Stimulus class formation and concept learning: establishment of within- and between-set generalization and transitive relationships via conditional discrimination procedures

Three students with moderate mental retardation were taught a complex stimulus class with a two-choice conditional discrimination procedure applied across eight 10-member stimulus sets. Each set was composed of five age-appropriate and five age-inappropriate examples of clothing, accessories, and leisure items (e.g., a Walkman radio). Discrimination training was programmed serially across each set, and generalization probes were conducted concurrently among all sets. Generalization probes consisted of unreinforced conditional matching trials with comparison items being drawn from (a) the set undergoing training (within-set probes), (b) sets not undergoing training (between-set probes), and (c) both sample and comparison items from different sets (transitive stimulus control probes). Results indicate that within-set generalization, between-set generalization, and transitive stimulus relations controlled responding by all 3 students for items that had been contingently associated with reinforcement. However, items that gained control of responding through within-set and between-set generalization alone (i.e., not acquired through contingent reinforcement) remained at baseline levels during transitive stimulus control probes. Results are discussed in terms of a taxonomy of multiple sources of stimulus control that underlie socially defined and maintained stimulus classes.     

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.     

Transfer of specific contextual functions to novel conditional discriminations

Three adolescents and 4 children participated in studies designed to examine contextually controlled conditional discrimination performance. In Study 1, participants selected Comparison B1 in the presence one stimulus (A1) and Comparison B2 in the presence of another stimulus (A2) using a matching-to-sample procedure. Next, contextual stimuli X1 or X2 were presented, such that in the presence of X1, selection of B1 given A1 and selection of B2 given A2 were reinforced; and in the presence of X2, selection of B2 given A1 and selection of B1 given A2 were reinforced. Then, new conditional discriminations were taught with Stimuli E and F. When the contextual Stimuli X1 and X2 were presented, participants selected the same comparisons as previously established in the EF relations in the presence of X1, but the opposite comparison as in the EF relations in the presence of X2. The results then were replicated with new Stimuli G and H. In Study 2, a new conditional discrimination, CD, was taught. Then, four combinations of two-element samples--C1 and D1, C2 and D2, C1 and D2, or C2 and D1--were presented with X1 and X2 as comparisons. Five of 6 participants selected X1 in the presence of C1 and D1 or C2 and D2, and selected X2 in the presence of C1 and D2 or C2 and D1. Finally, in Study 3, two new discriminations IJ and JK were taught. Then, the transitive IK relations were tested with X1 and X2 as contextual stimuli. The 4 participants selected K1 in the presence of I1 and K2 in the presence of I2 when the contextual stimulus was X1--demonstrating class formation--and selected the other comparisons when the contextual stimulus was X2. These results suggest that the contextual control functions of X1 and X2 transferred even to relations that had not been directly taught. These results extend those demonstrating generalized contextual control by showing transfer of functions of the contextual stimuli in transitivity tests and when the former contextual stimuli were presented as comparisons.     

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.     

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.     

Transfer of a conditional ordering response through conditional equivalence classes

Eight adult humans were taught conditional discriminations in a matching-to-sample format that led to the formation of two four-member equivalence classes. When subjects were taught to select one comparison stimulus from each class in a set order, they then ordered all other members of the equivalence classes without explicit training. When the ordering response itself was brought under conditional control, conditional sequencing also transferred to all other members of the two equivalence classes. When the conditional discriminations in the matching-to-sample task were brought under higher order conditional control, the eight stimulus members were arranged into four conditional equivalence classes. Both ordering and conditional ordering transferred to all members of the four conditional equivalence classes; for some subjects this occurred without a typical test for equivalence. One hundred twenty untrained sequences emerged from eight trained sequences for all subjects. Transfer of functions through equivalence classes may contribute to a behavior-analytic approach to semantics and generative grammar.     

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.     

