Expansion of arbitrary stimulus classes and function-transfer measured by sorting performances.

Sorting (SRT) and matching-to-sample (MTS) tests have measured the formation of arbitrary stimulus classes. This experiment used SRT and MTS tests to document the expansion of class size. Thirty-two participants learned 12 conditional discriminations with a linear series training structure (A➔B➔C➔D➔E). SRT tests documented the formation of 5-member classes by 17 of the participants. Thereafter, 6-member class expansion was implemented by FC training. Nine of these 17 participants showed class expansion when tracked with a sequence of an SRT, MTS, and a final SRT test, and the other 8 showed expansion when tracked with a sequence of MTS and SRT tests. Thus, SRT tests documented class expansion, and the sequence of tests did not influence class expansion. The 15 participants who did not form the 5-member classes learned the baselines for new 3-member classes (A➔B➔C) and formed them as documented by an SRT test. Then, 4-member class expansion was implemented by FB training. Expansion was assessed using the above-mentioned testing sequences. All 15 showed class expansion with 100% correspondence between the SRT and MTS performances. Sorting documented the expansion of arbitrary stimulus classes, while the MTS tests showed that the stimuli also functioned as members of equivalence classes.

Equivalence class formation when responding is separated from sample and comparison stimuli: Working memory, priming, and sorting.

The experiment determined whether equivalence class formation required overlap of comparison stimuli and responding. Each trial contained a sample first, a single, nonoverlapping comparison second, and a nonoverlapping response-window (RW) third, during which the participant made one of two responses (2R). All 11 participants formed two 3-member ABC equivalence classes using these "trace-stimulus-pairing two-response with response window" (TSP-2R-RW) trials. After adding a fourth stimulus (D) by CD training, ABCD tests showed immediate expansion to 4-member ABCD classes. When 4-member probes (AD, DA, BD, DB, CD, DC) were administered without 3-member probes, many participants showed decrements in class-indicative responding that then resurged to mastery with test repetition. Thus, 3-member probes enhanced class expansion. Class formation occurred for all participants when responding was temporally dissociated from the comparisons. In a matched, contemporaneously published experiment, where responding occurred during comparisons, only 54% of participants formed the classes. Thus, the comparison-response-separation nearly doubled class formation. Additionally, a special post-class-formation sorting test documented the emergence of two explicit equivalence classes. Finally, we noted a 1:1 correspondence for TSP-2R-RW and priming trials. Since priming measures neural substrates of equivalence classes, TSP-2R-RW trials should do the same.

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.

Transfer of discriminative control during stimulus fading conducted without reinforcement.

Using trial-and-error training, eight pigeons did not learn to discriminate between 45° and 135° lines, but did learn to discriminate between red and green colors. Control by line tilt was induced by stimulus fading that did not include reinforcement while fading out the colors. After establishing the red-green discrimination, low-intensity lines were superimposed on colors and were gradually faded in. All of this was done using reinforcement. At the end of the line fade-in, the lines had not acquired control of responding. Finally, color intensity was gradually faded out in the absence of reinforcement, and the lines acquired discriminative control by six of the eight pigeons. Thus, reinforcement during the color fade-out was not necessary for the acquisition of discriminative control by the lines during fading. Acquisition of control by lines was attributed to overshadowing, the reduction of stimulus blocking by generalization, and the evocation of correct responding by the colors while the participants were attending to the lines. This last process was also responsible for the induction of discriminative control during sensory preconditioning, higher order conditioning, and response transfer in equivalence classes. Errors, however, were not correlated with discrimination learning during stimulus fading. Finally, transfer of control occurred very quickly with or without errors.

Meaningful Stimuli and the Enhancement of Equivalence Class Formation.

