Quantitative and methodological aspects of stimulus equivalence

The number of different ways of linking stimuli in the training phase of a conditional discrimination procedure designed to teach equivalence relations has hitherto been underestimated. An algorithm from graph theory that produces the correct number of such different ways is given. The establishment of equivalence relations requires transitive stimulus control. A misconception in a previous analysis of the conditions necessary for demonstrating transitive stimulus control is indicated. This misconception concerns responding in an unreinforced test trial to a negative rather than a positive comparison stimulus. Such behavior cannot be attributed to discriminative control by degree of association with reinforcement if the negative comparison stimulus has been less associated with reinforcement than the positive comparison stimulus in an antecedent training phase.     

Nodality effects during equivalence class formation: An extension to sight-word reading and concept development

Three students with moderate disabilities were taught to read and match-to-sample sight words comprising stimulus sets based upon the four food groups. We taught students conditional discriminations within four four-member sets using a single-sample/four-comparison procedure. Students were taught A-B, B-C, and C-D conditional discriminations for each of the four potential stimulus classes. Subsequent probes tested for relations based upon symmetry and one-node and two-node transitivity. The performances for all students indicated that symmetric relations emerged before one-node transitive relations, and that one-node transitive relations emerged before two-node transitive relations. These results are consistent with a pattern of responding, referred to as a "nodality effect," in which relations with fewer nodes are demonstrated prior to the demonstration of relations with a greater number of nodes. These results extend this area of research to sight-word reading for students with moderate disabilities.     

Stimulus equivalence and transitive associations: A methodological analysis

When a number of two-stimulus relations are established through training within a set of stimuli, other two-stimulus relations often emerge in the same set without direct training. These, termed "transitive stimulus relations," have been demonstrated with a variety of visual and auditory stimuli. The phenomenon has served as a behavioral model for explaining the emergence of rudimentary comprehension and reading skills, and the development of generative syntactic repertoires. This article considers the range of relations that can arise between a given number of stimuli in a class, the number of directly established two-stimulus relations necessary for the emergence of transitive relations, the forms that training sets of stimuli can take, and the number of transitive two-stimulus relations that can be induced without direct training. The procedures needed to establish and assess transitive stimulus control, the possible interactions between the training and testing procedures, and the constrainst these interactions place upon the analysis of transitive stimulus control are also examined. The present analysis indicates that in a transitivity test, choice among such stimuli may be controlled by (1) the relation between the sample and the positive comparison stimulus (transitive stimulus control), (2) the relation between the sample and the negative comparison stimulus (S- rule control), and (3) possible discriminative properties that may inadvertently be established in the positive and negative comparison stimuli (valence control). Methods are described for distinguishing these three forms of stimulus control.     

Contriving transitive conditioned establishing operations to establish derived manding skills in adults with severe developmental disabilities

The purpose of this study was to demonstrate derived manding skills in 2 adults with severe developmental disabilities and language deficits by contriving transitive conditioned establishing operations. Specifically, we evaluated whether a history of reinforced conditional discrimination learning would ultimately result in a derived mand repertoire, in which participants manded for items that were needed to complete chained tasks. After mastering the first three phases of the picture exchange communication system (PECS), participants were taught to mand for the needed items by exchanging pictures of the items for the items themselves. They were then taught to conditionally relate the dictated names of the items to the corresponding pictures of the items and to relate the dictated names to the corresponding printed words. We then tested, in the absence of reinforcement, whether participants would mand for the items needed to complete the chained tasks using text rather than pictures. Both participants showed the emergence of derived mands and some derived stimulus relations as a result of this instruction. Some of the derived relations were shown to be intact at 1-month follow-up, and scores on derived mand probes were higher at follow-up than before training. In addition, the 2 participants vocally requested the needed items on maintenance test probes, a skill that was never trained and was not previously in their repertoires. These results suggest that a history of reinforced relational responding may facilitate the expansion of a number of verbal skills and emphasize the possibility of a synthesis of Skinner's (1957) analysis of verbal behavior and derived stimulus relations into language-training efforts for persons with significant disabilities.     

