The Problem of Class Breakdown in Sidman's (1994, 2000) Theory about the Origin of Stimulus Equivalence.

Sidman (1994, 2000) hypothesized that equivalence relations are a direct outcome of reinforcement contingencies. This theory is problematic because contingencies do not always result in equivalence. Sidman proposed that equivalence relations may conflict with analytic units, the other outcome of contingencies (e.g., in conditional discriminations with common responses/reinforcers). This conflict may result in a generalized class breakdown and a failure to pass equivalence tests. This is more likely in nonhumans, very young humans, etc. The conflict can also result in a selective class breakdown and success in equivalence tests. This occurs after experience shows the organism the necessity and utility of this process. The nature of that experience and the class breakdown processes were not described by Sidman. I explored the implications of the following hypotheses for Sidman's theory. First, conditional discriminations with a common response/reinforcer result in a generalized class breakdown when participants fail to discriminate emergent relations incompatible with contingencies from those compatible. Second, learning to discriminate between the two requires a history of multiple exemplar training (MET). This implies that equivalence class breakdown is a common response to exemplars that have nothing in common except their relations. This, however, contradicts Sidman's views about the impossibility of such process in the absence of a complex verbal repertoire. If that type of learning from MET is possible, then the possibility that MET results in the selective formation of equivalence classes must be admitted, and the utility of hypothesizing that equivalence is a direct outcome of reinforcement contingencies can be questioned.

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).

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.

Aprendizagem Simbólica de Crianças com Autismo: Potencial Preditivo de uma Tarefa / Symbolic Learning in Children with Autism: Predictive Value of a Prototype Task

RESUMO Testes preditivos de aprendizagem podem ser úteis para planejar intervenções mais efetivas para crianças com autismo. O objetivo desse estudo foi avaliar se um protótipo de tarefa, desenvolvido para estender o Teste ABLA-R (Avaliação de Habilidades Básicas de Aprendizagem), seria preditivo de aprendizagem simbólica (formação de classes de equivalência). Três crianças com autismo foram avaliadas pelo ABLA-R e pela tarefa protótipo (denominada Nível 7) e, em seguida, foram expostas a um protocolo de ensino e teste de relações de equivalência. As predições do Nível 7 se confirmaram para dois participantes e parcialmente para o terceiro. Embora sejam necessários mais estudos, os resultados sugerem que a tarefa do Nível 7 pode ser uma potencial adição ao ABLA-R.

ABSTRACT Predictive learning assessments may be useful for developing behavioral interventions for children with autism. The present study evaluated whether a prototype task, developed to extend the ABLA-R (Assessment of Basic Learning Abilities), would be predictive of symbolic learning (establishing equivalence classes). Three children with autism were assessed by the ABLA-R and the prototype task (referred as Level 7) and then exposed to training and testing for emergent conditional discriminations. The Level 7 predictions were confirmed for two participants and partially for the third. Although more studies are needed, the results suggest that the Level 7 task may be a potential addition to the ABLA-R.

Teaching Metaphorical Generation via Tact and Match-to-Sample Instructions: A Brief Report.

The purpose of the study was to examine the effects of an instructional sequence involving simple tact, category tact, and match-to-sample instructions on the emergence of metaphorical extensions about emotions for children with autism spectrum disorder. Three Chinese children (1 girl, 2 boys, 7-8 years old) with autism spectrum disorder participated. Results indicate that the participants' intraverbal responses for metaphorical extensions about emotions emerged or increased without direct training after completion of the instructional sequence to which verbal instruction had been added. All three children maintained the metaphorical extensions about emotions for 4 weeks.

Variables' classification via equivalence relations for the trophic state of a Mediterranean ecosystem.

The trophic state of an aquatic body is influenced by many biotic and abiotic factors. When lots of parameters affect a phenomenon, such as eutrophication, it is difficult to distinguish which are the ones that affect the ecosystem the most. In this paper, we propose an alternative way for data analysis, in order to avoid complex systems with many variables. For the examined Mediterranean shallow lake, the studied parameters are water temperature (°C), ammonia (NH4 -N) (mg/L), dissolved oxygen (mg/L), turbidity (NTU), pH, conductivity (mS/cm), and chlorophyll-a (µg/L). We formed groups with the variables above based on fuzzy equivalence relations and from each group we chose the parameter influence the studied phenomenon the most. Numerical results of fuzzy linear regression showed strong agreement with the proposed method above and pH, NH4 -N, and dissolved oxygen are the variables influence this ecosystem more than the others. PRACTITIONER POINTS: When having many parameters in a studied ecosystem, we propose a way we can distinguish the most representative ones, the parameters that influence more the phenomenon we study each time. Formation of groups in variables can be applied to many case studies in order to have a clear idea of our data and the relevance of each of them in our dependent one. Fuzzy linear regression can be used in order to check the final results and ensure that the equivalence relations are a such a good method used in the data analysis while the researchers save time in long procedures of analyzing parameters not very close involved to the phenomenon investigated every time.