Stimulus meaningfulness has been defined by its hedonic valence, denotative (definitional) and connotative (evaluative) properties, and its influence on forming categories called equivalence classes. Positive or negative hedonic value of a meaningful stimulus transfers to the other members of an equivalence class that contains such a stimulus, and also influences likelihood of class formation. The denotative and connotative properties of meaningful stimuli are instantiated by the responses they produced (simple discriminative functions) and by the selection of other related words (conditional discriminative functions). If a meaningless cue acquires one such stimulus control function, and is included in a set of otherwise meaningless stimuli, its inclusion enhances the formation of an equivalence class. These results suggest ways to enhance equivalence class formation in applied settings. When degree of enhancement matches that produced by the inclusion of a meaningful stimulus in a class, class enhancement can be accounted for by the stimulus control functions it serves, as well as its hedonic, denotative, and connotative properties. We also linked equivalence class formation and meaningfulness to semantic networks, relational frame theory, verbal behavior, and naming.

Optimizing equivalence-based instruction: Effects of training protocols on equivalence class formation.

Two experiments evaluated the effects of the simple-to-complex and simultaneous training protocols on the formation of academically relevant equivalence classes. The simple-to-complex protocol intersperses derived relations probes with training baseline relations. The simultaneous protocol conducts all training trials and test trials in separate portions of the protocol. In Experiments 1 and 2, participants formed 4 3- and 4-member neuroanatomy classes, respectively. When trained with the simple-to-complex protocol, 100% of participants immediately formed the 3- or 4-member classes. When trained with the simultaneous protocol, the 3- and 4-member classes were formed immediately by 75% and 42% of participants, respectively. Thus, the immediate emergence of equivalence classes was an interactive function of training protocol and class size. The remaining participants eventually formed classes after a few cycles of retraining. The incorporation of these training and testing parameters could optimize the use of equivalence-based instruction for teaching college-level course content.

Training order and structural location of meaningful stimuli: effects on equivalence class formation.

In the present study, equivalence class formation was influenced by the temporal point of inclusion of a meaningful stimulus when baseline relations were serially or sequentially trained, and much less so by the location of the meaningful stimulus in the nodal structure of the class. In Experiment 1, participants attempted to form three 3-node, 5-member classes (A→B→C→D→E) under the simultaneous protocol. After serially training the baseline relations AB, BC, CD, and DE, in that order, the emergence of all emergent relations was tested concurrently. In the A-as-PIC condition, A was meaningful stimulus and B to E were meaningless stimulus, and 60 % of the participants formed classes. In addition, classes were formed by 40 %, 70 %, 40 %, and 20 % of the participants in the B-as-PIC, C-as-PIC, D-as-PIC, and E-as-PIC groups, respectively. Thus, the likelihood of class formation could have been influenced by the location of a meaningful stimulus in the class structure and/or by its order of introduction during training. In Experiment 2, we controlled for any effect of order of introduction by the concurrent training of all of the baseline relations. Regardless of the location of the meaningful stimulus, 0-20 % of participants formed classes. Thus, the temporal order of introducing a meaningful stimulus was the primary modulator of the class-enhancing property of meaningful stimuli, and not the location of the meaningful stimulus in the class structure.

Learning to write without writing: writing accurate descriptions of interactions after learning graph-printed description relations.

Interpreting and describing complex information shown in graphs are essential skills to be mastered by students in many disciplines; both are skills that are difficult to learn. Thus, interventions that produce these outcomes are of great value. Previous research showed that conditional discrimination training that established stimulus control by some elements of graphs and their printed descriptions produced some improvement in the accuracy of students' written descriptions of graphs. In the present experiment, students wrote nearly perfect descriptions of the information conveyed in interaction-based graphs after the establishment of conditional relations between graphs and their printed descriptions. This outcome was achieved with the use of special conditional discrimination training procedures that required participants to attend to many of the key elements of the graphs and the phrases in the printed descriptions that corresponded to the elements in the graphs. Thus, students learned to write full descriptions of the information represented by complex graphs by an automated training procedure that did not involve the direct training of writing.

Enhanced equivalence class formation by the delay and relational functions of meaningful stimuli.

