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.     

Simple discrimination training with differential responses to establish functional and equivalence classes with preschool children

The present study assessed whether simple discrimination training with differential responses would produce functional and equivalence classes with preschool children. In Experiment 1, we exposed 10 children to simple successive discrimination training in which they had to press different buttons (selection‐based responses). Response 1 (R1) was reinforced only in the presence of A1, B1, or C1, and Response 2 (R2) was reinforced only in the presence of A2, B2, or C2. We assessed the formation of functional classes by training new selection responses in the presence of one member of each class (A1‐R3, A2‐R4) and testing to see if these responses would occur in the presence of other members. Eight children responded consistently with functional class formation. Four of these eight children also responded consistently with the formation of equivalence classes. Experiment 2 investigated whether differential motor responses (i.e., gestures) would improve equivalence class yields. Three of six children showed both functional and equivalence class formation. In general, the results indicate that the simple discrimination procedure with differential responses yielded functional and equivalence class formation.     

Stimulus equivalence instruction of fraction-decimal relations

Stimulus control technology was applied to the instruction of fraction ratio (e.g., (1/5)) and decimal (e.g., 0.20) relations, with 7 students who demonstrated difficulty in fraction and decimal tasks. The students were trained to match pictorial representations of fractions (B comparison stimuli) to printed counterpart fraction ratios (A sample stimuli), and to match printed decimals (C comparison stimuli) to pictorial representations of counterpart quantities (B sample stimuli). Posttest performance by all participants indicated the emergence of equivalence relations between fractions represented as ratios, decimals, and pictures. Limited generalization of fraction-decimal relations was observed.     

Development of conditional and equivalence relations without differential consequences

Two experiments were conducted to establish conditional stimulus relations without differential consequences and to test for the emergence of other relations. In Experiment 1, 3 adults responded to match-to-sample displays in which sample-comparison pairs were constant while the second comparison presented with each pair changed periodically across trials. No differential consequences followed any comparison selections. All subjects learned conditional relations between constant samples and comparisons, but results of tests for transitivity in those relations were equivocal. In Experiment 2, 4 children were given unreinforced training and testing similar to that provided to the adults in Experiment 1, with procedural refinements. One child learned conditional relations and demonstrated emergent relations that confirmed the development of two four-member equivalence classes. Another child learned the conditional relations but did not demonstrate any emergent relations reliably. A 3rd child, after reinforced training on two conditional relations, learned four new conditional relations without differential consequences and demonstrated symmetry but not equivalence in the trained relations. The 4th child did not learn the conditional relations. These findings emphasize the importance of careful construction of tests for stimulus equivalence and suggest a need for critical analyses of the apparent emergence of untrained stimulus relations on unreinforced tests that has been observed in several stimulus equivalence studies.     

Equivalence class establishment, expansion, and modification in preschool children

Preschool children were taught four two-choice match-to-sample conditional discriminations with 10 arbitrary visual stimuli. For 6 participants, 2 of the 10 stimuli served as the sample, or conditional, stimuli in all discriminations. For 5 additional participants, the same pair of stimuli served as the discriminative, or comparison, stimuli in all discriminations. Equivalence classes were established with more participants in the latter group, replicating prior research with participants with retardation. Four participants, in whom equivalence classes were established and who were available for further participation, were exposed to new conditional discriminations without trial-by-trial feedback and involving some novel and some familiar stimuli. Consistent conditional responding was observed, and tests for inclusion of the novel stimuli in the original classes showed class expansion. Training to reverse the unreinforced conditional performances produced a reversal of class membership in 3 of 4 participants, an outcome not consistent with other studies. The results are discussed with respect to the interaction of class structure and size.     

Electrophysiological analysis of stimulus variables in equivalence relations

Recently, electrophysiological measures have been used to evaluate the functional overlap between semantic relations and laboratory-defined equivalence relations with abstract stimuli. Several studies using semantic judgment procedures have shown that accompanying EEG-measured neural activity for stimulus pairs from equivalence classes is very similar to that of word pairs from participants' native language. However, those studies often included pronounceable elements (e.g., written nonsense syllables) as at least one member of the experimentally defined classes. The present study conducted EEG studies that contrasted classes with and without such elements. Two groups of undergraduate students completed a matching-to-sample procedure to establish 3 4-member equivalence classes. For Group 1, samples and comparisons were pronounceable pseudowords and abstract figures. For Group 2, the matching-to-sample stimuli were abstract figures only. EEG data recorded during the semantic judgment tasks showed waveform patterns compatible with prior studies of semantic relations in Group 1 but not in Group 2.     