The influence of training procedure and stimulus valence on the long-term maintenance of equivalence relations.

In the current research, we aimed at extending Silveira et al. (2016) results by verifying whether the long-term maintenance of the equivalence classes is influenced by stimulus valence and MTS training procedures. The delayed and simultaneous MTS were used to train two groups of participants in series of conditional relation trials involving pictures of humans' faces expressing familiar emotions (A) and abstract forms (B, C, and D). The participants that demonstrated the emergence of novel BD and DB relations and class-consistent derived transfer of functions returned to the laboratory thirty days later. Follow-up assessments were given in which the probability of class-consistent responses was higher for the happy class only for participants exposed to DMTS training. This result shows that the maintenance of equivalence classes cannot be accounted for only in terms of the affective valence of the familiar stimulus. The affective valence of the happy faces may have yoked with the properties of DMTS, favoring the maintenance of the happy class. Thereby, we discussed the role of mediating verbal behavior evoked selectively by the pictures of happy faces appearing as samples that may have persisted during the delay interval as a possible mechanism underlying performances of participants trained in DMTS procedure.

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.

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.

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.

Equivalence Class Formation in Individuals With Autism: Predictions From ABLA-R Levels.

Children who are diagnosed with autism spectrum disorder (ASD) often fail to show equivalence class formation. This may be related to their difficulty in learning the programmed baseline conditional discriminations. The present study investigated equivalence class formation after training visual identity-matching performance with auditory class-specific consequences in 6 individuals who were diagnosed with ASD and who achieved different levels (Levels 4, 5, and 6) on the Assessment of Basic Learning Abilities-Revised (ABLA-R). The potentially emergent relations were all arbitrary (relations between completely dissimilar stimuli): visual-visual (AB and BA) and auditory-visual (SA and SB). None of the participants who achieved ABLA-R Level 4 or 5 responded in accord with equivalence class formation. They did not present any emergent arbitrary conditional relations (either visual-visual relations or auditory-visual relations). Only participants who achieved ABLA-R Level 6 demonstrated equivalence class formation. These findings are consistent with the predictive ability of the ABLA-R with regard to the acquisition of discriminations and to the emergence of the same type of conditional relations and the same hierarchy of complexity.

Classifying equivalence relations in the Ershov hierarchy.

Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽ c . This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the Δ 2 0 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by ⩽ c on the Σ a - 1 \ Π a - 1 equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.

Efficiency of equivalence-based instruction: A laboratory evaluation.

In equivalence-based instruction (EBI), a large number of stimulus relations can be established through direct instruction of a smaller number of strategically selected relations. We evaluated the efficiency and other potential benefits of EBI in 2 between-subjects experiments with college students that compared EBI with complete instruction (CI). In Experiment 1 (n = 50), mastery criteria in both conditions required an equal number of equally sized trial blocks at equal accuracy. Under those conditions, trials to passing posttests did not differ significantly between groups during the establishment of 3-member classes or during expansion to 4- and 5-member classes. In Experiment 2 (n = 48), mastery criteria were equated across conditions in terms of the number of consecutive correct trials required for each trial type. Under those conditions, EBI required fewer trials to complete than did CI. Neither experiment found an advantage of EBI over CI in terms of facilitating future learning or maintenance of class-consistent responding. Overall, the results suggest that greater efficiency of EBI compared to CI may largely be attributed to learning assessment practices, but additional research is warranted with additional EBI training structures and trial arrangements.

Effect of the number of training trials on the event-related potential correlates of equivalence relations.

In the present study, we aimed to evaluate whether the number of training trials performed bythe participants during the baseline protocol in equivalence class experiments could modulatethe N400 evoked component. Two groups of 15 participants each followed a matching-tosampleprotocol to train on the conditional relations between four sets of abstract stimuli.Participants in the Extended Group performed approximately twice as many trials as those inthe Reduced Group. After having achieved the learning criteria in the equivalence tests,participants' neural activity was recorded during semantic judgment tasks that includedstimulus pairs of both the same (related pairs) and different (unrelated pairs) classes. Ourfindings indicate that participants in the Extended Group had similar N400 components forrelated and unrelated stimulus pairs. Conversely, participants in the Reduced Group had morenegative waveforms for unrelated stimulus pairs compared to the ones for related stimuluspairs. We discuss the necessity of a more careful analysis of the choice of the number ofbaseline training trials in experiments on equivalence relations and N400 component, anddraw parallels between our findings and the N400 effect previously described for high and low frequency words in the participants' native language.

