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.     

The effects of listener training on the development of analogical reasoning

We evaluated the effects of listener training on the emergence of analogical reasoning, as measured via equivalence‐equivalence and explored the role of verbal behavior when solving analogy‐type tasks. We taught 18 college students to select component stimuli from 2 classes, labeled “vek” and “zog,” and evaluated tacts and relational responding in the presence of baseline (AB and BC), symmetry (BA and CB), and transitivity (AC and CA) compounds. In Experiment 1, 5 out of 6 participants passed analogy tests, but none of them engaged in the relational tacts “same” and “different” during tact tests, possibly due to lack of instructional control. A change in instructions during Experiment 2 produced relational tacts in 4 of 6 participants, and 5 participants passed analogy tests. In Experiment 3, we implemented a talk‐aloud procedure to determine if the participants were emitting relational tacts during analogy tests. All 6 participants tacted stimuli relationally and engaged in problem‐solving statements to solve analogy tests. Results from these studies suggest that listener and speaker behavior in the form of relational tacts and other problem‐solving statements influenced the participants' equivalence–equivalence performance.     

Effect of observing response requirements to sample and comparison stimuli on the establishment of reject control (sample/S- relations)

The establishment of sample/S- relations (or reject control) during conditional discrimination training (AB, BC) affects transitivity (AC), equivalence (CA) and reflexivity (AA, BB, CC) test outcomes. The present study parametrically evaluated the effects of different observing patterns to comparison stimuli on the establishment of reject control during baseline conditional relation training. A matching-to-sample with observing requirements (MTS-OR) procedure was implemented during AB and BC conditional discrimination training. During training, the participants were required to observe the sample and incorrect comparison on every trial before responding. In addition, the participants were divided into three groups that differed regarding the percentage of training trials on which they were prevented from observing the correct comparison stimuli: 25%, 50%, and 75%. Once the mastery criteria were achieved during training, transitivity (AC), symmetry (BA, CB), equivalence (CA), and reflexivity (AA, BB, CC) tests were conducted with all comparison stimuli visible from the beginning. The results suggest that the number of errors during transitivity, equivalence, and reflexivity tests progressively increased as participants were prevented from observing the correct comparison on a greater number of trials during training. Symmetry test results, however, were not affected by the experimental manipulation. Moreover, the number of participants showing reject-control patterns during tests slightly increased and the number of participants showing select-control patterns decreased as a function of the number of trials on which the participants were prevented from observing the correct comparison. Thus, we suggest that observing patterns during training is a relevant variable that affects equivalence test outcomes.     

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.     

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.     

Reversal of baseline relations and stimulus equivalence: I. Adults

Following the emergence of two four-member equivalence classes (A1B1C1D1 and A2B2C2D2), 5 students were exposed to a series of phases including a baseline conditional discrimination reversal (i.e., choosing D2 was reinforced and D1 punished given Sample A1; choosing D1 was reinforced and D2 punished given Sample A2), the delayed introduction of CD/DC transitivity/equivalence probes, DE conditional discrimination training, a second baseline conditional discrimination reversal (i.e., choosing C2 was reinforced given B1, etc.), and a return to original baseline reinforcement contingencies. Results showed that baseline and symmetry probe performances were extremely sensitive to baseline modifications. In contrast, patterns on transitivity/equivalence probes remained predominantly consistent with the originally established equivalence classes, although there were exceptions on some E probe relations for 2 subjects. The dissociation between baseline and symmetry versus transitivity/equivalence patterns may have important implications because it is not easily accounted for by current models of equivalence phenomena.     

Naming and equivalence: Response latencies for emergent relations

In an attempt to distinguish between associative network and verbal mediation accounts of equivalence formation, three experiments were carried out in which conditional stimulus relations were established and response latencies assessed during tests for emergent relations. In Experiment 1, three groups of adults were trained with six three-member classes of visual stimuli, using different kinds of stimuli for each group: readily nameable pictograms, which were “preassociated” (Group 1); equally nameable but “non-associated” pictograms (Group 2); or non-associated “abstract” stimuli, designed to discourage the use of verbal mediators (Group 3). For those trained with pictograms, equal response latencies were observed on all tested relations, viz. trained associations, symmetry, transitivity, and transitivity with symmetry, but for subjects given abstract stimuli response latencies were greater on tests requiring transitivity. In Experiment 2 this result was replicated with methodological refinements, using only groups trained with preassociated pictograms or abstract stimuli. In Experiment 3 subjects were pretrained to label abstract stimuli with either individual names or class names. Latencies were longer for tests involving transitivity in the case of those subjects using individual names, but equal response latencies were observed on all four types of test for those using class names. The results suggest that equivalence classesMaybe supported by either an associative network or by verbal mediation, depending on stimulus conditions and the subsequent strategies employed by subjects.     

