Equivalence relations and the contextual control of multiple derived stimulus functions

Contextual control is a key aspect in equivalence research to support the claim that stimuli may have multiple functions or symbols may have multiple meanings. The present study investigated the contextual control of multiple derived stimulus functions in two experiments. In Experiment 1, equivalence classes were formed and one stimulus set from each class was used to establish two different functions: one via positive reinforcement (key-pressing) and another via negative reinforcement (button clicking), both under contextual control of two different background colors. Later, other stimuli from the equivalence class were presented on those background colors and contextual control of multiple derived stimulus functions was assessed. Experiment 2 added a third background in which no programmed response was reinforced, that is, responses were extinguished. Transfer-of-function tests revealed contextual control of three different functions, including derived extinction. Implications for equivalence relations as a behavior-analytical model of symbolic functioning are discussed.     

Development and crossmodal transfer of contextual control of emergent stimulus relations

Six normally capable adults first learned three conditional relations in each of two prospective equivalence classes via match-to-sample training with figures as conditional (sample) and discriminative (comparison) stimuli. Then one trained conditional relation in each prospective class was brought under the control of contextual stimuli, two dictated nonsense syllables. Test performances indicated the emergence of untrained conditional relations, and therefore two equivalence classes, that were conditional on the contextual stimuli. These tests involved untrained combinations of contextual stimuli and stimuli in conditional relations, suggesting that the contextual stimuli functioned independently to control conditional relations rather than forming compound stimuli with samples and comparisons in training. Next, two novel figures were made equivalent to each of the original dictated contextual stimuli by match-to-sample training and testing. On subsequent tests, all subjects demonstrated transfer of conditional control of untrained conditional relations from the original auditory contextual stimuli to equivalent visual stimuli. These outcomes further supported the conclusion that the contextual stimuli exerted true conditional control over conditional relations in the equivalence classes and were not merely elements of compound stimuli.     

Incongruous stimulus pairing and conditional discrimination training: effects on relational responding

In Experiment 1, 5 subjects were exposed to a stimulus-pairing procedure in which two nonsense syllables, identified by a letter-number code as A1 and C2, each predicted the onset of a sexual film clip, and the nonsense syllables A2 and C1 each predicted the onset of a nonsexual film clip. Subjects were then exposed to a matching-to-sample test in which the nonsense syllables A1 and A2 were presented as sample stimuli and C1 and C2 were presented as comparison stimuli and vice versa (i.e., C stimuli as samples and A stimuli as comparisons). All subjects matched A1 with C2 and A2 with C1. Subjects were then trained on the conditional discriminations A1-B1, A2-B2, B1-C1, B2-C2, after which the matching-to-sample test was again administered. All subjects continued to match A1 with C2 and A2 with C1 in accordance with the earlier stimulus-pairing contingencies. An additional 5 subjects were exposed first to conditional discrimination training and testing before being exposed to the incongruous stimulus pairing and matching-to-sample testing. Under these conditions, 4 of the 5 subjects always matched A1 with C1 and A2 with C2. Experiment 2 replicated Experiment 1, except that a matching-to-sample test was not administered following the initial training procedure. Under these conditions, matching-to-sample test performances were controlled by the contingencies that had immediately preceded the test. Experiment 3 indicated that initial matching-to-sample test performances were unlikely to change, even after repeated exposure to incongruous training and testing. Experiment 4 demonstrated that pretraining with unrelated stimulus sets increased the sensitivity of matching-to-sample test performances to incongruous contingencies when they were similar in format to those arranged during pretraining. These data may have implications for a behavior-analytic interpretation of attitude formation and change.     

Typicality effects in contingency-shaped generalized equivalence classes

Two experiments were conducted using match-to-sample methodologies in an effort to model lexical classes, which include both arbitrary and perceptual relations between class members. Training in both experiments used a one-to-many mapping procedure with nonsense syllables as samples and eight sets of abstract stimuli as comparisons. These abstract stimuli differed along a number of dimensions, four of which were critical to the experimenter-defined class membership. Stimuli in some comparison sets included only one of the class-defining features, but stimuli in other sets included two, three, or all four of the critical features. After mastery of the baseline training, three types of probe tests were conducted: symmetry, transitivity/equivalence, and novel probe tests in which the training nonsense syllables served as samples, and comparisons were novel abstract stimuli that included one or more of the class-defining features. Symmetry and transitivity/equivalence probe tests showed that the stimuli used in training became members of equivalence classes. The novel stimuli also became class members on the basis of inclusion of any of the critical features. Thus these probe tests revealed the formation of open-ended generalized equivalence classes. In addition, typicality effects were observed such that comparison sets with more critical features were learned with fewer errors, responded to more rapidly, and judged to be better exemplars of the class. Contingency-shaped stimulus classes established through a match-to-sample procedure thus show several important behavioral similarities to natural lexical categories.     

