A new approach to the formation of equivalence classes in pigeons

Four pigeons were given simultaneous discrimination training with visual patterns arbitrarily divided into two sets, with the stimuli in one set designated A1, B1, C1, and D1 and those in the other set designated A2, B2, C2, and D2. In sequentially introduced training phases, the pigeons were exposed to a series of reversals to establish AB and then CD equivalences. In subsequent testing sessions, a subset of stimuli from one set served as positive stimuli and those from the other set as negative stimuli on training trials, and transfer of the reinforced relation to other members of the sets was tested with nonreinforced probe trials. The pigeons were trained further on AC and BD equivalences and then were tested for the emergence of untrained AD and BC equivalences. Two of the 4 pigeons exhibited the emergence of one of these untrained equivalences, evidence for the emergence of transitive relations. This finding suggests that the pigeons established three-member functional equivalence classes by incorporating separately trained multiple equivalence relations. Repeated reversal training and probe testing enabled us to explore the formation and expansion of functional equivalence classes in pigeons.     

Effects of preliminary class membership on subsequent stimulus equivalence class formation

The present study examined the effects of including stimuli previously trained as members of functional classes or equivalence classes on subsequent equivalence class formation, and isolated the effects of preliminary training from those of the acquired function stimuli. Fifty-six adults were assigned to 1 of 5 conditions. The control group (CONT) received no preliminary training prior to the terminal phase. Participants in the other 4 groups learned two 3-member functional classes and two 3-member equivalence classes during the preliminary phase. The terminal equivalence phase trained two 5-member classes (A → B → C → D → E) comprising abstract forms; the C stimuli in the terminal phase were (a) from the preliminary functional classes for 1 group (ACQ-F), (b) from the preliminary equivalence classes for the second experimental group (ACQ-E), (c) pictures of everyday objects for the picture control group (PIC), and (d) novel, unfamiliar stimuli for the preliminary training control group (PRE-CONT). Class formation yields were 100% in the PIC condition and 11% in the CONT condition; however, low yields in the PRE-CONT, ACQ-F, and ACQ-E conditions were unexpected, suggesting that procedural variables in preliminary training account for more of the subsequent effects on class formation than the stimulus control properties of the acquired function stimuli.     

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.     

Evidence of precurrent responses expanding equivalence classes in a delayed matching-to-sample task

Delayed matching to sample (DMTS) increases the probability of equivalence class formation. Precurrent responses can mediate the retention interval in DMTS trials and control the selection of comparisons. In human participants, precurrent responses usually consist of naming the experimental stimuli based on their similarities to meaningful stimuli with preexperimental history. We tested whether precurrents expand classes by serving as nodes between experimental and meaningful stimuli. A DMTS (2 s) was used throughout the entire experiment. Eleven undergraduates learned A1B1 and A2B2 relations and then were submitted to ArC trials that required them to answer math problems presented during the DMTS interval: when the sample was A1, the problems resulted in 12 and C1 was correct; when the sample was A2, they resulted in 9 and C2 was correct. Response-as-node tests assessed whether participants would relate B1 and C1 to the printed number 12 and B2 and C2 to the printed number 9. Ten participants responded accordingly to this pattern, showing that the responses to the problems expanded the classes. Parity tests using the words “even” and “odd” further confirmed this hypothesis. These results contribute to understanding why DMTS enhances equivalence performances. Implications of using this procedure in stimulus-equivalence studies are discussed.     

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.     

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.     

