Equivalence class analysis of responding consistent with the relational frame of opposition

We replicated and extended studies showing that contextual cues for matching stimuli from 2 separate equivalence classes control the same derived relations as contextual cues for opposition frames in RFT studies. We conducted 2 experiments with 6 college students. In Phase 1, they received training in a conditional discrimination AB. Then, they received training for maintaining AB with X1 as context, and for reversing the sample–comparison relations of AB, with X2. In Phase 2, X1 functioned as context for matching same-class stimuli, and X2 functioned as context for matching separate-class stimuli. In Phase 3, X2 controlled the same derived arbitrary relations as cues for opposition frames in RFT studies. This functional equivalence may suggest that X2 functioned as a cue for opposition frames. In Phase 4, participants matched different stimuli with X2 as context, instead of matching most different (opposite) stimuli. In addition, Different, a cue for matching different stimuli, controlled the same derived arbitrary relations as X2. These results are incompatible with X2 being a cue for opposition frames. Contextual control over equivalence and responding by exclusion can explain these outcomes. The implications of these findings for RFT studies on opposition frames are discussed.     

Producing and Recognizing Analogical Relations

Analogical reasoning is an important component of intelligent behavior, and a key test of any approach to human language and cognition. Only a limited amount of empirical work has been conducted from a behavior analytic point of view, most of that within Relational Frame Theory (RFT), which views analogy as a matter of deriving relations among relations. The present series of four studies expands previous work by exploring the applicability of this model of analogy to topography-based rather than merely selection-based responses and by extending the work into additional relations, including nonsymmetrical ones. In each of the four studies participants pretrained in contextual control over nonarbitrary stimulus relations of sameness and opposition, or of sameness, smaller than, and larger than, learned arbitrary stimulus relations in the presence of these relational cues and derived analogies involving directly trained relations and derived relations of mutual and combinatorial entailment, measured using a variety of productive and selection-based measures. In Experiment 1 participants successfully recognized analogies among stimulus networks containing same and opposite relations; in Experiment 2 analogy was successfully used to extend derived relations to pairs of novel stimuli; in Experiment 3 the procedure used in Experiment 1 was extended to nonsymmetrical comparative relations; in Experiment 4 the procedure used in Experiment 2 was extended to nonsymmetrical comparative relations. Although not every participant showed the effects predicted, overall the procedures occasioned relational responses consistent with an RFT account that have not yet been demonstrated in a behavior-analytic laboratory setting, including productive responding on the basis of analogies.     

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

According to Relational Frame Theory (RFT) C_rel 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 C_rel contextual control through equivalence relations. Experiment 1 evaluated the transfer of C_rel contextual functions for relational responses based on sameness and opposition. Experiment 2 extended these findings by evaluating transfer of function using comparative C_rel stimuli. Both experiments followed a similar sequence of phases. First, abstract forms were established as C_rel 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 C_rel stimuli and other abstract forms were trained and tested (Phase 3). Transfer of function was evaluated by replacing the directly established C_rel stimuli with their equivalent stimuli in the former experimental tasks (Phases 1 and 2). Results from both experiments suggest that C_rel contextual control may be extended via equivalence relations, allowing other arbitrarily related stimuli to indirectly acquire C_rel functions and regulate behavior by evoking appropriate relational responses in the presence of both previously known and novel stimuli.     

The transformation of consequential functions in accordance with the relational frames of same and opposite

Although the literature on reinforcement in behavioral psychology is extensive, few studies have examined the derived transformation of reinforcing functions in accordance with equivalence classes, and no published research has yet examined the derived transformation of consequential functions in accordance with nonequivalence relations. In the present study, which consisted of four experiments, the basic preparation was as follows. First, an arbitrary stimulus, B2, was established as a conditioned punisher, using direct stimulus pairing. Following nonarbitrary relational training, designed to establish SAME and OPPOSITE contextual cues, subjects were exposed to arbitrary relational training using these contextual cues to establish A1 as the same as B1 and C1, and as opposite to B2 and C2. Subsequently, C2 (based on its Same relation with B2) functioned as a punisher and C1 (based on its Opposite relation with B2) functioned as a reinforcer in a simultaneous discrimination task. Critically, the C1 stimulus acquired reinforcing functions, based on the derived relation of Opposite, although no such function had actually been established for any member of the network. Furthermore, these effects were observed across ABA reversals in the baseline contingencies.     