Equivalence class formation in 11-month-old pre-linguistic infants / Formação de classes de equivalência em crianças pré-linguísticas de 11 meses de idade / Formación de clases de equivalencia en niños prelingüísticos de 11 meses de edad

Abstract Several studies have attempted to assess the role of naming in the emergence of equivalence relations, but results are inconsistent; on the one hand, there are reports of equivalence emerging without naming and on the other hand, some authors claim that naming is necessary for equivalence to emerge. The objective of the present study was to evaluate the emergence of equivalence relations in pre-linguistic infants. Five infants aged 11-to-12 months received training in four conditional discriminations (A1-B1, A2-B2, B1-C1, and B2-C2) in order to establish two three-member classes. The participants were tested in reflexivity, symmetry, transitivity and equivalence, and all scored higher than 75% on all tests. On the reflexivity tests, percentages were above 80%; on the symmetry tests, they varied from 75% to 100%; on the transitivity tests, they averaged 75%; while on the equivalence tests results ranged from 87.5% to 100% of correct responses. These results suggest that displaying some degree of expressive language is not necessary for the emergence of equivalence relations.

Resumo Em vários estudos, tem-se tentado avaliar o papel da nomeação na emergência de relações de equivalência, contudo os resultados são inconsistentes, visto que, por um lado, existem relatos de emergência de equivalência em ausência de nomeação e, por outro, alguns autores indicam que a nomeação é necessária para que emerja equivalência. O objetivo deste estudo foi avaliar a emergência de relações de equivalência em crianças pré-linguísticas; especificamente, usou-se uma amostra de cinco crianças de entre 11 e 12 meses que foram treinadas em quatro discriminações condicionais (A1-B1, A2-B2, B1-C1, B2-C2) para formar duas classes de três membros. Os participantes foram avaliados em reflexividade, simetria, transitividade e equivalência, e todos atingiram pontuações maiores a 75 % de acertos em todos os testes. Como resultado, as porcentagens de respostas corretas foram maiores a 80 % no teste de reflexividade, variaram entre 87.5 % e 100 % no de equivalência. Esses resultados apontam a que não é necessário contar com algum tipo de repertório linguístico expressivo para que relações de equivalência emerjam.

Resumen En varios estudios se ha intentado evaluar el rol del nombramiento en la emergencia de relaciones de equivalencia, sin embargo, los resultados son inconsistentes, ya que existen reportes de emergencia de equivalencia en ausencia de nombramiento, y algunos autores señalan que el nombramiento es necesario para que emerja equivalencia. El objetivo del presente estudio fue evaluar la emergencia de relaciones de equivalencia en niños prelingüísticos. Se usó una muestra de cinco infantes de entre 11 y 12 meses de edad que fueron entrenados en cuatro discriminaciones condicionales (A1-B1, A2-B2, B1-C1, B2-C2) para formar dos clases de tres miembros. Los participantes fueron evaluados en reflexividad, simetría, transitividad y equivalencia, y todos lograron puntajes mayores al 75 % de aciertos en todas las pruebas. Como resultado, los porcentajes de respuestas correctas fueron mayores al 80 % en la prueba de reflexividad, variaron entre 75 y 100 % en la de simetría, promediaron 75 % en la de transitividad, y variaron entre 87.5 % y 100 % en la de equivalencia. Estos resultados apuntan a que no es necesario contar con algún tipo de repertorio lingüístico expresivo para que emerjan relaciones de equivalencia.

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.

Generalization of equivalence relations from photos to objects by preschool children.

Generalized equivalence classes are stimulus classes that consist of equivalent stimuli and other physically similar class-member stimuli. The present study evaluated whether preschool children would form equivalence classes among photos of abstract objects (2D) and show equivalence generalization to the corresponding objects (3D), printed photos (2D stimuli), and to black-and-white drawn pictures (2D stimuli). Six typically developing children were taught arbitrary relations to establish three 3-member equivalence classes with 2D stimuli presented on a computer screen. AB-AC baseline relations (for half of the participants) and AB-BC relations (for the other half) were taught using a multiple-probe design to assess taught and tested relations. After class formation, three types of generalization probes were conducted: generalization to 3D stimuli, generalization between 2D (printed photos) and 3D stimuli, and generalization to drawn pictures (2D). All of the participants formed the equivalence classes. Two participants met the criterion for all three generalization probe types. Two participants presented mixed results across tests, and two participants did not exhibit equivalence generalization. The results demonstrated equivalence generalization from 2D to 3D stimuli in preschool children, although the variability across participants suggests that such generalization cannot be assumed a priori.

The transfer of Crel contextual control (same, opposite, less than, more than) through equivalence relations.

