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.     

Emergent equivalence relations between interoceptive (drug) and exteroceptive (visual) stimuli.

Conditional "if-then" relations between drug (interoceptive) stimuli and visual (exteroceptive) stimuli were taught to 4 normal humans. Interoceptive stimuli were the effects produced by 0.32 mg/70 kg triazolam (a prototypical benzodiazepine) and placebo (lactose-filled capsules); exteroceptive stimuli were black symbols on white flash cards. Following the training of the prerequisite conditional relations, tests of emergent relations were conducted between exteroceptive stimuli and between interoceptive and exteroceptive stimuli. Equivalence relations emerged immediately without explicit training for all 4 subjects. Accuracy of responding during the interoceptive-exteroceptive equivalence tests and subjects' self-reports showed consistent discrimination between the drug effects of triazolam and placebo. Finally, a generalization test assessed whether a novel visual stimulus presented in the context of the placebo (i.e., no drug) would generalize to visual stimuli belonging to the placebo stimulus class. All 3 subjects who completed this test reliably chose the visual stimuli belonging to the placebo class and not the visual stimuli belonging to the triazolam stimulus class. The development of equivalence relations between interoceptive and exteroceptive stimuli demonstrates that private and public stimulus events can emerge as members of the same equivalence class. Theoretical and clinical implications are discussed.     

Equivalence classes with requirements for short response latencies

Five adult humans were tested for emergent conditional discriminations under rapid-responding contingencies. During four-comparison matching-to-sample baseline training (AB and AC), limited-hold contingencies for responding to samples and comparisons were gradually restricted to the shortest duration consistent with at least 95% accuracy and no more than 5% failures to respond. The final limited-hold values were 0.4-0.5 s for samples and 1.2-1.3 s for comparisons; mean response latencies were 0.15-0.28 s for samples and 0.59-0.73 s for comparisons; inter-trial intervals were 0.4 s. With these fast-responding requirements, test blocks presented 72 probe trials interspersed among 72 baseline trials, all without programmed differential consequences. Four equivalence test blocks (BC and CB probes, which tested simultaneously for both symmetry and transitivity) were followed by four symmetry (BA and CA probes) test blocks. Three subjects' results documented emergent performances indicative of equivalence classes despite fast-responding requirements that severely limited the time available for mediating vocal or subvocal responses. For these three subjects, mean latencies were slightly shorter in baseline trials than in probes, and shorter on symmetry than on equivalence probes. These differences, however, were usually less than the differences among mean latencies on the different types of trials within the baseline and probed performances.     

Relations among equivalence, naming, and conflicting baseline control

Three studies were conducted with different groups of 6 students each to explore the effects of training class-inconsistent relations and naming on demonstrations of emergent arbitrary stimulus relations. In all studies, two three-member equivalence classes of Greek symbols (A1B1C1 and A2B2C2) emerged as a result of training in conditional discriminations. Two new symbols were introduced (X and Y), and additional conditional discriminations were trained, whereby X was designated as the positive discriminative stimulus (S+) and Y was designated as the negative discriminative stimulus (S-) for A1 and B2. Conversely, Y was designated as the S+ and X as the S- for B1 and A2. This introduced conflicting sources of control within and between classes. In Study 1, subjects were not provided with names for the stimuli. In Study 2, the experimenter provided common names for the stimuli within each class. In Study 3, the subjects were required to use the common names during conditional discrimination training and test-trial blocks. In all experiments, equivalence responding with respect to the original classes was disrupted for some subjects subsequent to learning the new relations. Furthermore, in Studies 2 and 3, there were frequent examples of noncorrespondence between observed (listener or speaker) naming patterns and derived relations. These results support the view that demonstrations of equivalence are subject to control from a variety of sources rather than being fundamentally dependent on naming.     

Equivalence relations and the reinforcement contingency

Where do equivalence relations come from? One possible answer is that they arise directly from the reinforcement contingency. That is to say, a reinforcement contingency produces two types of outcome: (a) 2‐, 3‐, 4‐, 5‐, or n‐term units of analysis that are known, respectively, as operant reinforcement, simple discrimination, conditional discrimination, second‐order conditional discrimination, and so on; and (b) equivalence relations that consist of ordered pairs of all positive elements that participate in the contingency. This conception of the origin of equivalence relations leads to a number of new and verifiable ways of conceptualizing equivalence relations and, more generally, the stimulus control of operant behavior. The theory is also capable of experimental disproof.     