Reorganization of equivalence classes: effects of preliminary training and meaningful stimuli

In Condition 1, adults learned the baseline relations for the three equivalence classes A1‐B1‐C1‐D1‐E1, A2‐B2‐C2‐D2‐E2, and A3‐B3‐C3‐D3‐E3. Classes contained abstract shapes in the ABS and four preliminary training groups. Each class in the PIC group contained one picture and four abstract shapes. Before class formation for four other groups, preliminary training involved establishing identity (CC) or arbitrary (CX) relations either with or without a delay. Without preliminary training, classes formed with low and high likelihoods in the ABS and PIC groups, respectively. Preliminary training with no delay produced modest increases in class formation, while preliminary training with delay produced large increases in class formation. Condition 2 replicated Condition 1 but with training of reassigned BC and CD relations that linked C from one class to B and D from another class: B1‐C2, B2‐C3, B3‐C1, C2‐D1, C3‐D2, and C1‐D3. Subsequent tests assessed the emergence of the reorganized classes A1‐B1 ‐C2 ‐D1‐E1, A2‐B2‐ C3 ‐D2‐E2, and A3‐B3‐ C1 ‐D3‐E3. All preliminary training procedures increased likelihood of forming the reorganized classes to the level seen in the PIC group. Greater gains were produced by preliminary training with no delays than with delays. Test performances also showed how preliminary training influenced baseline acquisition speed and participant‐defined relations.     

On the effectiveness of including meaningful pictures in the formation of equivalence classes

In three experiments, 165 adult participants were trained on 12 baseline conditional discriminations and tested for the formation of three 5-member equivalence classes (A➔B➔C➔D➔E). All experiments included two reference groups; the abstract (ABS) group was trained with all abstract stimuli and the picture (PIC) group with C-stimuli as meaningful pictorial stimuli but A, B, D, and E stimuli as abstract shapes. In Experiment 1, the color of the meaningful stimuli was manipulated. In the ABS, PIC, and black-and-white groups, 33.3%, 80%, and 93.3% formed equivalence classes, respectively. In Experiment 2, participants were exposed to a test block with and without trials that included C stimuli. For the groups with and without C trials in the test, 93.3% and 86.7% formed equivalence classes, respectively, compared to 20% in the ABS group. In Experiment 3, the number of meaningful pictures and their location in stimulus classes were manipulated. One group was trained with 3 pictures (C1/B2/D3, the 3-PIC) while the other groups had 2 pictures (C1/B2 and C1/D3, the 2-PIC). In the second test block for the ABS and PIC groups, 6.7% and 86% of the participants formed equivalence classes, respectively. For the 3-PIC and the 2-PIC groups, 66.7% and 50% of the participants formed equivalence classes, respectively. Results suggest that the effects of meaningful stimuli in equivalence classes (a) cannot be attributed to the use of colorful stimuli in previous studies, (b) occur during training and are not dependent on the presence of meaningful stimuli at test, and (c) are sensitive to stimulus location.     

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.     

Expansion of Sidman's theory: The inclusion of prompt stimuli in equivalence classes

Stimulus equivalence is defined as the ability to relate stimuli in novel ways after training in which not all of the stimuli had been directly linked to one another. Sidman (2000) suggested all elements of conditional discrimination training contingencies that result in equivalence potentially become class members. Research has demonstrated the inclusion of samples, comparisons, responses, and reinforcers in equivalence classes. Given the evidence that all elements of a conditional discrimination become part of the class, the purpose of this study was to determine if class-specific prompts would also enter into their relevant equivalence classes. Experiment 1 investigated the inclusion of prompts in an equivalence class using abstract stimuli with neurotypical students enrolled in higher education courses. Experiment 2 systematically replicated Experiment 1 using meaningful stimuli and individuals diagnosed with autism spectrum disorder. The results of both experiments demonstrated that class-specific prompts became part of equivalence classes with the other positive elements of the contingency. The results are discussed in terms of class expansion and the potential impact on equivalence-based instruction.     

Protocol analysis of the correspondence of verbal behavior and equivalence class formation.