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.     

Function transformation without reinforcement

In studies of function transformation, participants initially are taught to match stimuli in the presence of a contextual cue, X; the stimuli to be matched bear some formal relation to each other, for example, a relation of opposition or difference. In a second phase, the participants are taught to match arbitrary stimuli (say, A and B) in the presence of X. In a final test, A often displays behavioral functions that differ from those of B, and can be predicted from the nature of the relation associated with X in the initial training phase. Here we report function-transformation effects in the absence of selection responses and of their reinforcers. In three experiments with college students, exposure to relations of difference or identity modified the responses given to later stimuli. In Experiment 1, responses to a test stimulus A varied depending on preexposure to pairs of colors that were distinct from A but exemplified relations of difference or identity. In Experiment 2, a stimulus A acquired distinct functions, depending on its previous pairing with a contextual cue X that had itself been paired with identity or difference among colors. Experiment 3 confirmed the results of Experiment 2 with a modified design. Our data are consistent with the notion that relations of identity or difference can serve as stimuli for Pavlovian processes, and, in compound with other cues, produce apparent function-transformation effects.     

A transformation of respondently conditioned stimulus function in accordance with arbitrarily applicable relations.

Adult male subjects saw a sexual film clip paired with a nonsense syllable (C1). Similarly, an emotionally neutral film clip was paired with a second nonsense syllable (C3). Responses to the nonsense syllables were recorded as skin resistance responses. Subjects were also trained in a series of related conditional discriminations, using the C1 and C3 stimuli, from which the following equivalence relations were predicted; A1-B1-C1, A2-B2-C2, and A3-B3-C3. Some subjects were given matching-to-sample (equivalence) tests after the conditional discrimination training (Experiment 1), whereas others were not (Experiment 2). Subjects were tested for a transformation of eliciting functions by presenting the A1 and A3 stimuli, which were related through equivalence to C1 and C3, respectively. Five of the 6 subjects who showed significantly greater conditioned responses to C1 than to C3, also showed significantly greater skin resistance responses to A1 than to A3. Two additional subjects demonstrated a transformation of an eliciting stimulus function in accordance with five-member equivalence relations (Experiment 3), and another 5 subjects demonstrated similar effects in accordance with the relations of sameness and opposition (Experiment 4).     

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.     

Transformation of avoidance response functions in accordance with same and opposite relational frames

Research on the emergence of human avoidance behavior in the absence of direct contact with an aversive event is somewhat limited. Consistent with work on derived relational responding, the present study sought to investigate the transformation of avoidance response functions in accordance with the relational frames of Same and Opposite. Participants were first exposed to nonarbitrary and arbitrary relational training and testing in order to establish Same and Opposite relations among arbitrary stimuli. The training tasks were; Same-A1-B1, Same-A1-C1, Opposite-A1-B2, Opposite-A1-C2. Next, all possible combinatorially entailed (i.e., B-C and C-B) relations were tested. During the avoidance-conditioning phase, one stimulus (B1) from the relational network signaled a simple avoidance response that cancelled a scheduled presentation of an aversive image and sound. All but one of the participants who met the criteria for conditioned avoidance also demonstrated derived avoidance by emitting the avoidance response in the presence of C1 and the nonavoidance response in the presence of C2. Control participants who were not exposed to relational training and testing did not show derived avoidance. Implications of the findings for understanding clinically significant avoidance behavior are discussed.     

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.     

Arbitrarily applicable spatial relational responding

Spatial reasoning, where novel spatial relationships are inferred based on trained relationships, can be conceptualized as arbitrarily applicable spatial relational responding. Here, we conducted two experiments to develop and validate, for the first time, a laboratory procedure to establish arbitrarily applicable spatial relational responding in adult humans. In Experiment 1, participants were trained on nonarbitrary spatial relational tasks designed to establish contextual cues for left of, right of, above, and below. Contextual cues were then used to train a series of arbitrary spatial relations involving four abstract shapes. Following training in a subset of arbitrary relations (A is left of B, B is above C, C is right of D), subsequent testing examined the emergence of untrained spatial relations (B is right of A, C is below B, D is left of C, D is below A and A is above D). When absent in initial tests, spatial relational responding was facilitated by a remedial training procedure incorporating nonarbitrary relational guidance. Participants showed patterns of spatial relational responding consistent with test relations. In Experiment 2, a variant reversal design yielded predictable, reversed spatial relational responses. Overall, the present procedures represent the first empirical demonstration of arbitrarily applicable spatial relational responding and thus, arguably, the first functional analytic model of spatial reasoning.     