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.     

The establishment of auditory–visual equivalence classes with a go/no-go successive matching-to-sample procedure

The current study evaluated the effectiveness of a go/no-go successive matching-to-sample procedure (S-MTS) to establish auditory–visual equivalence classes with college students. A sample and a comparison were presented, one at a time, in the same location. During training, after an auditory stimulus was presented, a green box appeared in the center of the screen for participants to touch to produce the comparison. Touching the visual comparison that was related to the auditory sample (e.g., A1B1) produced points, while touching or refraining from touching an unrelated comparison (e.g., A1B2) produced no consequences. Following AB/AC training, participants were tested on untrained relations (i.e., BA/CA and BC/CB), as well as tacting and sorting. During BA/CA relations tests, after touching the visual sample, the auditory stimulus was presented along with a white box for participants to respond. During BC/CB relations tests, after touching the visual sample, a visual comparison appeared. Across 2 experiments, all participants met emergence criterion for untrained relations and for sorting. Additionally, 14 out of 24 participants tacted all visual stimuli correctly. Results suggest the auditory–visual S-MTS procedure is an effective alternative to simultaneous MTS for establishing conditional relations and auditory-visual equivalence classes.     

Transfer of baseline reject control to transitivity trials and its effect on equivalence class formation

This study explored the role of baseline reject control on transitivity responding. In Experiment 1, participants learned to respond to a baseline of arbitrary AB and AC conditional relations, and then they were exposed to transitivity‐like BC and CB trials in which the correct comparison stimulus was replaced by a novel stimulus (D). Five of 10 participants selected stimulus D, but only 1 showed expansion of the baseline stimulus classes to include the D stimuli. In Experiment 2, the emergence of symmetry and transitivity from baseline relations was assessed before participants were exposed to the transitivity‐like trials. Six of 8 participants who showed emergence of equivalence relations selected the D stimuli on transitivity‐like trials and provided evidence that baseline classes expanded to include these stimuli. In Experiment 3, these 6 participants selected novel stimuli (E) in additional transitivity‐like trials, and all showed that the E stimuli had become members of the previously established classes, which now comprised 5 members. A route for the emergence of transitivity by way of the transfer of baseline between‐classes reject control is discussed.     

A discrimination analysis of training-structure effects on stimulus equivalence outcomes.

Experiments designed to establish stimulus equivalence classes frequently produce differential outcomes that may be attributable to training structure, defined as the order and arrangement of baseline conditional discrimination training trials. Several possible explanations for these differences have been suggested. Here we develop a hypothesis based on an analysis of the simple simultaneous and successive discriminations embedded in conditional discrimination training and testing within each of the training structures that are typically used in stimulus equivalence experiments. Our analysis shows that only the comparison-as-node (many-to-one) structure presents all the simple discriminations in training that are subsequently required for consistently positive outcomes on all tests for the properties of equivalence. The sample-as-node (one-to-many) training structure does not present all the simple discriminations required for positive outcomes on either the symmetry or combined transitivity and symmetry (equivalence) tests. The linear-series training structure presents all the simple discriminations required for consistently positive outcomes on tests for symmetry, but not for symmetry and transitivity combined (equivalence) or transitivity alone. Further, the difference in the number of simple discriminations presented in comparison-as-node training versus the other training structures is larger when the intended class size is greater than three or the number of classes is larger than two. We discuss the relevance of this analysis to interpretations of stimulus equivalence research, as well as some methodological and theoretical implications.     

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.     