According to Relational Frame Theory (RFT) Crel denotes a contextual stimulus that controls a particular type of relational response (sameness, opposition, comparative, temporal, hierarchical etc.) in a given situation. Previous studies suggest that contextual functions may be indirectly acquired via transfer of function. The present study investigated the transfer of Crel contextual control through equivalence relations. Experiment 1 evaluated the transfer of Crel contextual functions for relational responses based on sameness and opposition. Experiment 2 extended these findings by evaluating transfer of function using comparative Crel stimuli. Both experiments followed a similar sequence of phases. First, abstract forms were established as Crel stimuli via multiple exemplar training (Phase 1). The contextual cues were then applied to establish arbitrary relations among nonsense words and to test derived relations (Phase 2). After that, equivalence relations involving the original Crel stimuli and other abstract forms were trained and tested (Phase 3). Transfer of function was evaluated by replacing the directly established Crel stimuli with their equivalent stimuli in the former experimental tasks (Phases 1 and 2). Results from both experiments suggest that Crel contextual control may be extended via equivalence relations, allowing other arbitrarily related stimuli to indirectly acquire Crel functions and regulate behavior by evoking appropriate relational responses in the presence of both previously known and novel stimuli.

Equivalence relations as an analysis criterion of scientific relevance of analytical categories / As relações de equivalência como critério de análise da pertinência científica de categorias analíticas / Las relaciones de equivalencia como criterio de análisis de la pertinencia científica de categorías analíticas

Abstract The aim of this paper is to propose equivalence relations as a structural criterion or analytical order, through which the functions of knowledge required in a scientific activity are delimited. It begins by considering knowledge as a phenomenon studied by psychology, whose explanation requires giving an account of the way in which such behavioral or knowledge functions are established, organized and updated. It is considered that the procedures of matching-to-sample allow understanding the way of abstracting the analytical categories that scientifically structure the knowledge of reality. When using these procedures, new relationships are derived that without the need for direct training, cannot be explained based on principles of stimulus generalization, but rather as equivalent relations differentiated through previous training. They get a closure in an analytical category, once the categorical criteria are abstracted or if desired, when these relationships are nominated. And when categorized or nominated, they transcend the situation, since nominating is understood as an adjustment to conventional criteria. Once situational interactions are nominated, they regulate all social practices, including practices of scientific knowledge.

Resumo O objetivo deste trabalho é propor as relações de equivalência como critério estrutural ou de ordenamento analítico pelo qual possam ser delimitadas as funções do conhecimento requeridas numa atividade científica. Parte-se de considerar o conhecimento como um fenômeno estudado pela psicologia e cuja explicação requer evidenciar a maneira na qual são estabelecidas, organizadas e atualizadas as funções comportamentais ou do conhecimento. Desse modo, considera-se que as tarefas de igualação à amostra permitem compreender o modo de abstrair as categorias analíticas que estruturam cientificamente o conhecimento da realidade. Quando são usados esses procedimentos, são derivadas novas relações que, sem a necessidade de um treinamento direto, não podem ser explicadas com base em princípios de generalização de estímulos, mas sim como relações equivalentes diferenciadas mediante os treinamentos prévios e que adquirem uma delimitação numa categoria analítica quando são abstraídos os critérios categoriais ou, se se quiser, quando essas relações são nominadas. Assim, ao serem categorizadas ou nominadas, elas transcendem a situação -porque nominar se entende como um ajuste a critérios convencionais- e, uma vez que as interações situacionais são nominadas, regulam todas as práticas sociais, incluídas as práticas do conhecimento científico.

Resumen El objetivo del presente trabajo es proponer las relaciones de equivalencia como criterio estructural o de ordenamiento analítico mediante el cual se puedan delimitar las funciones del conocimiento requeridas en una actividad científica. Se parte de considerar al conocimiento como un fenómeno estudiado por la psicología y cuya explicación requiere de dar cuenta de la manera en que se establecen, organizan y actualizan las funciones conductuales o del conocimiento. De este modo, se considera que las tareas de igualación a la muestra permiten comprender el modo de abstraer las categorías analíticas que estructuran científicamente el conocimiento de la realidad. Cuando se usan estos procedimiento, se derivan nuevas relaciones sin la necesidad de un entrenamiento directo y que no pueden explicarse con base en principios de generalización de estímulos, sino, más bien, como relaciones equivalentes diferenciadas mediante los entrenamientos previos y que adquieren un cierre en una categoría analítica cuando se abstraen los criterios categoriales o, si se quiere, cuando estas relaciones se nominan. Así, al categorizarse o nominarse, estas trascienden la situación -porque nominar se entiende como un ajuste a criterios convencionales- y una vez que las interacciones situacionales se nominan, regulan todas las prácticas sociales, incluidas las prácticas del conocimiento científico.