were brought under contextual control. This contextual control was hierarchical in that stimuli at the top of the hierarchy all evoked one response, whereas those at the bottom each evoked different responses. The evocative functions of these stimuli generalized in predictable ways along a dimension of physical similarity. Then, these functions were indirectly acquired by a set of nonsense syllables that were related via transitivity relations to the originally trained stimuli. These nonsense syllables effectively served as names for the different stimulus classes within each level of the hierarchy.