Equivalence relations do exist before they are tested: Confirmatory evidence revealed by EEG measurements

We examined equivalence-based N400 effects by comparing EEG data from participants with different experiences with equivalence testing. Before a priming task used in EEG measurement, Group 1 was given only matching-to-sample training trials whereas Group 2 was exposed to matching-to-sample training and equivalence probe trials. We asked whether exposure to the reinforcement contingency was sufficient to bring about an N400 outcome that might indicate potentially emergent equivalence relations or if such a response depended on experience with equivalence tests. Results showed robust N400 in both groups. Experience with equivalence tests did not further increase the N400 effects. Our findings add confirmatory evidence that equivalence relations may originate via the reinforcement contingency alone. Furthermore, complementary EEG data collected from priming tasks involving words from natural language showed functional overlap between laboratory-defined equivalence and natural word-based N400 effects.     

Nonhumans have not yet shown stimulus equivalence

Recently, two published articles have reported finding stimulus equivalence in nonhumans. One suggested that equivalence was due to the mediation of names. The procedure used trained all components of all tested relations. Because nothing was derived, the defining characteristics of equivalence were not achieved. In the second study a definition of equivalence was proposed that fails to distinguish functional stimulus classes from equivalence classes. The resulting data are not clearly relevant to stimulus equivalence in Sidman's sense of the term. Stimulus equivalence has not yet been shown in nonhumans.     

Speed analyses of stimulus equivalence.

The functional substitutability of stimuli in equivalence classes was examined through analyses of the speed of college students'' accurate responding. After training subjects to respond to 18 conditional relations, subjects'' accuracy and speed of accurate responding were compared across trial types (baseline, symmetry, transitivity, and combined transitivity and symmetry) and nodal distance (one- through five-node transitive and combined transitive and symmetric relations). Differences in accuracy across nodal distance and trial type were significant only on the first tests of equivalence, whereas differences in speed were significant even after extended testing. Response speed was inversely related to the number of nodes on which the tested relations were based. Significant differences in response speed were also found across trial types, except between transitivity and combined trials. To determine the generality of these comparisons, three groups of subjects were included: An instructed group was given an instruction that specified the interchangeability of stimuli related through training; a queried group was queried about the basis for test-trial responding: and a standard group was neither instructed nor queried. There were no significant differences among groups. These results suggest the use of response speed and response accuracy to measure the strength of matching relations.     

Effects of mastery criterion on the emergence of derived equivalence relations

In this study, we manipulated mastery criterion form (rolling or block) and stringency (across 6 or 12 trials) and measured the emergence of derived relations. College students learned neuroanatomy equivalence classes and experienced one of two rolling mastery criteria (6 or 12 consecutive correct responses) or a block mastery criterion (12 trials in a block) during training. The study found that block and rolling mastery criteria produced similar outcomes. Effectiveness was hampered when the criterion was less stringent.     

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.     

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.     

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.     

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.     

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.     

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.     

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.     

Testing response-stimulus equivalence relations using differential responses as a sample

This study tested the notion that an equivalence relation may include a response when differential responses are paired with stimuli presented during training. Eight normal adults learned three kinds of computer mouse movements as differential response topographies (R1, R2, and R3). Next, in matching-to-sample training, one of the response topographies was used to select a comparison stimulus B (B1, B2, or B3) conditionally upon presentation of sample stimulus A (A1, A2, or A3), and to select stimulus D (D1, D2, or D3) conditionally upon presentation of stimulus C (C1, C2, or C3). After two sample-comparison-response relations (ABR and CDR) were established, 18 sample-comparison relations were tested (BA, DC, RA, RB, RC, RD, AC, CA, AD, DA, BC, CB, BD, DB, AA, BB, CC, and DD). In the RA, RB, RC, and RD tests, the differential responses (R1, R2, and R3) were used as sample stimuli. All subjects made class-consistent comparison selections in the tests. This study provides evidence that responses may become members of an equivalence class.     

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.     

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.     