Conditional discrimination and equivalence relations: Control by negative stimuli

Three adult subjects were taught the following two-sample, two-comparison conditional discriminations (each sample is shown with its positive and negative comparison, in that order): A1-B1B2, A2-B2B1; B1-C1C2, B2-C2C1; and C1-D1D2, C2-D2D1. A teaching procedure was designed to encourage control by negative comparisons. Subjects were then tested for emergent performances that would indicate whether the baseline conditional discriminations were reflexive, symmetric, and transitive. The tests documented the emergence of two classes of equivalent stimuli: A1, B2, C1, D2 and A2, B1, C2, D1. These were the classes to be expected if the negative comparisons were the controlling comparisons in the baseline conditional discriminations. The negative comparisons, however, were not the comparisons that subjects were recorded as having chosen in the baseline conditional discriminations. Differential test results confirmed predictions arising from a stimulus-control analysis: In reflexivity tests (AA, BB, CC, DD), subjects chose comparisons that differed from the sample; one-node transitivity (AC, BD) and "equivalence" (CA, DB) tests also yielded results that were the opposite of those to be expected from control by positive comparisons; symmetry tests (BA, CB, DC), two-node transitivity (AD) tests, and two-node "equivalence" (DA) tests yielded results that were to be expected from control by either positive or negative comparisons.     

Compound stimuli in emergent stimulus relations: Extending the scope of stimulus equivalence

Three experiments were conducted to investigate stimulus relations that might emerge when college students are taught relations between compound sample stimuli and unitary comparison stimuli using match-to-sample procedures. In Experiment 1, subjects were taught nine AB-C stimulus relations, then tested for the emergence of 18 AC-B and BC-A relations. All subjects showed the emergence of all tested relations. Twelve subjects participated in Experiment 2. Six subjects were taught nine AB-C relations and were then tested for symmetrical (C-AB) relations. Six subjects were taught nine AB-C and three C-D relations and were then tested for nine AB-D (transitive) relations. Five of 6 subjects demonstrated the emergence of symmetrical relations, and 6 subjects showed the emergence of transitivity. In Experiment 3, 5 college students were taught nine AB-C and three C-D relations and were then tested for nine equivalence (D-AB) relations and 18 AD-B and BD-A relations. Three subjects demonstrated all tested relations. One subject demonstrated the AD-B and BD-A relations but not the D-AB relations. One subject did not respond systematically during testing. The results of these experiments extend stimulus equivalence research to more complex cases.     

The development of functional and equivalence classes in high-functioning autistic children: the role of naming.

The development of functional and equivalence classes was studied in four high-functioning, preschool-aged autistic children. Initially, all subjects failed to demonstrate match-to-sample relations indicative of stimulus equivalence among two three-member classes of visual stimuli. Then, 2 subjects showed emergence of those relations after they were taught to assign the same name to all members in each class. Next, subjects were taught names for new stimuli outside the match-to-sample format. On subsequent match-to-sample tests, 2 subjects demonstrated untrained conditional relations among the stimuli given a common name. New, unnamed stimuli were then related via match-to-sample training to stimuli from sets of named stimuli. Tests for emergent conditional relations between the new unnamed stimuli and the named stimuli yielded positive results for 1 subject and somewhat mixed results for 3 subjects. Finally, without naming, 2 subjects developed stimulus equivalence among two new three-member classes of visual stimuli. These data suggest that naming may remediate failures to develop untrained conditional relations, some of which are indicative of stimulus equivalence.     

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.     