Six-member stimulus classes generated by conditional-discrimination procedures

In conditional-discrimination procedures with three sets of stimuli, A, B, and C, three stimuli per set (A1A2A3, B1B2B3, and C1C2C3), subjects (children and adults) learned to select Set-B and Set-C comparisons conditionally upon Set-A samples (A1B1, A1C1, A2B2, A2C2, A3B3, A3C3). If the conditional-discrimination procedures also generated equivalence relations, three 3-member stimulus classes would be demonstrable, A1B1C1, A2B2C2, and A3B3C3. In addition to these three sets, the present experiments used three other sets of stimuli--D, E, and F. The subjects learned to select Set-E and Set-F comparisons conditionally upon Set-D samples (D1E1, D1F1, D2E2, D2F2, D3E3, D3F3). This established a second group of three 3-member stimulus classes, D1E1F1, D2E2F2, and D3E3F3. In all, two groups of three 3-member classes were established by teaching subjects 12 conditional discriminations. The two groups of 3-member classes were then combined (successfully for 5 of 8 subjects) into a single group of three 6-member classes by teaching the subjects three more conditional relations (E1C1, E2C2, and E3C3). With three other children, enlarging the classes one member at a time also produced 6-member classes. As a consequence of class formation, 60 untrained conditional relations emerged from 15 that had been explicitly taught. Six of the subjects also proved capable of naming the stimuli consistently in accord with their class membership, but two subjects demonstrated class formation even in the absence of consistent naming.     

Relations among equivalence, naming, and conflicting baseline control

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

A comparison of methods for teaching receptive labeling to children with autism spectrum disorders

Many early intervention curricular manuals recommend teaching auditory-visual conditional discriminations (i.e., receptive labeling) using the simple-conditional method in which component simple discriminations are taught in isolation and in the presence of a distracter stimulus before the learner is required to respond conditionally. Some have argued that this procedure might be susceptible to faulty stimulus control such as stimulus overselectivity (Green, 2001). Consequently, there has been a call for the use of alternative teaching procedures such as the conditional-only method, which involves conditional discrimination training from the onset of intervention. The purpose of the present study was to compare the simple-conditional and conditional-only methods for teaching receptive labeling to 3 young children diagnosed with autism spectrum disorders. The data indicated that the conditional-only method was a more reliable and efficient teaching procedure. In addition, several error patterns emerged during training using the simple-conditional method. The implications of the results with respect to current teaching practices in early intervention programs are discussed.     

Transfer of contextual stimulus function via equivalence class development

In a conditional discrimination, 6 college students arranged six Cyrillic letters into groups of three based upon which of two additional Cyrillic letters (contextual stimuli) was present. All subjects demonstrated symmetry and transitivity within each class of equivalent stimuli. In a second conditional discrimination, two more Cyrillic letters were related to each contextual stimulus. Testing of symmetrical and transitive relations between the original contextual stimulus and the two new ones confirmed the development of two three-member classes of contextual stimuli. Subsequent tests demonstrated that the new contextual stimuli controlled the previously trained sample-comparison relations for all subjects.     

Contriving transitive conditioned establishing operations to establish derived manding skills in adults with severe developmental disabilities

The purpose of this study was to demonstrate derived manding skills in 2 adults with severe developmental disabilities and language deficits by contriving transitive conditioned establishing operations. Specifically, we evaluated whether a history of reinforced conditional discrimination learning would ultimately result in a derived mand repertoire, in which participants manded for items that were needed to complete chained tasks. After mastering the first three phases of the picture exchange communication system (PECS), participants were taught to mand for the needed items by exchanging pictures of the items for the items themselves. They were then taught to conditionally relate the dictated names of the items to the corresponding pictures of the items and to relate the dictated names to the corresponding printed words. We then tested, in the absence of reinforcement, whether participants would mand for the items needed to complete the chained tasks using text rather than pictures. Both participants showed the emergence of derived mands and some derived stimulus relations as a result of this instruction. Some of the derived relations were shown to be intact at 1-month follow-up, and scores on derived mand probes were higher at follow-up than before training. In addition, the 2 participants vocally requested the needed items on maintenance test probes, a skill that was never trained and was not previously in their repertoires. These results suggest that a history of reinforced relational responding may facilitate the expansion of a number of verbal skills and emphasize the possibility of a synthesis of Skinner's (1957) analysis of verbal behavior and derived stimulus relations into language-training efforts for persons with significant disabilities.     

