Mental representation of equivalence and order

With mental models based on relational information, the present research shows that the semantics expressed by the relation can determine the structural properties of the constructed model. In particular, we demonstrate a reversal of the classical, well-replicated symbolic distance effect (SDE), as a function of relational semantics. The classical SDE shows that responses are more accurate, and faster, the wider the distance between queried elements on a mentally constructed rank order. We replicate this effect in a study using a relation that expresses a rank hierarchy ("older than," Experiment 4). In contrast, we obtain a clear reversal of the same effect for accuracy data when the relation expresses a number of equivalence classes ("is from the same city," Experiments 1-3). In Experiment 3, we find clear evidence of a reversed SDE for accuracy and latency in the above standard condition, and flat curves of means, across pair distances, for accuracy and latency in a condition that makes equivalence classes salient from the beginning. We discuss these findings in the context of a process model of equivalence class formation based on learned piecemeal information.

Generalized contextual control based on nonarbitrary and arbitrary transfer of stimulus functions

Two experiments with human adults investigated the extent to which the transfer of function in accordance with nonarbitrary versus arbitrary stimulus relations may be brought under contextual control. Experiment 1 comprised four phases. Phase 1 consisted of multiple-exemplar training to establish discriminative functions for solid, dashed, or dotted lines. Phase 2 trained and tested two equivalence classes, each containing a 3D picture, a solid, a dashed, and a dotted form. During Phase 3, a discriminative function was established for each 3D picture. Phase 4 presented the solid, dashed, and dotted stimuli in two different frames, black or gray. The black frame cued function transfer based on nonarbitrary stimulus relations (Frame Physical); the gray frame cued function transfer based on equivalence relations (Frame Arbitrary). Testing and training with the frames was continued until contextual control was established; subsequently contextual control was demonstrated with novel equivalence classes with stimuli composed of the same forms. Experiment 2 replicated and extended Experiment 1 by demonstrating that such contextual control generalized to novel equivalence classes comprising novel forms and responses. The potential implications of the findings for developing increasingly precise experimental analyses of clinically relevant phenomena are considered (e.g., defusion).

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.

Electrophysiological analysis of stimulus variables in equivalence relations

Recently, electrophysiological measures have been used to evaluate the functional overlap between semantic relations and laboratory-defined equivalence relations with abstract stimuli. Several studies using semantic judgment procedures have shown that accompanying EEG-measured neural activity for stimulus pairs from equivalence classes is very similar to that of word pairs from participants' native language. However, those studies often included pronounceable elements (e.g., written nonsense syllables) as at least one member of the experimentally defined classes. The present study conducted EEG studies that contrasted classes with and without such elements. Two groups of undergraduate students completed a matching-to-sample procedure to establish 3 4-member equivalence classes. For Group 1, samples and comparisons were pronounceable pseudowords and abstract figures. For Group 2, the matching-to-sample stimuli were abstract figures only. EEG data recorded during the semantic judgment tasks showed waveform patterns compatible with prior studies of semantic relations in Group 1 but not in Group 2.

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.

Variables affecting the emergence of untaught equivalence relations in children with and without autism

OBJECTIVE

This study examined the formation of equivalence classes among children with ASD and typically developing children.

DESIGN

A single-subject AB and BA design was used.

METHODS

Two of the six equivalence relations were taught. Participants were then tested to determine whether the remaining four equivalence relations were acquired without teaching. Half of the children were taught naming responses first, then selecting responses. Half were taught in the reverse order.

RESULTS

Five out of 10 participants with ASD demonstrated the emergence of all four untaught relations. The remaining five participants showed variability. Nine of the 10 typically developing children demonstrated emergence of all untaught relations. Variation in teaching conditions had no significant effect on outcomes.

CONCLUSIONS

Many children with ASD are capable of generalising to untaught equivalence relations. The results fail to support the claim that acquisition of naming responses is a pre-requisite for the emergence of untaught equivalence relations.

A computational theory for the learning of equivalence relations

Equivalence relations (ERs) are logical entities that emerge concurrently with the development of language capabilities. In this work we propose a computational model that learns to build ERs by learning simple conditional rules. The model includes visual areas, dopaminergic, and noradrenergic structures as well as prefrontal and motor areas, each of them modeled as a group of continuous valued units that simulate clusters of real neurons. In the model, lateral interaction between neurons of visual structures and top-down modulation of prefrontal/premotor structures over the activity of neurons in visual structures are necessary conditions for learning the paradigm. In terms of the number of neurons and their interaction, we show that a minimal structural complexity is required for learning ERs among conditioned stimuli. Paradoxically, the emergence of the ER drives a reduction in the number of neurons needed to maintain those previously specific stimulus–response learned rules, allowing an efficient use of neuronal resources.