Naming and categorization in young children: vocal tact training

In three experiments, 2- to 4-year-old children, following pretraining with everyday objects, were presented with arbitrary stimuli of differing shapes. In Experiment 1A, 9 subjects were trained one common tact response, "zag," to three of these and a second tact, "vek," to another three. In category match-to-sample Test 1, 4 subjects sorted accurately when required only to look at the sample before selecting from five comparisons. The remaining 5 subjects succeeded in Test 2, in which they were required to tact the sample before selecting comparisons. Experiment 1B showed, for 2 of these subjects, that tact training with 12 arbitrary stimuli established two six-member classes that were still intact 6 weeks later. In Experiment 2, 3 new subjects participated in a common tact training procedure that ensured that none of the exemplars from the same class were presented together prior to the test for three-member classes. Two subjects passed category Test 1 and the third passed Test 2. Tests showed subjects' listener behavior in response to hearing /zog/ and /vek/ to be in place. These experiments indicate that common naming is effective in establishing arbitrary stimulus classes and that category match-to-sample testing provides a robust measure of categorization.     

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.     

The role of naming in stimulus categorization by preschool children

The purpose of the current study was to assess whether children would categorize pictures when taught the relevant listener and speaker behaviors separately. A category-sort test was used to assess emergent conditional relations. Category-sort trials consisted of looking at (Test 1) or tacting/labeling (Test 2) a sample stimulus and selecting the appropriate comparison stimuli. In Experiment 1, 4 children (3-5 years) were taught to tact pictures of six U.S. state maps as either north or south. An assessment was conducted to determine whether they would (1) correctly categorize or sort when presented with a visual sample and (2) select the correct stimuli when hearing their category names (listener behavior). Two of the children categorized the pictures during Posttest 1 after the initial (pairwise) tact training. The other 2 categorized after receiving additional tact training with all pictures presented together. However, one of them categorized only during Posttest 2. In Experiment 2, 4 children (3-5 years) were taught to select pictures when hearing their category names. An assessment was conducted to determine whether they would (1) correctly categorize or sort and (2) tact the stimuli (speaker behavior). One child categorized the pictures during Posttest 1, and two during Posttest 2. The other child required additional training with all pictures grouped together. When participants failed to categorize, they also failed to tact the pictures accurately. Taken together, results from Experiments 1 and 2 show that both speaker and listener behavior play an important role in stimulus categorization.     

Conditional discrimination and equivalence relations: A theoretical analysis of control by negative stimuli

A detailed analysis is presented of the ways in which control by the negative stimulus in two-comparison conditional discriminations may be expected to affect the outcome of tests for the properties of equivalence relations. Control by the negative stimulus should produce the following results: (a) no observable effect on symmetry tests; (b) reflexivity test results should look like “oddity” rather than “identity”; and (c) transitivity tests that involve an odd number of nodes should yield results that are 100% opposite to tests that involve an even number of nodes. The analysis also considers the effects of variation in the type of comparison-stimulus control between and within baseline conditional discriminations. Methods are suggested for experimentally regulating the type of control, and for verifying the predictions that the analysis generates. If suggested experiments continue to support the analysis, investigators who use two-comparison conditional discriminations to study equivalence relations will either have to control explicitly whether the positive or the negative comparison governs their subjects' choices, or they will have to abandon two comparisons and use three or more comparisons instead.     

On the origins of naming and other symbolic behavior

We identify naming as the basic unit of verbal behavior, describe the conditions under which it is learned, and outline its crucial role in the development of stimulus classes and, hence, of symbolic behavior. Drawing upon B. F. Skinner's functional analysis and the theoretical work of G. H. Mead and L. S. Vygotsky, we chart how a child, through learning listener behavior and then echoic responding, learns bidirectional relations between classes of objects or events and his or her own speaker-listener behavior, thus acquiring naming-a higher order behavioral relation. Once established, the bidirectionality incorporated in naming extends across behavior classes such as those identified by Skinner as the mand, tact, and intraverbal so that each becomes a variant of the name relation. We indicate how our account informs the specification of rule-governed behavior and provides the basis for an experimental analysis of symbolic behavior. Furthermore, because naming is both evoked by, and itself evokes, classes of events it brings about new or emergent behavior such as that reported in studies of stimulus equivalence. This account is supported by data from a wide range of match-to-sample studies that also provide evidence that stimulus equivalence in humans is not a unitary phenomenon but the outcome of a number of different types of naming behavior.     