An evaluation of a visual–visual successive matching‐to‐sample procedure to establish equivalence classes in adults

Traditionally, behavior analysts have studied stimulus equivalence using a matching‐to‐sample (MTS) preparation. Although researchers have shown the utility of MTS to yield equivalence classes, the procedure requires several prerequisite skills for a learner to accurately respond. Previous research with humans and nonhumans has shown that relational responding can be produced via compound stimulus discrimination and successive matching‐to‐sample (S‐MTS). We conducted four experiments with college students to further evaluate the effectiveness of S‐MTS in the establishment of stimulus relations. S‐MTS trials consisted of the presentation of a single sample stimulus followed by one comparison in a fixed location on a computer screen. Depending upon the sample–comparison relation, participants touched (i.e., go) or did not touch (i.e., no‐go) the comparison stimulus. Following training of the baseline relations (AB/BC), we assessed the emergence of symmetry, transitivity, and equivalence performances (i.e., BA/CB and AC/CA). Results support the utility of the S‐MTS procedure as a possible alternative to traditional MTS. This study has direct implications for participants for whom traditional three‐array MTS procedures may be challenging.     

Equivalence classes in individuals with minimal verbal repertoires

Studies from two different laboratories tested for equivalence classes in individuals with severe mental retardation and minimal verbal repertoires. In the first study, 3 individuals learned several matching-to-sample performances: matching picture comparison stimuli to dictated-word sample stimuli (AB), matching those same pictures to printed letter samples (CB), and also matching the pictures to nonrepresentative forms (DB). On subsequent tests, all individuals immediately displayed Emergent Relations AC, AD, BC, BD, CD, and DC, together constituting a positive demonstration of equivalence (as defined by Sidman). The second study obtained a positive equivalence test outcome in 1 of 2 individuals with similarly minimal verbal repertoires. Taken together, these studies call into question previous assertions that equivalence classes are demonstrable only in individuals with well-developed language repertoires.     

REVERSAL OF BASELINE RELATIONS AND STIMULUS EQUIVALENCE: II. CHILDREN

In a systematic replication of a study using college-student subjects (Pilgrim & Galizio, 1990), 5- to 7-year-old children learned two conditional discriminations (i.e., A1B1, A2B2, A1C1, and A2C2) in a two-choice arbitrary match-to-sample task and showed the emergence of two three-member equivalence classes (A1B1C1 and A2B2C2). Baseline conditional discrimination performances were quickly controlled by reversals of the AC reinforcement contingencies (i.e., choosing Comparison Stimulus C2 was reinforced given Sample A1, and choosing C1 was reinforced given Sample A2) when the reversals were introduced in restricted baselines. On reflexivity, symmetry, and transitivity/equivalence probes following the reversal, there was some limited indication of equivalence-class reorganization (i.e., A1B1C2 and A2B2C1) in keeping with the concurrently performed baseline relations for 2 of 5 subjects, but the predominant pattern across probe trials was one of inconsistent conditional control. These findings suggest that, given similar challenges, equivalence-class performances may be more easily disrupted in young children than in adults.     

Speed analyses of stimulus equivalence.

The functional substitutability of stimuli in equivalence classes was examined through analyses of the speed of college students'' accurate responding. After training subjects to respond to 18 conditional relations, subjects'' accuracy and speed of accurate responding were compared across trial types (baseline, symmetry, transitivity, and combined transitivity and symmetry) and nodal distance (one- through five-node transitive and combined transitive and symmetric relations). Differences in accuracy across nodal distance and trial type were significant only on the first tests of equivalence, whereas differences in speed were significant even after extended testing. Response speed was inversely related to the number of nodes on which the tested relations were based. Significant differences in response speed were also found across trial types, except between transitivity and combined trials. To determine the generality of these comparisons, three groups of subjects were included: An instructed group was given an instruction that specified the interchangeability of stimuli related through training; a queried group was queried about the basis for test-trial responding: and a standard group was neither instructed nor queried. There were no significant differences among groups. These results suggest the use of response speed and response accuracy to measure the strength of matching relations.     

Nodal structure and stimulus relatedness in equivalence classes: post-class formation preference tests