Transfer of contextual stimulus function via equivalence class development

In a conditional discrimination, 6 college students arranged six Cyrillic letters into groups of three based upon which of two additional Cyrillic letters (contextual stimuli) was present. All subjects demonstrated symmetry and transitivity within each class of equivalent stimuli. In a second conditional discrimination, two more Cyrillic letters were related to each contextual stimulus. Testing of symmetrical and transitive relations between the original contextual stimulus and the two new ones confirmed the development of two three-member classes of contextual stimuli. Subsequent tests demonstrated that the new contextual stimuli controlled the previously trained sample-comparison relations for all subjects.     

Generalization of a tactile stimulus in horses.

Using horses, we investigated the control of operant behavior by a tactile stimulus (the training stimulus) and the generalization of behavior to six other similar test stimuli. In a stall, the experimenters mounted a response panel in the doorway. Located on this panel were a response lever and a grain dispenser. The experimenters secured a tactile-stimulus belt to the horse's back. The stimulus belt was constructed by mounting seven solenoids along a piece of burlap in a manner that allowed each to provide the delivery of a tactile stimulus, a repetitive light tapping, at different locations (spaced 10.0 cm apart) along the horse's back. Two preliminary steps were necessary before generalization testing: training a measurable response (lip pressing) and training on several reinforcement schedules in the presence of a training stimulus (tapping by one of the solenoids). We then gave each horse two generalization test sessions. Results indicated that the horses' behavior was effectively controlled by the training stimulus. Horses made the greatest number of responses to the training stimulus, and the tendency to respond to the other test stimuli diminished as the stimuli became farther away from the training stimulus. These findings are discussed in the context of behavioral principles and their relevance to the training of horses.     

Contextual control by function and form of transfer of functions

This study investigated conditions leading to contextual control by stimulus topography over transfer of functions. Three 4-member stimulus equivalence classes, each consisting of four (A, B, C, D) topographically distinct visual stimuli, were established for 5 college students. Across classes, designated A stimuli were open-ended linear figures, B stimuli were circular, C stimuli three-sided, and D stimuli four-sided. Three different computer tasks then were trained with the B stimuli. Differential reinforcement and punishment procedures were then used to establish control over function transfer by the topography of the class members. For Task 1, function transfer, responding to C and D stimuli as subjects had to B stimuli, was reinforced. For Task 2, function transfer was reinforced for C stimuli but punished for D stimuli. For Task 3, function transfer was punished for both C and D stimuli. New equivalence classes were then established and tests for generalized contextual control were presented. All 5 subjects showed generalized contextual control of transfer of functions by stimulus topography. Implications of contextual control over function transfer in natural settings are discussed.     

Reinforcer frequency and restricted stimulus control.

Stimulus control was evaluated in 3 individuals with moderate to severe mental retardation by delayed identity matching-to-sample procedures that presented either one or two discrete forms as sample stimuli on each trial. On pretests, accuracy scores on one-sample trials were uniformly high. On two-sample trials, the correct stimulus (i.e., the one that subsequently appeared in the comparison array) varied unpredictably, and accuracy scores were substantially lower, suggesting that both sample stimuli did not exert stimulus control on every trial. Subjects were then given training sessions with the one-sample task and with a new set of four stimuli. For two of the stimuli, correct matching responses were followed by reinforcers on a variable-ratio schedule that led to a high reinforcer rate. For the other two stimuli, correct responses were followed by reinforcers on a variable-ratio schedule that led to a substantially lower reinforcer rate. Results on two-sample tests that followed showed that (a) on trials in which comparison arrays consisted of one high reinforcer-rate and one low reinforcer-rate stimulus, subjects most often selected the high-rate stimulus; and (b) on trials in which the comparison arrays were either two high reinforcer-rate stimuli or two low reinforcer-rate stimuli and the samples were one high reinforcer- and one low reinforcer-rate stimulus, accuracy was higher on trials with the high-rate comparisons. These results indicate that the frequency of stimulus control by high reinforcer-rate samples was greater than that by low reinforcer-rate samples. Following more training with the one-sample task and reversed reinforcement schedules for all stimuli, the differences in stimulus control frequencies on two-sample tests also reversed. These results demonstrate experimental control by reinforcement contingencies of which of two sample stimuli controlled selections in the two-sample task. The procedures and results may prove to be relevant for understanding restricted stimulus control and stimulus overselectivity.     