Undergraduates in six groups of 10 attempted to form three 3-node 5-member equivalence classes (A → B → C → D → E) under the simultaneous protocol. In five of six groups, all stimuli were abstract shapes; in the PIC group, C stimuli were pictures with the remainder being abstract shapes. Before class formation, participants in the Identity-S and Identity-D groups were given preliminary training to form identity conditional discriminations with the C stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. In the Arbitrary-S and Arbitrary-D groups, before class formation, arbitrary conditional discriminations were formed between C and X stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. With no preliminary training, classes in the PIC and ABS groups were formed by 80% and 0% of participants, respectively. After preliminary training, class formation (yield) increased with delay, regardless of relational type. For each of the two delays, yield was slightly greater after forming arbitrary- instead of identity-relations. Yield was greatest, however, when a class contained a meaningful stimulus (PIC). During failed class formation, probes produced experimenter-defined relations, participant-defined relations, and unsystematic responding; delay, but not the relation type in preliminary training influenced relational and indeterminate responding. These results suggest how meaningful stimuli enhance equivalence class formation.

Arbitrary conditional discriminative functions of meaningful stimuli and enhanced equivalence class formation.

Equivalence class formation by college students was influenced through the prior acquisition of conditional discriminative functions by one of the abstract stimuli (C) in the to-be-formed classes. Participants in the GR-0, GR-1, and GR-5 groups attempted to form classes under the simultaneous protocol, after mastering 0, 1, or 5 conditional relations between C and other abstract stimuli (V, W, X, Y, Z) that were not included in the to-be-formed classes (ABCDE). Participants in the GR-many group attempted to form classes that contained four abstract stimuli and one meaningful picture as the C stimulus. In the GR-0, GR-1, GR-5, and GR-many groups, classes were formed by 17, 25, 58, and 67% of participants, respectively. Thus, likelihood of class formation was enhanced by the prior formation of five C-based conditional relations (the GR-5 vs. GR-0 condition), or the inclusion of a meaningful stimulus as a class member (the GR-many vs. GR-0 condition). The GR-5 and GR-many conditions produced very similar yields, indicating that class formation was enhanced to a similar degree by including a meaningful stimulus or an abstract stimulus that had become a member of five conditional relations prior to equivalence class formation. Finally, the low and high yields produced by the GR-1 and GR-5 conditions showed that the class enhancement effect of the GR-5 condition was due to the number of conditional relations established during preliminary training and not to the sheer amount of reinforcement provided while learning these conditional relations. Class enhancement produced by meaningful stimuli, then, can be attributed to their acquired conditional discriminative functions as well as their discriminative, connotative, and denotative properties.

Enhancement of equivalence class formation by pretraining discriminative functions.

The present experiment showed that a simple discriminative function acquired by an abstract stimulus through simultaneous and/or successive discrimination training enhanced the formation of an equivalence class of which that stimulus was a member. College students attempted to form three equivalence classes composed of three nodes and five members (A→B→C→D→E), using the simultaneous protocol. In the PIC group, the C stimuli were pictures and the A, B, D, and E stimuli were abstract shapes. In the ABS group, all of the stimuli were abstract shapes. In the SIM + SUCC (simultaneous and successive) group, simple discriminations were formed with the C stimuli through both simultaneous and successive discrimination training before class formation. Finally, in the SIM-only and SUCC-only groups, prior to class formation, simple discriminations were established for the C stimuli with a simultaneous procedure and a successive procedure, respectively. Equivalence classes were formed by 80% and 70% of the participants in the PIC and SIM + SUCC groups respectively, by 30% in the SUCC-only group, and by 10% apiece in the ABS and SIM-only groups. Thus, pretraining of combined simultaneous and successive discriminations enhanced class formation, as did the inclusion of a meaningful stimulus in a class. The isolated effect of forming successive discriminations was more influential than that of forming simultaneous discriminations. The establishment of both discriminations together produced an enhancement greater than the sum of the two procedures alone. Finally, a sorting test documented the maintenance of the classes formed during the simultaneous protocol. These results also provide a stimulus control-function account of the class-enhancing effects of meaningful stimuli.

Discriminative functions and over-training as class-enhancing determinants of meaningful stimuli.

