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

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

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.     

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.     

Development and crossmodal transfer of contextual control of emergent stimulus relations

Six normally capable adults first learned three conditional relations in each of two prospective equivalence classes via match-to-sample training with figures as conditional (sample) and discriminative (comparison) stimuli. Then one trained conditional relation in each prospective class was brought under the control of contextual stimuli, two dictated nonsense syllables. Test performances indicated the emergence of untrained conditional relations, and therefore two equivalence classes, that were conditional on the contextual stimuli. These tests involved untrained combinations of contextual stimuli and stimuli in conditional relations, suggesting that the contextual stimuli functioned independently to control conditional relations rather than forming compound stimuli with samples and comparisons in training. Next, two novel figures were made equivalent to each of the original dictated contextual stimuli by match-to-sample training and testing. On subsequent tests, all subjects demonstrated transfer of conditional control of untrained conditional relations from the original auditory contextual stimuli to equivalent visual stimuli. These outcomes further supported the conclusion that the contextual stimuli exerted true conditional control over conditional relations in the equivalence classes and were not merely elements of compound stimuli.     

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.     

Maintained nodal-distance effects in equivalence classes

Twelve subjects were trained to select one of two stimuli from a pair (the B pair) when presented with one of two stimuli from another pair (the A pair), thus establishing two AB relations, A1-B1 and A2-B2. In a similar fashion, additional stimuli were used to establish BC, CD, and DE relations. Trials used to train all relations occurred in each session. Once performances were established, probe trials were introduced that tested for the emergence of untrained relations (e.g., B1-D1 or A1-E1). These emergent relations were categorized according to nodal distance (i.e., the number of stimuli across which transitivity would have to hold in order for the relation to emerge). For example, a test for A2-C2 crosses one node (B2), whereas a test for A1-E1 crosses three nodes (B1, C1, and D1). Only 2 of the subjects formed equivalence classes. The evocation of class-appropriate responding by each emergent-relation probe was an inverse function of nodal distance for all 12 subjects. In addition, performance on the originally trained relations was disrupted by the introduction of probes. The 2 subjects who exhibited equivalence classes were then trained to make different numbers of key presses in the presence of each of the four A and E stimuli. In a response-transfer test, the B, C, and D stimuli evoked the responses trained to the A and E stimuli in the same equivalence class. Likelihood of class-appropriate responses was an inverse function of nodal distance, and this pattern persisted across testing. Reaction times in the transfer test were an inverted U-shaped function of nodal distance. Because training of the baseline relations occurred concurrently and the B, C, and D stimuli were presented an equal number of times before the transfer test, the test performances illustrate effects of nodal distance that were not confounded by order or amount of experience with the stimuli. The results imply that ordered, sequential exposure to individual stimulus relations may facilitate the development of equivalence classes and that the relatedness of stimuli within an equivalence class is a relatively permanent inverse function of nodal distance.     

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.     

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.     

Symmetry training in pigeons can produce functional equivalences

Functional stimulus equivalence has been demonstrated using a transfer of training design with matching-to-sample training in which two sample stimuli are associated with the same comparison stimulus (A-B, C-B; many-to-one matching). Equivalence is shown by training a new association (A-D) and demonstrating the presence of an emergent relation (C-D). In the present experiment, we show that symmetry training, in which a bidirectional association is trained between two stimuli (A-B, B-A, using successive stimulus presentations followed by reinforcement), can also produce functional equivalence using a transfer of training design (i.e., train B-C, test A-C). The results suggest that training pigeons in the substitutability of two stimuli may be sufficient to produce functional stimulus equivalence between them. The results also have implications for the development of an emergent transitive relation, because training on A-B and B-C relations results in the emergence of an untrained A-C relation, if B-A training also is provided.     

Verbal self-reports of emergent relations in a stimulus equivalence procedure.

During a preliminary training phase, college students were taught to categorize each of their responses accurately in a conditional discrimination task as either correct or incorrect. Next, in the absence of self-reports, subjects acquired conditional discriminations (involving novel stimuli) prerequisite to the formation of two four-member equivalence classes. The self-report procedure was reinstated during probe sessions that tested for untrained relations indicative of equivalence class formation. Interspersed trials involving trained relations provided a positive control, and trials with no class-consistent comparison provided a negative control. Eight of 10 subjects demonstrated equivalence class formation; all accurately reported their performance on trained relations and on trials with no class-consistent comparison. Subjects also reported their performance on most untrained (emergent) relations accurately, but in several instances self-reports indicated failure or uncertainty despite nearly perfect emergent-relations performance. These inconsistencies add to a growing body of literature that suggests there are differences between individual types of emergent relations. We suggest that the present procedure may be helpful in understanding these differences and other equivalence-related effects.     