Stimulus equivalence: testing Sidman's (2000) theory

Sidman's (2000) theory regarding the origin of equivalence relations predicts that a reinforcing stimulus common to distinct equivalence classes must drop out of the equivalence relations. This prediction was tested in the present study by arranging class-specific reinforcers, R1 and R2, following correct responding on the prerequisite conditional discriminations (Ax-Bx, Cx-Bx) for two stimulus classes, A1B1C1 and A2B2C2. A class-common reinforcer, R3, was presented following correct responding on the prerequisite conditional discriminations for a further two stimulus classes, A3B3C3 and A4B4C4. Sidman's theory predicts reinforcer inclusion within Classes 1 and 2 only, given this training arrangement. Experiment 1 tested for the emergence of four equivalence classes and of stimulus-reinforcer and reinforcer-stimulus relations in each class. Four of the 6 subjects demonstrated the reinforcer-based relations in all four equivalence classes, rather than in only those classes with a class-specific reinforcer, as Sidman's theory predicts. One of the remaining 2 subjects showed the reinforcer-based relations in three of the four classes. Experiment 2 extended these findings to document the emergence of interclass matching relations based on the common reinforcer R3, in 5 of 6 subjects, such that a Class 3 sample occasioned the selection of a Class 4 sample when the Class 3 comparison was absent, and similarly, a Class 4 sample occasioned the selection of a Class 3 comparison when the Class 4 comparison was absent. These interclass relations emerged despite the simultaneous maintenance of Class 3 and 4 baseline conditional discriminations, so that the Class 3 and 4 stimuli and reinforcer simultaneously were, and were not, part of a single larger equivalence class. These data are irreconcilable with Sidman's theory, and question the utility of the application of the equivalence relation in describing derived stimulus relations.     

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.     

Common control by compound samples in conditional discriminations

We tested whether teaching control by single stimulus samples in conditional discriminations would result in common control of two-stimuli compound samples, and vice versa. In Experiment 1, 5 participants were first taught four single-sample conditional discriminations. The first conditional discrimination was as follows: given sample stimulus P1, select comparison stimulus A1 and not A2; given sample P2 select comparison A2 and not A1. The second conditional discrimination was as follows: given sample P1 select comparison B1 and not B2; given sample P2 select B2 and not B1. Different sample stimuli (Q1 and Q2) were used in the third and fourth conditional discriminations. Moreover, A1 and B1 were presented together as comparisons, such that, if Q1 was presented as the sample, A1 was correct and B1 was incorrect; and if Q2 was presented as the sample, B1 was correct and A1 was incorrect. A2 and B2 were also presented as comparisons. When Q1 was presented, A2 was correct and when Q2 was presented B2 was correct. After training with these four single stimulus sample discriminations, participants were tested with compound PQ samples presented with A1, A2, B1, and B2 as comparisons. If common control were established by the PQ stimuli, a participant would select A1 when P1Q1 was presented, A2 when P2Q1 was presented, B1 when P1Q2 was presented, and B2 when P2Q2 was presented. Such common control by PQ samples occurred in 4 of 5 participants. In Experiment 2, 4 participants were given reverse training. They were first taught to select the A1, A2, B1, and B2 stimuli in response to the appropriate PQ combinations and then probed on the single stimulus sample discriminations. All 4 participants were successful on this probe. Experiments 3 and 4 investigated the effects of teaching additional conditional discriminations with novel stimuli on subsequent transfer from the single-sample discriminations to performance on the compound-sample conditional discrimination.     