An Examination of Stimulus Control in Fluency-Based Strategies: SAFMEDS and Generalization

Fluency-based strategies such as Say All Fast a Minute Each Day Shuffled (SAFMEDS) effectively promote fluent responding (i.e., high rate and accuracy). It is possible, however, that the stimulus control developed through these activities inhibits stimulus generalization. We investigated this concern in a two-part study with college students. Study 1 assessed generalization of rates of responding from training with SAFMEDS to a novel set of equivalent SAFMEDS flashcards. Results indicate that SAFMEDS promoted fluent responding, but rates of responding decreased during generalization probes. Furthermore, higher rates of responding during training were correlated with a greater decrease in rates of responding during generalization probes. This may indicate that students attend to irrelevant stimulus features of SAFMEDS during training. Study 2 examined the effects of embedding multiple-exemplar training within SAFMEDS. Results indicate that multiple-exemplar training can promote generalization of accurate and high-rate responding when incorporated in a SAFMEDS activity.     

Generalization and response mediation of a conditional discrimination

Fifteen pigeons were given conditional discrimination training in which a colored sample stimulus determined which of two line comparison stimuli (vertical and horizontal) was correct. As part of the conditional discrimination procedure, birds were required to make an "observing response" to the sample stimulus presented on a wide key. The location on this key of the required observing response for the two sample stimuli differed by 0, 3, or 6 in. (0, 7.6, or 15.2 cm) for three groups of birds. Accuracy of conditional discrimination performance was directly related to the amount of separation. In subsequent generalization tests with novel sample stimuli, both observing-response location and comparison responding changed within the same region of the wavelength continuum from that appropriate for one of the training samples to that appropriate for the other. A maintained generalization test (continued reinforcement for training stimuli) revealed this relation more strongly. A test in which observing-response location was the only sample stimulus of a conditional discrimination revealed stimulus control by this observing response, supporting a response mediation interpretation of the data.     

The influence of correlations between noncritical features and reinforcement on stimulus generalization

One strategy to program for generalization is to vary noncritical features in teaching exemplars, thereby avoiding noncritical features from being highly correlated with reinforcement and thus gaining faulty stimulus control. In the current translational evaluation, 2 groups of adults of typical development were taught to respond to arbitrary stimuli with experimenter‐defined critical and noncritical features in a matching‐to‐sample task. The teaching arrangement used for 1 group programmed for low correlation between noncritical features and reinforcement; the teaching arrangement used for the other group programmed for high correlation between noncritical features and reinforcement. Participants in the former group displayed (a) faster acquisition of matching, (b) less variability in correct responding, and (c) a decreased likelihood of faulty stimulus control developing during training. The results contribute towards advancing the study of stimulus control and developing an explicit technology of generalization to better serve consumers of the application of our science.     

On Stimulus Generalization and Stimulus Classes

Stimulus generalization has been defined as the spread of effect of reinforcement for responses emitted in the presence of one stimulus to different stimuli presented under extinction conditions. As a result of stimulus generalization, novel stimuli come to exert stimulus control over members of the response class. Studies in the applied behavior analysis literature, however, have reported experimental preparations that included prompting and reinforcement procedures during what were claimed to be stimulus generalization conditions. These studies violated the procedural requirement that stimulus generalization be tested under extinction conditions. Responses that come under the control of a class of stimuli may do so by direct training or by stimulus generalization. It is desirable for organisms to respond in the presence of members of an appropriately constructed stimulus class, but we should understand the mechanism of entry into the class by its members. If inaccurate claims of stimulus generalization are made when training procedures are used in the ostensible generalization conditions, the robustness of the original training procedures will be over estimated. By adhering to the operational requirements of behavioral definitions, we could better understand the power and limits of our educational and training procedures.     

Stimulus averaging and the context for judgment

Loudness judgments of stimulus sets composed of four bursts of noise were analyzed for two types of contextual effects: between-set and within-set. Experiment I demonstrated between-set effects for these four-component stimuli; they were shown to be similar to those found in previous work with single stimuli. Experiment 2 tested an averaging model for within-set contextual effects. The results were inconsistent with the model. One interpretation is that there are within-set effects and that these are caused by shifts in the effective range of stimuli. Alternative interpretations attribute the apparent contextual effects either to an averaging of physical values or to an inappropriate scale of judgment.     

Simple discrimination in stingless bees (Melipona quadrifasciata): Probing for select‐ and reject‐stimulus control

Simple and conditional discrimination training may produce various types of controlling relations. Responses may be controlled primarily by the positive stimulus (select–control relation) or by the negative stimulus (reject–control relation; the subject excludes the negative stimulus and chooses the positive). Bees learn to respond in simple and conditional discriminations. However, no study has searched for reject–control responding in Melipona bees. We trained Melipona quadrifasciata on a simple discrimination task (S+ vs. S‐; e.g., blue vs. yellow) and then probed for stimulus control with two types of probe trials, S+ versus a new stimulus (Select–control probes) and S‐ versus a new stimulus (Reject–control probes). For Group Different, a new‐stimulus color (e.g., white) was used in one type of probe and another color (e.g., black) was used in the other type. For Group Same, a single new‐stimulus color was used in both types of probes. On Select probes, the bees always preferred S+ to the new stimulus. On Reject probes, results were mixed. Depending on the colors used in training and probing, bees responded to both stimuli, and even preferred the S‐. The data suggest no control by the negative function of the S‐ and support the select‐stimulus control hypothesis of responding.     