Equivalence class formation as a function of preliminary training with pictorial stimuli

The present experiment investigated the effects of preliminary training with pictorial stimuli on the subsequent formation of three 5‐member equivalence classes (A?B?C?D?E) in 84 university students assigned to seven groups of 12. In the Abstract (ABS) group, all stimuli were abstract shapes. In the Picture (PIC) group, the C stimuli were pictures, and the remaining stimuli were the same abstract shapes as in the ABS group. For the remaining five groups, all stimuli were the same abstract shapes as in the ABS group. However, across groups, preliminary training involved either the establishment of conditional relations with simultaneous (SMTS) or delayed (DMTS) matching‐to‐sample with 0 s, 3 s, 6 s, or 9 s between the abstract C stimuli and the meaningful pictures. For the ABS and the PIC groups, 16.7% and 83.3% of participants formed classes, respectively. Preliminary training with SMTS and DMTS with 0 s, 3 s, and 6 s produced a linear increase in the likelihood of equivalence class formation, 41.7%, 50%, and 75%, respectively. Increasing the duration of delay further from 6 s to 9 s produced a substantial decline, 50%. This experiment extends knowledge about how including meaningful pictures enhances equivalence class formation.     

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.     

Conditional relations with compound abstract stimuli using a go/no-go procedure

The aim of this study was to evaluate whether emergent conditional relations could be established with a go/no-go procedure using compound abstract stimuli. The procedure was conducted with 6 adult humans. During training, responses emitted in the presence of certain stimulus compounds (A1B1, A2B2, A3B3, B1C1, B2C2, and B3C3) were followed by reinforcing consequences (points); responses emitted in the presence of other compounds (A1B2, A1B3, A2B1, A2B3, A3B1, A3B2, B1C2, B1C3, B2C1, B2C3, B3C1 and B3C2) were not (i.e., extinction). During subsequent tests of emergent relations, new configurations (BA, CB, AC, and CA relations) were presented, formed by the recombination of training stimuli and structurally resembling tests usually employed in stimulus equivalence studies. Results showed that all 6 participants displayed immediate emergence of relations consistent with symmetry. Four participants exhibited emergent relations consistent with both transitivity and equivalence. These results indicate that a go/no-go procedure with compound stimuli can establish emergent conditional relations, thus providing a procedural alternative to the matching-to-sample procedures commonly used in studies of stimulus equivalence.     

Using equivalence‐based instruction to teach the visual analysis of graphs

Previous research has demonstrated low rater agreement when visually inspecting trends in single‐subject design graphs (see Wolfe, Seaman, & Drasgow, 2016). Didactic instruction of visual analysis of practicing behavior analysts has resulted in generally poor and unreliable performances (Danov & Symons, 2008; Diller, Barry, & Gelino, 2016). Therefore, a refined instructional technology to improve the reliability among behavior analysts is warranted. Developing research has focused on the application of equivalence‐based instruction (Brodsky & Fienup, 2018; Rehfeldt, 2011) for a variety of complex human behaviors. In the current study, equivalence‐based instruction was used to train four participants to identify functional relations displayed in five different classes of graphs. Training resulted in the formation of five equivalence classes by all participants consisting of three members (graph, functional relation rule, and functional relation statement). In addition, the skills were maintained for up to 2 weeks and generalized to novel graphs.     

Development of conditional and equivalence relations without differential consequences

Two experiments were conducted to establish conditional stimulus relations without differential consequences and to test for the emergence of other relations. In Experiment 1, 3 adults responded to match-to-sample displays in which sample-comparison pairs were constant while the second comparison presented with each pair changed periodically across trials. No differential consequences followed any comparison selections. All subjects learned conditional relations between constant samples and comparisons, but results of tests for transitivity in those relations were equivocal. In Experiment 2, 4 children were given unreinforced training and testing similar to that provided to the adults in Experiment 1, with procedural refinements. One child learned conditional relations and demonstrated emergent relations that confirmed the development of two four-member equivalence classes. Another child learned the conditional relations but did not demonstrate any emergent relations reliably. A 3rd child, after reinforced training on two conditional relations, learned four new conditional relations without differential consequences and demonstrated symmetry but not equivalence in the trained relations. The 4th child did not learn the conditional relations. These findings emphasize the importance of careful construction of tests for stimulus equivalence and suggest a need for critical analyses of the apparent emergence of untrained stimulus relations on unreinforced tests that has been observed in several stimulus equivalence studies.