Three experiments used postclass formation within-class preference test performances to evaluate the effects of nodal distance on the relatedness of stimuli in equivalence classes. In Experiment 1, two 2-node four-member equivalence classes were established using the simultaneous protocol in which all of the baseline relations were trained together, after which all emergent relations probes were presented together. All training and testing was done using match-to-sample trials that contained two comparisons. After class formation, the effects of nodal distance were evaluated using within-class preference tests that contained samples and both comparisons from the same class. These tests yielded inconsistent performances for most participants. Experiment 2 replicated Experiment 1, but a third null comparison was used on all trials during class formation. Thereafter, virtually all of the within-class probes, for all participants, evoked performances that were consistent with the predicted effects of nodal distance, that is, the selection of comparisons that were nodally closer to the samples. It appears, then, that the establishment of the equivalence classes with a third null comparison induced control by nodal structure of the classes. Experiment 3 demonstrated the generality of these findings with larger classes that contained more nodal separations, that is, three-node five-member classes. Emergent-relations tests conducted immediately after the within-class tests showed the classes to be intact. Thus, the differential relatedness of stimuli in a class or their interchangeability depended on the content of a test trial: within-class probes occasioned responding indicative of differential strength among the stimuli in the class, while cross-class tests occasioned responding indicative of interchangeability of stimuli in the same class.     

EQUIVALENCE CLASS FORMATION IN A TRACE STIMULUS PAIRING TWO‐RESPONSE FORMAT: EFFECTS OF RESPONSE LABELS AND PRIOR PROGRAMMED TRANSITIVITY INDUCTION

Three experiments identified factors that did and did not enhance the formation of two‐node four‐member equivalence classes when training and testing were conducted with trials presented in a trace stimulus pairing two‐response (SP2R) format. All trials contained two separately presented stimuli. Half of the trials, called within‐class trials, contained stimuli from the same class while the other half, called cross class trials, contained stimuli from different classes. On within class trials, making a YES response was correct and making a NO response was wrong. On cross class trials, making a NO response was correct and making a YES response was wrong. In Experiment 1, similar intermediate percentages of participants (about 50%) formed classes, regardless of whether the responses were labeled YES and NO or SAME and DIFF. Response labeling thus did not influence class formation. Regardless of response labels, failures of class formation were primarily due to failure of class‐indicative responding produced by within‐class transitivity probes. In Experiment 2, only 50% of participants formed classes without prior training, as in Experiment 1, but 100% of participants formed equivalence classes after the establishment of a generalized transitivity repertoire by use of a programmed transitivity induction protocol. Experiment 3 examined two components of the programmed transitivity induction protocol and found that the exclusion of AC trials had no effect on the percentage of participants who formed equivalence classes, while presenting the stimulus sets in randomized order interfered with equivalence class formation. A further analysis found that a number of stimulus control topographies differentiated between individuals who did and did not form equivalence classes. In general, then, these experiments demonstrate that equivalence classes can be formed reliably when training and testing are conducted in an SP2R format, supporting the view that equivalence class formation can account for the development of conceptual categories in natural settings.     

Testing response-stimulus equivalence relations using differential responses as a sample

This study tested the notion that an equivalence relation may include a response when differential responses are paired with stimuli presented during training. Eight normal adults learned three kinds of computer mouse movements as differential response topographies (R1, R2, and R3). Next, in matching-to-sample training, one of the response topographies was used to select a comparison stimulus B (B1, B2, or B3) conditionally upon presentation of sample stimulus A (A1, A2, or A3), and to select stimulus D (D1, D2, or D3) conditionally upon presentation of stimulus C (C1, C2, or C3). After two sample-comparison-response relations (ABR and CDR) were established, 18 sample-comparison relations were tested (BA, DC, RA, RB, RC, RD, AC, CA, AD, DA, BC, CB, BD, DB, AA, BB, CC, and DD). In the RA, RB, RC, and RD tests, the differential responses (R1, R2, and R3) were used as sample stimuli. All subjects made class-consistent comparison selections in the tests. This study provides evidence that responses may become members of an equivalence class.     

Testing for symmetry in the conditional discriminations of language-trained chimpanzees

If subjects are taught to match Stimulus A to B and then, without further training, match B to A, they have passed a test of symmetry. It has been suggested that non-humans' lack of success on symmetry tests might be overcome by giving them a history of symmetry exemplar training, that is, by directly teaching a large number of conditional relations (e.g., AB, CD, EF,...) and also directly training the "reverse" of these relations (e.g., BA, DC, FE,...). The chimpanzee subjects of the present study, Sherman, Austin, and Lana, had already received extensive symmetry exemplar training as a result of attempts to teach a selection-based language system of lexigrams. The present study systematically subjected 2 of these chimps (Sherman and Lana), for the first time, to standard symmetry tests in controlled conditions. Both chimps failed the tests, even when their correct responses on test trials were reinforced. The findings do not support the exemplar training hypothesis, and cast doubt upon whether the chimps can pass tests of stimulus equivalence.