A transformation of self-discrimination response functions in accordance with the arbitrarily applicable relations of sameness, more than, and less than

In Experiment 1, 2 experimental subjects were given pretraining of nonarbitrary relations that brought their responses under the control of four contextual stimuli; same, opposite, more than, and less than. One control subject was not exposed to this pretraining. The 2 pretrained subjects and the 3rd nonpretrained subject then received training in six arbitrary relations, the following four relations being the most critical: same/A1-B1, same/A1-C1, less than/A1-B2, more than/A1-C2. All 3 subjects were then tested for seven derived relations, the following three relations being the most important: same/B1-C1, more than/B1-C2, less than/B1-B2. The 2 pretrained subjects, but not the nonpretrained subject, showed the derived relations. One of the stimuli (B1) from the relational network and two novel stimuli (X1 and X2) were then used to train three different self-discrimination responses on three complex schedules of reinforcement. That is, all 3 subjects were trained to pick X1 if they had not emitted a response, to pick B1 if they had emitted one response only, and to pick X2 if they had emitted two responses only. The 2 pretrained subjects, but not the nonpretrained subject, showed the predicted transformation of self-discrimination response functions in accordance with the relations of sameness, more than, and less than (i.e., no response, pick B2; one response only, pick C1; and two responses only, pick C2). In Experiment 2, 2 new subjects were employed, and the arbitrary relational training and testing phases were modified to control for a procedural artifact that may have contributed to the results of the first experiment. Experiment 2 replicated the findings of Experiment 1. The pattern of results support the utility of a relational frames approach to understanding derived stimulus relations.     

The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.     

Relating derived relations as a model of analogical reasoning: reaction times and event-related potentials

The current study aimed to test a Relational Frame Theory (RFT) model of analogical reasoning based on the relating of derived same and derived difference relations. Experiment 1 recorded reaction time measures of similar-similar (e.g., "apple is to orange as dog is to cat") versus different-different (e.g., "he is to his brother as chalk is to cheese") derived relational responding, in both speed-contingent and speed-noncontingent conditions. Experiment 2 examined the event-related potentials (ERPs) associated with these two response patterns. Both experiments showed similar-similar responding to be significantly faster than different-different responding. Experiment 2 revealed significant differences between the waveforms of the two response patterns in the left-hemispheric prefrontal regions; different-different waveforms were significantly more negative than similar-similar waveforms. The behavioral and neurophysiological data support the RFT prediction that, all things being equal, similar-similar responding is relationally "simpler" than, and functionally distinct from, different-different analogical responding. The ERP data were fully consistent with findings in the neurocognitive literature on analogy. These findings strengthen the validity of the RFT model of analogical reasoning and supplement the behavior-analytic approach to analogy based on the relating of derived relations.     

Perceptual equivalence of acoustic cues in speech and nonspeech perception

Trading relations show that diverse acoustic consequences of minimal contrasts in speech are equivalent in perception of phonetic categories. This perceptual equivalence received stronger support from a recent finding that discrimination was differentially affected by the phonetic cooperation or conflict between two cues for the /slIt/-/splIt/contrast. Experiment 1 extended the trading relations and perceptual equivalence findings to the /sei/-/stei/contrast. With a more sensitive discrimination test, Experiment 2 found that cue equivalence is a characteristic of perceptual sensitivity to phonetic information. Using “sine-wave analogues” of the /sei/-/stei/stimuli, Experiment 3 showed that perceptual integration of the cues was phonetic, not psychoacoustic, in origin. Only subjects who perceived the sine-wave stimuli as “say” and “stay” showed a trading relation and perceptual equivalence; subjects who perceived them as nonspeech failed to integrate the two dimensions perceptually. Moreover, the pattern of differences between obtained and predicted discrimination was quite similar across the first two experiments and the “say”-“stay” group of Experiment 3, and suggested that phonetic perception was responsible even for better-than-predicted performance by these groups. Trading relations between speech cues, and the perceptual equivalence that underlies them, thus appear to derive specifically from perception of phonetic information.     