The relation between stimulus function and equivalence class formation

Fifty participants were exposed to a simple discrimination-training procedure during which six S+ functions were established for six arbitrary stimuli, and S- functions were established for a further six stimuli. Following this training, each participant was exposed to one of five conditions. In the S+ condition, participants were exposed to a stimulus equivalence training and testing procedure using only the six S+ stimuli as samples and comparisons. In the S+/S- condition, participants were exposed to the same training and testing sequence as in the S+ condition, the difference being that three S+ and three S- stimuli were used as sample and comparison stimuli, with each set of three corresponding to the trained equivalence relations. In the S+/S- mixed condition, the S+ and S- stimuli were assigned to their roles as samples and comparisons in a quasi-random order. In the S- condition, all six S- stimuli were used. The no-function condition served as a control condition and employed stimuli for which no stimulus-control functions had been established. The results showed that, on average, participants required more testing trials to form equivalence relations when the stimuli involved were functionally similar rather than functionally different. Moreover, participants required more test trials to form equivalence relations when novel arbitrary stimuli, rather than functionally distinct stimuli, were used as samples and comparisons. The speed of acquisition of stimulus equivalence was also related to the number of functionally similar stimuli established before training. These findings indicate a variety of ways in which the emergence of equivalence relations is affected by the functional classes in which the relevant stimuli participate.     

Discrete and continuous measures of dimensional stimulus control

In two sets of experiments, we examined dimensional stimulus control of pigeons' responses to a visual flicker-rate continuum. In the first experiment, responses to a single key were reinforced periodically during stimuli from one half of the stimulus continuum, and responses during other stimuli were extinguished. In the second experiment, two response keys were simultaneously available, with reinforcement for each response alternative associated with different halves of the stimulus continuum. Conditions of the second experiment involved either free-operant or discrete-trial stimulus presentations. Results from these experiments show that positive dimensional contrast appeared in discrimination tasks with one or two response alternatives, but only with free-operant procedures. In addition, discrimination between stimulus classes established by differential reinforcement was assessed as accurately by continuous rate measures as by discrete response choice in the two-alternative situation. The general implication of these experiments is that response rate measures, when properly applied, may reveal sources of variation within stimulus classes, such as dimensional contrast, that are not evident with discrete measures.     

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.     

Projector slide changing and focusing as operant reinforcers

Uninstructed subjects choose to view, in sharp focus where possible, projected visual images in preference to various simpler auditory and visual stimuli (e.g., buzzers of flashing lights). The rate of responding on the lever rapidly increased above the operant level (projector inoperative) even though the stimuli were nonsense syllables. When focusing also was made contingent on responses, the subjects promptly started sharpening the focus of legible but blurred nonsense syllables. When the visual material was colored landscape scenes, the rates of slide-changing generally decreased, because of increased viewing time relative to the nonsense syllables, at the same time that the latencies of focusing decreased. Both the sharpness of focus and the total time spent with the image in sharp focus increased greatly with the colored slides, establishing that the subjects were under control of the stimulus events. Extinction of both responses occurred very rapidly when the controls became inoperative.     

Relational and absolute stimulus learning by monkeys in a memory task.

Three experiments showed stimulus control by either the absolute properties of probe stimuli, relational properties of the probe-list relationship, or both in a serial probe recognition memory task in which a four-item memory list was followed by a single probe (test) item. In Experiment 1, 3 rhesus monkeys received 39 to 75 repetitions of the same 24-trial stimulus sequence. Special tests showed stimulus control by the absolute properties of the probe stimuli. Retention of previous relational control was demonstrated by the good transfer (83%) to novel list and probe stimuli at the beginning of Experiment 2. During Experiment 2, control by absolute properties of the probe stimuli gradually reoccurred. Only a small measure of control by list stimuli could be detected or promoted. In Experiment 3, 4 monkeys were shown to have largely lost their ability to perform on the basis of the list-probe relationship, and were performing primarily on the basis of the absolute properties of the probe stimuli. Over the next 15 weeks, these monkeys were transferred to new stimuli at the beginning of each week. Control by the relational aspects of the task gradually returned. As transfer performance increased, control by the absolute properties of the probe stimuli was eliminated. The results are discussed in terms of stimulus control and performance strategies used by the monkeys.     

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).     

Stimulus control and compounding with ambient odor as a discriminative stimulus on a free-operant baseline

Previous experiments have demonstrated that the simultaneous presentation of independently established discriminative stimuli can control rates of operant responding substantially higher than the rates occasioned by the individual stimuli. This "additive summation" phenomenon has been shown with a variety of different reinforcers (e.g., food, water, shock avoidance, cocaine, and heroin). Discriminative stimuli previously used in such studies have been limited to the visual and auditory sensory modalities. The present experiment sought to (1) establish stimulus control on a free-operant baseline with an ambient olfactory discriminative stimulus, (2) compare olfactory control to that produced with an auditory discriminative stimulus, and (3) determine whether compounding independently established olfactory and auditory discriminative stimuli produces additive summation. Rats lever pressed for food on a variable-interval schedule in the presence of either a tone or an odor, with comparable control developed to each stimulus. In the absence of these stimuli responding was not reinforced. During stimulus compounding tests, the tone-plus-odor compound occasioned more than double the responses occasioned by either the tone or odor presented individually. Thus, the current study (1) established stimulus control with an ambient olfactory discriminative stimulus in a traditional free-operant setting and (2) extended the generality of stimulus-compounding effects by demonstrating additive summation when olfactory and auditory discriminative stimuli were presented simultaneously.     