In two equivalence experiments, a "think aloud" procedure modeled after Ericsson and Simon's (1980) protocol analysis was implemented to examine subjects' covert verbal responses during matching to sample. The purpose was to identify variables that might explain individual differences in equivalence class formation. The results from Experiment 1 suggested that subjects who formed equivalence classes described the relations among stimuli, whereas those not showing equivalence described sample and comparison stimuli as unitary compounds. Because Experiment 1 only demonstrated a correlation between describing stimulus compounds and the absence of equivalence classes, a second study was conducted. In Experiment 2, equivalence class formation was brought under experimental control through pretraining manipulations that facilitated responding either to stimulus compounds or to relations among stimuli. The results demonstrated that a history of describing stimulus compounds, when compared with describing the relations among the stimuli, interfered with the emergence of stimulus equivalence. These findings clarify individual differences in stimulus equivalence. They also demonstrate the utility of analyzing verbal reports to identify possible variables that can be manipulated experimentally.     

The effects of nodality on the formation of equivalence classes

A four-member equivalence class (A → B → C → D) can be formed by training AB, BC, and CD. The nodal stimuli, B and C, mediate all of the derivative (transitive and equivalence) relations in the class. The derivative relations AC, CA, BD, and DB are separated by one node, whereas AD and DA are separated by two nodes. How do the number of nodes that separate the stimuli in a derivative relation influence the induction of stimulus control exerted by that relation? Seven college students learned two four-member classes made up of nonsense syllables. After training, all derivative relations were presented repeatedly without informative feedback. Stimulus control exerted by each derivative relation was assessed concurrently. For the 7 subjects, control exerted by the derivative relations increased gradually with repeated presentations. With 6 of the 7 subjects, the one-node relations exerted more control than the two-node relations during the process. However, the disparity between the one- and two-node relations decreased with repeated presentations. Eventually, all derivative relations exerted complete control. The control exerted by derivative relations during induction was inversely related to the number of nodes separating the terms in the derivative relations. These results demonstrate that nodal distance is a determinant of the relatedness of stimuli in equivalence classes. The findings are discussed in terms of remote association, semantic memory networks, and the study of transitive inference.     

Predicting the extension of equivalence classes from primary generalization gradients: the merger of equivalence classes and perceptual classes.

In Experiment 1, 6 college students were given generalization tests using 25 line lengths as samples with a long line, a short line, and a “neither” option as comparisons. The neither option was to be used if a sample did not go with the other comparisons. Then, four-member equivalence classes were formed. Class 1 included three nonsense words and the short line. Class 2 included three other nonsense words and the long line. After repeating the generalization test for line length, additional tests were conducted using members of the equivalence classes (i.e., nonsense words and lines) as comparisons and intermediate-length lines as samples. All Class 2 comparisons were selected in the presence of the test lines that also evoked the selection of the long line in the generalization test that had been given before equivalence class formation. Class 1 yielded complementary findings. Thus, the preclass primary generalization gradient predicted which test lines acted as members of each equivalence class. Regardless of using comparisons that were nonsense words or lines, the post-class-formation gradients overlapped, showing the substitutability of class members. Experiment 2 assessed the discriminability of the intermediate-length test lines from the Class 1 (shortest) and Class 2 (longest) lines. The test lines that functioned as members of an equivalence class were discriminable from the line that was a member of the same class by training. Thus, these test lines also acted as members of a dimensionally defined class of “long” or “short” lines. Extension of an equivalence class, then, involved its merger with a dimensionally defined class, which converted a close-ended class to an open-ended class. These data suggest a means of predicting class membership in naturally occurring categories.     

Using the simultaneous protocol to study equivalence class formation: the facilitating effects of nodal number and size of previously established equivalence classes

The emergence of equivalence classes in college students is unlikely when all baseline relations are trained concurrently and all probes for emergent relations are then introduced concurrently (the simultaneous protocol). This experiment showed how the number of nodes and the size of previously established equivalence classes enhanced the emergence of new equivalence classes under the simultaneous protocol. First, one-node three-, five-, or seven-member classes or three-node five- or seven-member classes were established with college students. A sixth group received no pretraining. Then, the simultaneous protocol was used to establish new three-node five-member equivalence classes with all students. The speed and variability with which the baseline relations were established in the simultaneous protocol were inverse functions of number of nodes in the previously established classes, but not of their size. The percentage of subjects who showed the emergence of new equivalence classes under the simultaneous protocol was a direct function of number of nodes and size of pretrained classes. The additional time spent for pretraining greatly reduced the total training time needed to produce individuals who showed the emergence of classes under the simultaneous protocol. The total time saved was a direct function of number of nodes and number of stimuli in the pretrained classes.     