Relations between baseline contingencies and equivalence probe performances

Following the emergence of two three-member equivalence classes (A1B1C1 and A2B2C2), 5 college students were exposed to one or more changes in the reinforcement contingencies controlling baseline conditional discriminations. AC relations were either reversed (i.e., C2 was reinforced and C1 punished when A1 was the sample; C1 was reinforced and C2 punished when A2 was the sample) or arranged randomly (i.e., C2 and C1 were reinforced and punished equally often in the presence of A1 and A2). In a third condition, the original AB and AC relations were reversed. Results showed that although baseline conditional discrimination performances were under the control of reinforcement contingencies, and performances on symmetry trials varied with baseline responding for 3 of 4 subjects when contingencies were reversed, performances on transitivity probes remained consistent with the initial equivalence class. These inconsistencies between probe and baseline performances were striking because conditional discriminations are thought to be the determinants of equivalence class performance. Similarly, the contrast between performances on symmetry and transitivity probes was of theoretical interest because equivalence classes are defined by congruent patterns of responding on probe trials.     

Contextual control of stimulus generalization and stimulus equivalence in hierarchical categorization

The purpose of this study was to determine whether hierarchical categorization would result from a combination of contextually controlled conditional discrimination training, stimulus generalization, and stimulus equivalence. First, differential selection responses to a specific stimulus feature were brought under contextual control. This contextual control was hierarchical in that stimuli at the top of the hierarchy all evoked one response, whereas those at the bottom each evoked different responses. The evocative functions of these stimuli generalized in predictable ways along a dimension of physical similarity. Then, these functions were indirectly acquired by a set of nonsense syllables that were related via transitivity relations to the originally trained stimuli. These nonsense syllables effectively served as names for the different stimulus classes within each level of the hierarchy.     

ASSESSING STIMULUS CONTROL IN NATURAL SETTINGS: AN ANALYSIS OF STIMULI THAT ACQUIRE CONTROL DURING TRAINING

When a learner is taught a new response, the stimuli that influence its display are often unknown. The presence or absence of these stimuli alters the probability of occurrence of the response. By identifying the stimuli influencing the probability of newly acquired responses, interventionists may program for their generalization more effectively and efficiently. This investigation describes the application of an operant methodology to assess functional relationships between responses and specific stimulus variables. Four young adults with moderate mental retardation were taught to include “please” as part of requests they made in school. Four environmental stimuli, present during training, were assessed for the controlling properties they acquired. Each of the four was assessed prior to and after training by presenting it in isolation (i.e., the other three were varied). If the presence of a single stimulus associated with training did not occasion “please,” then pairs of stimuli were probed. The results revealed that single-stimulus probing occasioned responding by only 1 learner; paired-stimulus probing set the occasion for including “please” by 2 others. Control of the 4th learner's responding was lost before training was introduced, because he began including “please” in his requests during baseline. The implications of these results are discussed in terms of analyzing stimulus control and promoting stimulus generalization.     

Generalization of cross-modal stimulus equivalence classes: operant processes as components in human category formation.

This study employed a stimulus-class rating procedure to explore whether stimulus equivalence and stimulus generalization can combine to promote the formation of open-ended categories incorporating cross-modal stimuli. A pretest of simple auditory discrimination indicated that subjects (college students) could discriminate among a range of tones used in the main study. Before beginning the main study, 10 subjects learned to use a rating procedure for categorizing sets of stimuli as class consistent or class inconsistent. After completing conditional discrimination training with new stimuli (shapes and tones), the subjects demonstrated the formation of cross-modal equivalence classes. Subsequently, the class-inclusion rating procedure was reinstituted, this time with cross-modal sets of stimuli drawn from the equivalence classes. On some occasions, the tones of the equivalence classes were replaced by novel tones. The probability that these novel sets would be rated as class consistent was generally a function of the auditory distance between the novel tone and the tone that was explicitly included in the equivalence class. These data extend prior work on generalization of equivalence classes, and support the role of operant processes in human category formation.     