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.     

Acquisition of stimulus control while introducing new stimuli in fading.

After establishing discrimination between a red positive stimulus and a green negative stimulus, the lowest intensity colors that restricted all responding to the positive stimulus were determined. Then, two new white lines differing in terms of line orientation were each superimposed on one of the colors and were increased in intensity. Thereafter, the intensity of the colors was decreased and eventually eliminated. Probe stimuli consisting of the lines presented against dark backgrounds were presented before each change of stimulus intensity, and probe responding was used to assess the control acquired by various dimension of the new stimuli during the course of fading. The lines acquired control of responding while they were being introduced, and control was strengthened as the colors were attenuated. Such a locus of acquisition was attributed to the starting intensity of the original controlling stimuli and was explained in terms of stimulus blocking. Finally, using probes while introducing the new stimuli enhanced the acquisition of control by the new stimuli.     

Stability of functional equivalence and stimulus equivalence: effects of baseline reversals

Functional equivalence and stimulus equivalence classes were established, reversed, and tested for stability with college students. Functional stimulus classes were established using a task in which students were trained to say nonsense words in the presence of arbitrarily assigned sets of symbols. Computer-controlled speech-recognition technology was used to record and analyze students' vocal responses for accuracy. After the establishment of stimulus classes was demonstrated with a transfer-of-function test, the effects of reversing selected baseline simple discriminations were assessed during an additional transfer-of-function test and a follow-up test that occurred several weeks later. With the same students, stimulus equivalence classes were established and demonstrated with computerized matching-to-sample procedures. The effects of reversing selected baseline conditional discriminations also were assessed during a postreversal equivalence test and a follow-up test. Both functional stimulus classes and stimulus equivalence were sensitive to contingency reversals, but the reversals with stimulus equivalence closses affected stimulus class organization whereas reversals with functional stimulus classes did not. Follow-up performances were largely consistent with the original baseline contingencies. The similarities and differences between stimulus equivalence and functional equivalence are related to the specific contingencies that select responding in the presence of the stimuli that form the classes.     

Controlling relations in conditional discrimination and matching by exclusion.

Normally capable adults learned two-choice identity matching of three-digit numerals and arbitrary matching of physically dissimilar nonsense syllables. The stimuli were displayed on a computer terminal, and responses consisted of typing on the terminal's keyboard. In Experiment 1, every trial displayed a sample numeral, a comparison numeral, and three equal signs (= = =). The comparison stimulus was to be selected if it was identical with the sample; otherwise the equal sign was to be selected. This "single comparison" method was then used to show that arbitrary matching could be based upon either sample-S+ or sample-S- relations. In Experiment 2, a series of probe trials displayed a novel sample, a comparison stimulus from the arbitrary matching baseline, and = = =. Subjects typically selected = = =; they apparently were excluding the baseline comparison stimulus. Experiments 3 through 5 investigated which variables in training would lead to the selection of baseline comparison stimuli in response to novel samples. Behavior was usually unchanged when baseline training included relating comparison stimuli to as many as four different samples. Punishment contingencies were effective, but performance did not generalize unless those contingencies were applied in relation to more than one baseline comparison stimulus.     

Stimulus control of habits: Evidence for both stimulus specificity and devaluation insensitivity in a dual-response task

Goal-directed and habitual actions are clearly defined by their associative relations. Whereas goal-directed control can be confirmed via tests of outcome devaluation and contingency-degradation sensitivity, a comparable criterion for positively detecting habits has not been established. To confirm habitual responding, a test of control by the stimulus–response association is required while also ruling out goal-directed control. Here we describe an approach to developing such a test in rats using two discriminative stimuli that set the occasion for two different responses that then earn the same outcome. Performance was insensitive to outcome devaluation and showed stimulus–response specificity, indicative of stimulus-controlled behavior. The reliance of stimulus–response associations was further supported by a lack of sensitivity during the single extinction test session used here. These results demonstrate that two concurrently trained responses can come under habitual control when they share a common outcome. By reducing the ability of one stimulus to signal its corresponding response–outcome association, we found evidence for goal-directed control that can be dissociated from habits. Overall, these experiments provide evidence that tests assessing specific stimulus–response associations can be used to investigate habits.