The effects of a training package to teach note taking on the formation of equivalence classes

Effective note taking may enhance learning outcomes for students and serve as a directly observable form of mediation within a test context. Frampton et al. (2023) used stimulus fading to teach note taking in the form of a graphic organizer (GO) during matching-to-sample baseline relations training (MTS-BRT). Moderately high yields were observed with young adults despite the use of linear series training, abstract stimuli, and five-member classes. The present study taught the same note taking strategy using an intervention package including video illustration, voice-over instructions, and feedback to eight college students. Participants were taught to construct the GO during MTS-BRT with three three-member classes of familiar stimuli. Then the effects of MTS-BRT alone with three five-member classes of abstract stimuli was evaluated. Participants efficiently completed training with familiar stimuli and passed the posttest on the first attempt. With the abstract stimuli, participants engaged in GO construction during MTS-BRT and the six participants that demonstrated high levels of fidelity to the trained note taking strategy passed the posttest on the first attempt. These results replicate findings from Frampton et al. while using a more efficient intervention package. Benefits of teaching overt mediation responses are discussed as well as future directions for translation to applied contexts.     

Symmetry and stimulus class formation in humans: Control by temporal location in a successive matching task

Symmetry refers to the observation that subjects will derive B‐A (e.g., in the presence of B, select A) after being trained on A‐B (e.g., in the presence of A, select B). Whereas symmetry is readily shown in humans, it has been difficult to demonstrate in nonhuman animals. This difficulty, at least in pigeons, may result from responding to specific stimulus properties that change when sample and comparison stimuli switch roles between training and testing. In three experiments with humans, we investigated to what extent human responding is influenced by the temporal location of stimuli using a successive matching‐to‐sample procedure. Our results indicate that temporal location does not spontaneously control responding in humans, although it does in pigeons. Therefore, the number of functional stimuli that humans respond to in this procedure may be half of the number of functional stimuli that the pigeons respond to. In a fourth experiment, we tested this assumption by doubling the number of functional stimuli controlling responding in human participants in an attempt to make the test more comparable to symmetry tests with pigeons. Here, we found that humans responded according to indirect class formation in the same manner as pigeons do. In sum, our results indicate that functional symmetry is readily observed in humans, even in cases where the temporal features of the stimuli prevent functional symmetry in pigeons. We argue that this difference in behavior between the two species does not necessarily reflect a difference in capacity to show functional symmetry between both species, but could also reflect a difference in the functional stimuli each species responds to.     

Functional equivalence classes in rats: Repeated olfactory discrimination reversals and delayed stimulus probes

The simultaneous matching-to-sample procedures that are widely used to study stimulus equivalence in human participants have generally been unsuccessful in animals. However, functional equivalence classes have been demonstrated in pigeons and sea lions using a concurrent repeated reversal discrimination procedure. In this procedure, responding to one set of stimuli is reinforced but responding to a different set is not and the set associated with reinforcement is changed with multiple reversals during the experiment. The experiments reported here were designed to assess whether functional equivalence classes could be demonstrated in rats using similar techniques. Rats were initially trained with two sets of olfactory stimuli (six odors/set). Following many reversals, probe reversal sessions were conducted in which rats were exposed to a subset of the members of each set and, later in the session, the withheld stimuli were introduced. Responding to these delayed probe trials in accord with the reversed contingencies constituted transfer of function. There was some evidence of transfer in Experiment 1, but the effects were relatively weak and variable. Experiment 2 introduced procedural changes and found strong evidence of transfer of function consistent with the formation of functional equivalence classes. These procedures offer a promising strategy to study symbolic behavior in rodents.     

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.