A test of symmetry and transitivity in the conditional discrimination performances of pigeons

In a matching-to-sample context, pigeons were taught two conditional discriminations according to one of three equivalence paradigms: train if A, then select B and if B, then select C; train if B, then A and if B, then C; or train if A, then B and if C, then B. Test trials without reinforcement revealed that the conditional relations did not satisfy the symmetrical and transitive properties of an equivalence relation. Apparently, only specific if... then relations were learned. Contrary to Kendall's (1983) findings, and probably as a consequence of procedural differences, none of the pigeons in the present experiment were observed to emit mediating behavior during the transitivity probe trials. The absence of symmetry and transitivity may be related to the individual stimuli not being reflexive. Behavioral techniques other than the commonly used matching-to-sample technique might better succeed in avoiding unintended stimulus control in the study of the formation of stimulus classes.     

Abstraction of tactile properties by individuals with autism and Down syndrome using a picture‐based communication system

The present study evaluated the efficacy of a set of procedures for bringing tact extensions of abstract tactile properties under stimulus control. Two participants with disabilities who communicated via a picture‐based communication system received reinforcement for tacts of tactile properties of four wet/dry and four hard/soft stimuli. Test trials were conducted to evaluate the extent to which the participants' correct responding generalized to novel stimuli with the same tactile properties. The results suggest that the procedures were effective in bringing tact extensions of abstract tactile properties under stimulus control. Both participants' correct responding generalized to a set of novel stimuli. Mastery level responding to training and test targets maintained for 2 weeks following training. The results provide further evidence supporting the use of DTT to teach stimulus abstraction to nonvocal verbal individuals who use augmentative forms of communication.     

Establishing a normal peer as a behavioral model for developmentally delayed toddlers.

The present investigation demonstrated a systematic teaching procedure for establishing a normal toddler as a peer-model for three children showing delayed development, each one under 27 mo. of age. For each delayed subject, training consisted of adult-directed prompting and social reinforcement contingent upon the delayed children's imitations of material use and motor responses emitted by a normal peer. Within-subjects multiple-baseline designs across responses were used to demonstrate intrasubject control over imitative responding. Indices of stimulus and response generalization were assessed through having the peer-model present the trained responses along with untrained responses in a situation free of adult prompting and social reinforcement for imitative responding. Results indicated that the training in peer-imitation was successful for establishing the peer-model's behavior in a stimulus control relationship with the imitative responding of the delayed children. Moreover, the findings generally demonstrated transfer of training across stimulus situations and responses. Implications for educational programming with developmentally delayed children are discussed.     

Dimensional stimulus control following brief wavelength training

Pigeons with extensive training pecking a key illuminated by a white line then had brief training with the key illuminated by 555 nanometers. This was immediately followed by a wavelength generalization test in extinction. Dimensional stimulus control about the training wavelength increased with the duration and number of reinforcements given on variable-interval 30-sec and variable-interval 10-sec schedules in Experiment I. In Experiment II, dimensional stimulus control was obtained after only 4 min of wavelength training from birds with prior and independent discrimination training. Experiment III provided groups equated in number of reinforcers with groups in Experiment I and two 8-min duration groups. Analyses, which included results from both Experiments I and III, showed that dimensional stimulus control increased: (a) more rapidly as a function of the duration of variable-interval 10-sec than variable-interval 30-sec reinforcement; (b) at the same rate across variable-interval reinforcement schedules, as a function of the number of reinforcers available during brief wavelength training.     

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.     

An investigation of peak shift and behavioral contrast for autoshaped and operant behavior.

Instrumental treadle press and nonreinforced key peck responses were monitored during discrimination training and generalization testing in pigeons on positive and negative reinforcement schedules. In Experiment 1, six pigeons pressed a treadle for food on a multiple variable-interval extinction schedule. In Experiment 2, three pigeons pressed a treadle to avoid shock on a multiple free-operant avoidance extinction schedule. Different color keylights signaled S+ and S- components. Some positive behavioral contrast occurred during discrimination training, but the effect was small. Pecking occurred to the S+ keylight in Experiment 1 but not in Experiment 2. On stimulus generalization tests, all subjects displayed a positive peak shift when pressing the treadle for food or to avoid shock. However, peak shift was not found for nonreinforced "autopecks" on the stimulus key, although an area shift was observed in Experiment 1. This is the first demonstration of peak shift for pigeons pressing treadles and the only reliable demonstration of peak shift when negative reinforcement maintained responding. These results, in combination with previous demonstrations of peak shift for rats pressing levers and pigeons pecking keys, indicate that peak shift is a general by-product of operant discrimination learning, since it occurs across a variety of the organisms, responses, and reinforcers.