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.     

Signaled Delay of Reinforcement: Effects of Postconditioning Manipulation of Context Associative Strength on Instrumental Performance

Two experiments examined the influence of postconditioning treatments of contextual cues on instrumental responding acquired with a signaled delay of reinforcement schedule. In Experiment 1, mere exposure to the conditioning context after instrumental training resulted in an attenuated response rate during an extinction test. In the second experiment, responding was decreased by exposure to the contextual cues or sessions in which signaled noncontingent reinforcements occurred. The greatest response decrement, however, occurred following unsignaled noncontingent food presentations. The results are discussed with respect to the different roles of contextual cues on operant responding.     

Facilitation of the equivalence--equivalence responding

Equivalence-Equivalence responding, based on equivalence class formation, is a key concept of the functional-analytic model of analogical reasoning held by RFT theorists. Relational stimulus control is supposed to play an important role in this arbitrary relational response. Previous research showed that mere training of the prerequisites for equivalence class formation is not always enough for the derivation of equivalence-equivalence responding, even in adults. In the first experiment, with 12 adult participants, we designed a matching-to-sample training and testing procedure that, although it provided all necessary conditions, did not lead to Equivalence-Equivalence responding in most participants, so that the efficacy of a facilitation procedure could be assessed. In Experiment 2, with 32 valid participants, a matching-to-sample procedure based on non-arbitrary relations was introduced to assess its efficacy in enhancing stimulus control by the relational properties of sample and comparisons. Results showed a moderate effect: 40.6% of the participants passed the test after being exposed to a non-arbitrary relational matching task (but none without it). This research underlines the importance of non-arbitrary relational responses in the derivation of more complex repertoires.     

Contextual dependencies in a stimulus equivalence paradigm

Two experiments with human subjects assessed contextual dependencies in a stimulus equivalence paradigm. Subjects learned to form two sets of stimuli in a matching-to-sample training procedure. Each set was presented against one of two different background colours, the contextual cues. At test, the influence of a context change--that is, presenting each set against the other context--was measured on baseline, symmetry, and equivalence trials. These three trial types reflect a difference in task complexity. It was predicted that the magnitude of context-dependent effects would be a positive function of task complexity. In Experiment 1, the context change was realized by switching the stimulus set at test while keeping the background colour constant. In Experiment 2, the stimulus set remained constant, and the background colour was switched. In both experiments, a change in context only resulted in an increase in response latency on equivalence trials; no effect was seen on symmetry and baseline trials. Results were discussed in the framework of switch costs, habituation to contextual stimuli, and a model based on Shea and Wright (1995) that explains the differential influence of a context switch on easy versus difficult tasks.     

Equivalence relations, contextual control, and naming

This paper reports two experiments that investigated the role of verbal behavior in the emergence and generalization of contextually controlled equivalence classes. During both experiments, participants were trained with two different combinations of the same easily nameable, yet formally unrelated, pictorial stimuli. Match-to-sample baselines for eight four-member classes were established under the contextual control of two colors. In the presence of one color, conditional relations were established between stimuli whose normative names rhymed. In the presence of the other color, conditional relations were established between stimuli whose normative names did not rhyme. Although, during Experiment 1, all participants demonstrated equivalence classes involving rhyming stimuli, none demonstrated the formation of nonrhyme equivalence classes. To investigate this finding, Experiment 2 evaluated whether participants would demonstrate both rhyme and nonrhyme equivalence classes given more extensive exposure to the experimental contingencies. All participants demonstrated contextually controlled rhyme and nonrhyme equivalence classes, although rhyme classes were demonstrated with greater facility than nonrhyme classes. Results indicate that visual stimuli are named, that verbal bases for stimulus classification can affect the emergence of contextually controlled equivalence classes, and that untrained contextually controlled conditional discriminations involving novel stimuli can emerge on the basis of participants' verbal behavior.