Functional classes and equivalence relations

Three adult subjects were taught a set of two-choice simultaneous discriminations, with three positive and three negative stimuli; all possible combinations of positive and negative stimuli yielded nine different pairs. The discriminations were repeatedly reversed and rereversed, the former positive stimuli becoming negative and the former negative stimuli becoming positive. With all subjects, a reversal of the contingencies for one pair of stimuli became sufficient to change their responses to all of the other pairs. The reversals had produced functional stimulus classes. Then, all subjects showed conditional discriminations emerging between members of a functional class; given a sample from one class and comparisons from both classes, they selected the comparison that was in the same class as the sample. Next, 2 of the subjects showed that the within-class conditional relations possessed the symmetric and transitive properties of equivalence relations; after having been taught to relate new stimuli to existing class members, the subjects then matched other class members to the new stimuli. Subsequent tests of two-choice discriminations showed that the conditional discriminations had transferred functional class membership to the new stimuli. The 3rd subject, who did not show equivalence relations among functional class members, was also found to have lost the within-class conditional relations after the equivalence tests.     

Equivalence relations between visual stimuli: the functional role of naming

The functionality of verbal behavior in equivalence class formation was demonstrated by training 30 verbally able adults using different combinations of the same easily nameable, yet formally unrelated, pictorial stimuli. Match-to-sample baselines for four four-member classes were established sequentially (i.e., AB-BC-CD), with participants in the rhyme condition trained to select comparisons whose normative names rhymed with those of the samples. For the orthogonal condition, class rearrangement was such that on every trial all available comparisons' names rhymed with each other, but not with the name of the sample. In the diagonal condition, stimuli were allocated pseudorandomly as samples and comparisons. Although all participants maintained baseline discriminations prior to emergent testing, equivalence was confined almost exclusively to the rhyme condition, in which it was ubiquitous. These participants also required less training than those in the control conditions, among whom effects of nodal distance were observed most strongly. Subsequent testing presented participants with no-reinforcement trials involving novel pictorial stimuli, in which one of the available comparisons' names always rhymed with that of the sample. All rhyme participants consistently selected these comparisons. Results indicate that visual stimuli are named, that the phonological properties of those names can influence equivalence class formation, and that the emergence of untrained discriminations may, under certain circumstances, be rule governed.     

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.     

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.     

Nodal structure and the partitioning of equivalence classes

By definition, all of the stimuli in an equivalence class have to be functionally interchangeable with each other. The present experiment, however, demonstrated that this was not the case when using post-class-formation dual-option response transfer tests. With college students, two 4-node 6-member equivalence classes with nodal structures of A-->B-->C-->D-->E-->F were produced by training AB, BC, CD, DE, and EF. Then, unique responses were trained to the C and D stimuli in each class. The responses trained to C generalized to B and A, while the responses trained to D generalized to E and F. Thus, each 4-node 6-member equivalence class was bifurcated into two 3-member functional classes: A-->B-->C and D-->E-->F, with class membership precisely predicted by nodal structure. A final emergent relations test documented the intactness of the underlying 4-node 6-member equivalence classes. The coexistence of the interchangeability of stimuli in an equivalence class and the bifurcation of such a class in terms of nodal structure was explained in the following manner. The conditional discriminations that are used to establish a class also imposes a nodal structure on the stimuli in the class. Thus, the stimuli in the class acquire two sets of relational properties. If the format of a test trial allows only one response option per class, responding on those trials will be in accordance with class membership and will not express the effects of nodal distance. If the format of a test trial allows more than one response option per class, responding on those trials will be determined by the nodal structure of the class. Thus, the relational properties expressed by the stimuli in an equivalence class are determined by the discriminative function served by the format of a test trial.     

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'.     

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.     

The transfer of contextual control over equivalence classes through equivalence classes: a possible model of social stereotyping.

In Experiment 1, subjects acquired conditional equivalence classes controlled by three male and three female names as contextual stimuli. When equivalence relations were tested using new names not used in training (three male and three female), contextual control remained intact. Thus, generalized control of the composition of conditional equivalence classes by characteristically gender-identified names was shown. A basic analysis of this finding was tested in Experiment 2. Contextual equivalence classes were established using as contextual stimuli nonrepresentational visual figures that were members of additional pretrained three-member equivalence classes. When other stimuli in the pretrained equivalence classes were used as contextual stimuli, the conditional equivalence classes remained intact. Control subjects showed that this effect depended on the equivalence relations established in pretraining. The results show that contextual control over equivalence classes can transfer through equivalence classes. The implications of this phenomenon for social stereotyping are discussed.     

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.     

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

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