Stimulus equivalence and transitive associations: A methodological analysis

When a number of two-stimulus relations are established through training within a set of stimuli, other two-stimulus relations often emerge in the same set without direct training. These, termed "transitive stimulus relations," have been demonstrated with a variety of visual and auditory stimuli. The phenomenon has served as a behavioral model for explaining the emergence of rudimentary comprehension and reading skills, and the development of generative syntactic repertoires. This article considers the range of relations that can arise between a given number of stimuli in a class, the number of directly established two-stimulus relations necessary for the emergence of transitive relations, the forms that training sets of stimuli can take, and the number of transitive two-stimulus relations that can be induced without direct training. The procedures needed to establish and assess transitive stimulus control, the possible interactions between the training and testing procedures, and the constrainst these interactions place upon the analysis of transitive stimulus control are also examined. The present analysis indicates that in a transitivity test, choice among such stimuli may be controlled by (1) the relation between the sample and the positive comparison stimulus (transitive stimulus control), (2) the relation between the sample and the negative comparison stimulus (S- rule control), and (3) possible discriminative properties that may inadvertently be established in the positive and negative comparison stimuli (valence control). Methods are described for distinguishing these three forms of stimulus control.     

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

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

CONDITIONAL DISCRIMINATION VS. MATCHING TO SAMPLE: AN EXPANSION OF THE TESTING PARADIGM

A subject's performance under a conditional-discrimination procedure defines conditional relations between stimuli: “If A1, then B1; if A2, then B2.” The procedure may also generate matching to sample. If so, the stimuli will be related not only by conditionality, but by equivalence: A1 and B1 will become equivalent members of one stimulus class, A2 and B2 of another. One paradigm for testing whether a conditional-discrimination procedure has generated equivalence relations uses three sets of stimuli, A, B, and C, three stimuli per set. Subjects learn to select Set-B and Set-C comparisons conditionally upon Set-A samples. Having been explicitly taught six sample-comparison relations, A1B1, A1C1, A2B2, A2C2, A3B3, and A3C3, subjects prove immediately capable of matching the B- and C-stimuli; six new relations emerge (B1C1, B2C2, B3C3, C1B1, C2B2, C3B3). The 12 stimulus relations, six taught and six emergent, define the existence of three three-member stimulus classes, A1B1C1, A2B2C2, and A3B3C3. This paradigm was expanded by introducing three more stimuli (Set D), and teaching eight children not only the AB and AC relations but DC relations also—selecting Set-C comparisons conditionally upon Set-D samples. Six of the children proved immediately capable of matching the B- and D-stimuli to each other. By selecting appropriate Set-B comparisons conditionally upon Set-D samples, and Set-D comparisons conditionally upon Set-B samples, they demonstrated the existence of three four-member stimulus classes, A1B1C1D1, A2B2C2D2, and A3B3C3D3. These larger classes were confirmed by the subjects' success with the prerequisite lower-level conditional relations; they were also able to select Set-D comparisons conditionally upon samples from Sets A and C, and to do the BC and CB matching that defined the original three-member classes. Adding the three DC relations therefore generated 12 more, three each in BD, DB, AD, and CD. Enlarging each class by one member brought about a disproportionate increase in the number of emergent relations. Ancillary oral naming tests suggested that the subject's application of the same name to each stimulus was neither necessary nor sufficient to establish classes of equivalent stimuli.     

Quantitative and methodological aspects of stimulus equivalence

The number of different ways of linking stimuli in the training phase of a conditional discrimination procedure designed to teach equivalence relations has hitherto been underestimated. An algorithm from graph theory that produces the correct number of such different ways is given. The establishment of equivalence relations requires transitive stimulus control. A misconception in a previous analysis of the conditions necessary for demonstrating transitive stimulus control is indicated. This misconception concerns responding in an unreinforced test trial to a negative rather than a positive comparison stimulus. Such behavior cannot be attributed to discriminative control by degree of association with reinforcement if the negative comparison stimulus has been less associated with reinforcement than the positive comparison stimulus in an antecedent training phase.