Likelihood of equivalence class formation (yield) was influenced by pre-class formation of simultaneous and successive discriminations, their mastery criteria, and overtraining of the successive discriminations. Each undergraduate in seven groups attempted to form two 3-node, 5-member equivalence classes (ABCDE). In the pictorial (PIC) group, meaningless nonsense syllables were used as the A, B, D, and E stimuli and meaningful pictures as the C stimuli. Nonsense syllables only were used in the other groups. The abstract (ABS) or 0-0-0 group involved no pre-class training. In the 84-0-0, 84-5-0 and 84-20-0 groups, simultaneous discriminations were trained among C stimuli to a mastery criterion of 84 trials, followed by successive discriminations trained to mastery criteria of 0, 5, and 20 trials, respectively. In the 84-20-0, 84-20-100, and 84-20-500 groups, simultaneous and successive discriminations were trained as noted, followed by overtraining with 0, 100, 500 successive-discrimination trials, respectively. The ABS group produced a 6% yield with the 84-0-0, 84-5-0, and 84-20-0 groups producing further modest increments. Overtraining produced a linear increase in yield, reaching 85% after 500 overtraining trials, a yield matching that produced by classes containing pictures as C stimuli (PIC). Thus, acquired discriminative functions and the overtraining of at least one function can account for class enhancement by meaningful stimuli.

All stimuli are equal, but some are more equal than others: measuring relational preferences within an equivalence class.

Two experiments used post-class formation within-class relational assessment test performances to evaluate whether participants demonstrated preference for certain members of an equivalence class based on the type of relation that existed between class members. In Experiment 1, two 5-node 7-member equivalence classes, consisting entirely of nonsense syllables, were established using the simultaneous protocol. Only 1 of the 6 participants in Experiment 1 formed classes. After class formation, the effects of the different relations between stimuli were evaluated using within-class relational assessment tests, and the 1 participant showed an absolute preference for transitive over equivalence relations, and for baseline over symmetrical relations. Experiment 2 was identical to Experiment 1, except that one of the nonsense syllable stimuli in each class was replaced by a pictorial stimulus. Under these conditions, classes were formed by 5 of 13 participants. During the relational assessment tests, the 5 participants who formed classes demonstrated almost exclusive preferences for transitive relations over equivalence relations and for trained baseline relations over symmetrical relations. Thus, this research demonstrates that the members of equivalence classes are differentially related to each other based on relational type.

Effects of a meaningful, a discriminative, and a meaningless stimulus on equivalence class formation.

Thirty college students attempted to form three 3-node 5-member equivalence classes under the simultaneous protocol. After concurrent training of AB, BC, CD, and DE relations, all probes used to assess the emergence of symmetrical, transitive, and equivalence relations were presented for two test blocks. When the A-E stimuli were all abstract shapes, none of 10 participants formed classes. When the A, B, D, and E stimuli were abstract shapes and the C stimuli were meaningful pictures, 8 of 10 participants formed classes. This high yield may reflect the expansion of existing classes that consist of the associates of the meaningful stimuli, rather than the formation of the ABCDE classes, per se. When the A-E stimuli were abstract shapes and the C stimuli became S(D)s prior to class formation, 5 out of 10 participants formed classes. Thus, the discriminative functions served by the meaningful stimuli can account for some of the enhancement of class formation produced by the inclusion of a meaningful stimulus as a class member. A sorting task, which provided a secondary measure of class formation, indicated the formation of all three classes when the emergent relations probes indicated the same outcome. In contrast, the sorting test indicated "partial" class formation when the emergent relations test indicated no class formation. Finally, the effects of nodal distance on the relatedness of stimuli in the equivalence classes were not influenced by the functions served by the C stimuli in the equivalence classes.

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.

The contextually controlled, feature-mediated classification of symbols.

The classification of names of people or objects based on the features acquired by the names and the sorting instructions provided is a commonplace occurrence. For example, given the names Renoir, Pollock, James and Voltaire the average adult would be able to classify them differentially based on the instruction to classify them based on vocation or nationality. In general, such a repertoire reflects the reclassification of symbols (i.e, the names of individuals) in terms of contextual cues (instructions to sort by vocation or nationality) and the features acquired by the symbols (the specific nationalities and vocations). The present experiment studied this phenomenon with the use of arbitrary stimuli that did not have clear preexperimental associations. Two of 4 participants classified the symbols into different equivalence classes based on the prevailing contextual cues and the features that had been acquired by the symbols. Using an ABA reversal design we then demonstrated that 1 participant classified the symbols in accordance with the contextual cues and acquired features when present, but not in the absence of the contextual cues. A 3rd participant showed symbol classification that differed from that predicted by the procedures, and the 4th classified the symbols based on one set of features but not on context. These data describe one set of conditions that could account for the establishment of complex classification repertoires that occur in natural settings.