Derived transformation of children's pregambling game playing

Contemporary behavior-analytic perspectives on gambling emphasize the impact of verbal relations, or derived relational responding and the transformation of stimulus functions, on the initiation and maintenance of gambling. Approached in this way, it is possible to undertake experimental analysis of the role of verbal/mediational variables in gambling behavior. The present study therefore sought to demonstrate the ways new stimuli could come to have functions relevant to gambling without those functions being trained directly. Following a successful derived-equivalence-relations test, a simulated board game established high- and low-roll functions for two concurrently presented dice labelled with members of the derived relations. During the test for derived transformation, children were reexposed to the board game with dice labelled with indirectly related stimuli. All participants except 1 who passed the equivalence relations test selected the die that was indirectly related to the trained high-roll die more often than the die that was indirectly related to low-roll die, despite the absence of differential outcomes. All participants except 3 also gave the derived high-roll die higher liking ratings than the derived low-roll die. The implications of the findings for behavior-analytic research on gambling and the development of verbally-based interventions for disordered gambling are discussed.

Equivalence relations and behavior: an introductory tutorial

With an emphasis on procedural fundamentals, the original behavior-analytic equivalence experiments and the equivalence paradigm are described briefly. A few of the subsequent developments and implications are noted, with special reference to the possible significance of the findings with respect to language and cognition.

The role of multiple-exemplar training and naming in establishing derived equivalence in an infant

The conditions under which symmetry and equivalence relations develop are still controversial. This paper reports three experiments that attempt to analyze the impact of multiple-exemplar training (MET) in receptive symmetry on the emergence of visual-visual equivalence relations with a very young child, Gloria. At the age of 15 months 24 days (15m24d), Gloria was tested for receptive symmetry and naming and showed no evidence of either repertoire. In the first experiment, MET in immediate and delayed receptive symmetrical responding or listener behavior (from object-sound to immediate and delayed sound-object selection) proceeded for one month with 10 different objects. This was followed, at 16m25d, by a second test conducted with six new objects. Gloria showed generalized receptive symmetry with a 3-hr delay; however no evidence of naming with new objects was found. Experiment 2 began at 17m with the aim of establishing derived visual-visual equivalence relations using a matching-to-sample format with two comparisons. Visual-visual equivalence responding emerged at 19m, although Gloria still had not shown evidence of naming. Experiment 3 (22m to 23m25d) used a three-comparison matching-to-sample procedure to establish visual-visual equivalence. Equivalence responding emerged as in Experiment 2, and naming emerged by the end of Experiment 3. Results are discussed in terms of the history of training in bidirectional relations responsible for the emergence of visual-visual equivalence relations and of their implications for current theories of stimulus equivalence.

Stimulus equivalence: testing Sidman's (2000) theory

Sidman's (2000) theory regarding the origin of equivalence relations predicts that a reinforcing stimulus common to distinct equivalence classes must drop out of the equivalence relations. This prediction was tested in the present study by arranging class-specific reinforcers, R1 and R2, following correct responding on the prerequisite conditional discriminations (Ax-Bx, Cx-Bx) for two stimulus classes, A1B1C1 and A2B2C2. A class-common reinforcer, R3, was presented following correct responding on the prerequisite conditional discriminations for a further two stimulus classes, A3B3C3 and A4B4C4. Sidman's theory predicts reinforcer inclusion within Classes 1 and 2 only, given this training arrangement. Experiment 1 tested for the emergence of four equivalence classes and of stimulus-reinforcer and reinforcer-stimulus relations in each class. Four of the 6 subjects demonstrated the reinforcer-based relations in all four equivalence classes, rather than in only those classes with a class-specific reinforcer, as Sidman's theory predicts. One of the remaining 2 subjects showed the reinforcer-based relations in three of the four classes. Experiment 2 extended these findings to document the emergence of interclass matching relations based on the common reinforcer R3, in 5 of 6 subjects, such that a Class 3 sample occasioned the selection of a Class 4 sample when the Class 3 comparison was absent, and similarly, a Class 4 sample occasioned the selection of a Class 3 comparison when the Class 4 comparison was absent. These interclass relations emerged despite the simultaneous maintenance of Class 3 and 4 baseline conditional discriminations, so that the Class 3 and 4 stimuli and reinforcer simultaneously were, and were not, part of a single larger equivalence class. These data are irreconcilable with Sidman's theory, and question the utility of the application of the equivalence relation in describing derived stimulus relations.