Conditional discrimination and equivalence relations: A theoretical analysis of control by negative stimuli

A detailed analysis is presented of the ways in which control by the negative stimulus in two-comparison conditional discriminations may be expected to affect the outcome of tests for the properties of equivalence relations. Control by the negative stimulus should produce the following results: (a) no observable effect on symmetry tests; (b) reflexivity test results should look like “oddity” rather than “identity”; and (c) transitivity tests that involve an odd number of nodes should yield results that are 100% opposite to tests that involve an even number of nodes. The analysis also considers the effects of variation in the type of comparison-stimulus control between and within baseline conditional discriminations. Methods are suggested for experimentally regulating the type of control, and for verifying the predictions that the analysis generates. If suggested experiments continue to support the analysis, investigators who use two-comparison conditional discriminations to study equivalence relations will either have to control explicitly whether the positive or the negative comparison governs their subjects' choices, or they will have to abandon two comparisons and use three or more comparisons instead.     

Emergent stimulus relations depend on stimulus correlation and not on reinforcement contingencies

We aimed to investigate whether novel stimulus relations would emerge from stimulus correlations when those relations explicitly conflicted with reinforced relations. In a symbolic matching-to-sample task using kanji characters as stimuli, we arranged class-specific incorrect comparison stimuli in each of three classes. After presenting either Ax or Cx stimuli as samples, choices of Bx were reinforced and choices of Gx or Hx were not. Tests for symmetry, and combined symmetry and transitivity, showed the emergence of three 3-member (AxBxCx) stimulus classes in 5 of 5 human participants. Subsequent tests for all possible emergent relations between Ax, Bx, Cx and the class-specific incorrect comparisons Gx and Hx showed that these relations emerged for 4 of 5 the participants after extended overtraining of the baseline relations. These emergent relations must have been based on stimulus-stimulus correlations, and were not properties of the trained discriminated operants, because they required control by relations explicitly extinguished during training. This result supports theoretical accounts of emergent relations that emphasize stimulus correlation over operant contingencies.     

Translational evaluation of training structures in equivalence-based instruction

We used a laboratory preparation to evaluate the claim that equivalence-based instruction (EBI) is an efficient form of instruction due to eliminating the need for emergent relations to be taught. Three groups of college students received training to establish 3 stimulus classes with 4 members in each class. Two groups received either a linear series (EBI-LS) or a 1-to-many training structure (EBI-OTM group). A control group received complete instruction (CI) that targeted all possible relations between the members of each class. The EBI-OTM group required fewer trials to complete instruction compared to CI, whereas EBI-LS did not. The EBI-OTM and the CI groups performed equally well on a posttest that followed initial attainment of the mastery criterion, whereas the EBI-LS group performed more poorly than the other 2. The groups' performance on a function transfer test did not differ. The results support the claim that compared to CI, EBI is an efficient form of instruction when it follows an OTM structure. However, they also suggest this efficiency advantage cannot be attributed to the fewer relations that need to be taught in EBI, as the EBI-OTM and the EBI-LS groups were trained on the same number of relations.     

Emergence of response‐response relations

The present study examined whether bidirectional response‐response relations could be established without direct reinforcement. In AB training for 12 undergraduates, higher rates of touches to a white circle on the monitor screen (A1) produced two stimuli (B1 and B2) on half of the trials, whereas lower rates (A2) produced the same effect on the other half. Choosing one of the two stimuli was reinforced according to the preceding responding (A1B1 and A2B2). In BC training, touching a stimulus (B1 or B2) produced three white circles lined up horizontally on the screen, after which one of two different response sequences to the circles (left‐center‐right, C1 or C2, and right‐center‐left, C2 or C1) were reinforced, depending on the stimulus presented (B1C1 and B2C2). After AB and BC relations were established, 11 of 12 participants showed the emergence of untrained relations (BA, CB, AC, and CA) throughout five test sessions, and the remaining participant showed it in the first four test sessions. These response‐response relations were replicated with five other undergraduates and different trained relations.     

Toward a technology of derived stimulus relations: an analysis of articles published in the journal of applied behavior analysis, 1992-2009

Every article on stimulus equivalence or derived stimulus relations published in the Journal of Applied Behavior Analysis was evaluated in terms of characteristics that are relevant to the development of applied technologies: the type of participants, settings, procedure (automated vs. tabletop), stimuli, and stimulus sensory modality; types of relations targeted and emergent skills demonstrated by participants; and presence versus absence of evaluation of generalization and maintenance. In most respects, published reports suggested the possibility of applied technologies but left the difficult work of technology development to future investigations, suggestions for which are provided.