Optimizing linked perceptual class formation and transfer of function.

A linked perceptual class consists of two distinct perceptual classes, A' and B', the members of which have become related to each other. For example, a linked perceptual class might be composed of many pictures of a woman (one perceptual class) and the sounds of that woman's voice (the other perceptual class). In this case, any sound of the woman's voice would occasion the selection of any picture of the woman and vice versa. In addition, after learning to name the woman in the presence of one picture, that name would be uttered when presented with all of the images of the woman's face and all of the sounds of her voice. This study involved 15 participants and sought to (a) maximize the percentage of participants who formed linked perceptual classes, and (b) determine whether those classes acted as transfer networks, that is, whether the discriminative function of one class member would generalize to other members of the class and not to members of a different class. The rate of emergence of each linked perceptual class was maximized by establishing a single class-linking conditional relation between the clearest member of one class used as a sample stimulus and the most ambiguous member of the other class used as a comparison stimulus. Class formation was demonstrated using the serial and programmed presentation of A'-B' probes that consisted of untrained pairs of stimuli drawn from the A' and B' classes. Most participants showed immediate emergence of the two linked perceptual classes. The remaining participants showed delayed emergence following a second exposure to each originally error-producing probes. Once the linked perceptual classes had emerged, a differential response to a specific member of one perceptual class generalized mostly or completely to the other members of that linked class and rarely, if ever, to members of the other linked class. Thus, generalization did not depend on the specific class members that had been used for discrimination training.

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.

Equivalence class formation: a method for teaching statistical interactions.

Many students struggle with statistical concepts such as interaction. In an experimental group, participants took a paper-and-pencil test and then were given training to establish equivalent classes containing four different statistical interactions. All participants formed the equivalence classes and showed maintenance when probes contained novel negative exemplars. Thereafter, participants took a second paper-and-pencil test. Participants in the control group received two versions of the paper-and-pencil test without equivalence-based instruction. All participants in the experimental group showed increased paper-and-pencil test scores after forming the interaction-indicative equivalence classes. Class-indicative responding also generalized to novel exemplars and the novel question format used in the paper-and-pencil test. Test scores did not change with repetition for control group participants. Implications for behavioral diagnostics and teaching technology are discussed.

Formation of partially and fully elaborated generalized equivalence classes.

Most complex categories observed in real-world settings consist of perceptually disparate stimuli, such as a picture of a person's face, the person's name as written, and the same name as heard, as well as dimensional variants of some or all of these stimuli. The stimuli function as members of a single partially or fully elaborated generalized equivalence class when they occasion the mutual selection of each other after the establishment of some subset of relations among the stimuli. Indeed, it is these generalized relations among stimuli that enable an individual to respond appropriately to the inevitable flux of natural environments. The present experiments involved procedures for producing both types of generalized equivalence class and for evaluating their retention. Granting the formal and functional similarities that exist between generalized equivalence classes and natural categories, natural kinds, and fuzzy superordinate classes, the variables responsible for the emergence of the former might also account for the emergence of the latter three phenomena. In Experiment 1, After forming an A'-B' class, a B'-C relation was trained and generalization tests were conducted with B'-C, C-B', A'-C, and C'-A. Two of 5 participants passed the tests documenting the formation of A'-B'-C classes. Failures occurred in the A'-C and C-A' tests but not the B'-C and C-B' tests. Failures were also correlated with time between A'-B' class formation and C-based testing and with the absence of baseline confirmation when training and testing were separated by about one week. Experiment 2 replicated Experiment 1 but presented baseline confirmation probes immediatley prior to testing when training and testing were separated by one week; all participants then formed partially elaborated generalized equivalence classes. In Experiment 3, 5 of 6 participants formed fully elaborated generalized equivalence classes, represented as A' = B' = C'.