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

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

Effects of mastery criterion on the emergence of derived equivalence relations

In this study, we manipulated mastery criterion form (rolling or block) and stringency (across 6 or 12 trials) and measured the emergence of derived relations. College students learned neuroanatomy equivalence classes and experienced one of two rolling mastery criteria (6 or 12 consecutive correct responses) or a block mastery criterion (12 trials in a block) during training. The study found that block and rolling mastery criteria produced similar outcomes. Effectiveness was hampered when the criterion was less stringent.     

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'.     

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.     

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.     

The role of naming in stimulus categorization by preschool children

The purpose of the current study was to assess whether children would categorize pictures when taught the relevant listener and speaker behaviors separately. A category-sort test was used to assess emergent conditional relations. Category-sort trials consisted of looking at (Test 1) or tacting/labeling (Test 2) a sample stimulus and selecting the appropriate comparison stimuli. In Experiment 1, 4 children (3-5 years) were taught to tact pictures of six U.S. state maps as either north or south. An assessment was conducted to determine whether they would (1) correctly categorize or sort when presented with a visual sample and (2) select the correct stimuli when hearing their category names (listener behavior). Two of the children categorized the pictures during Posttest 1 after the initial (pairwise) tact training. The other 2 categorized after receiving additional tact training with all pictures presented together. However, one of them categorized only during Posttest 2. In Experiment 2, 4 children (3-5 years) were taught to select pictures when hearing their category names. An assessment was conducted to determine whether they would (1) correctly categorize or sort and (2) tact the stimuli (speaker behavior). One child categorized the pictures during Posttest 1, and two during Posttest 2. The other child required additional training with all pictures grouped together. When participants failed to categorize, they also failed to tact the pictures accurately. Taken together, results from Experiments 1 and 2 show that both speaker and listener behavior play an important role in stimulus categorization.     

Formation of new stimulus equivalence classes by exclusion

This study presents three experiments that aimed to show the formation of stimulus equivalence relations among stimuli that had been previously related only by exclusion. In Experiment 1, participants were trained on baseline conditional discriminations to establish two 3‐member equivalence classes. Then, they were exposed to exclusion trials, without feedback, in which undefined stimuli had to be matched by rejecting the defined baseline stimuli. Finally, participants responded to test trials evaluating the emergence of symmetry and transitivity among the undefined stimuli from the exclusion trials. For half of the participants, the stimuli related by exclusion were introduced as S‐ stimuli in the baseline trials, whereas for the other half they were not. Further, half of the participants were assessed for emergent relations with stimuli from all the classes, whereas the other half was assessed for emergent relations with only the stimuli related by exclusion. In Experiment 2, the S‐ comparisons in the emergent relations test trials with stimuli only related by exclusion were stimuli from a null class. In Experiment 3, the number of exclusion trials was doubled. Across experiments, most participants showed emergence of equivalence relations among the stimuli related by exclusion. Some conditions of stimulus control associated with exclusion learning and the emergence of equivalence relations are discussed.     

Using conditional discrimination training to produce emergent relations between coins and their values in children with autism

The current study evaluated the effects of conditional discrimination (listener) training with coins on the emergence of novel stimulus relations, textual behavior, tacts, and intraverbals. Two preschoolers with autism were taught 3 relations among coins, their names, and values. After initial training, 4 relations emerged for the first participant and 7 for the second participant, suggesting that this technology can be incorporated into educational curricula for teaching prerequisite money skills to children with autism.     

The role of common motor responses in stimulus categorization by preschool children

The purpose of this study was to assess the role of common motor responses as the "speaker" behavior on stimulus class formation, and the emergence of functional classes. Experiment 1 examined whether training one motor response to a set of three stimuli and a second motor response to another set of three stimuli would result in correct category-sort responses for 5 typically developing preschool children. Three of the children passed the categorization tests. Experiment 2 examined whether the classes formed in Experiment 1 were functional classes, and whether participants who did not pass categorization tests in Experiment 1 would do so following common vocal tact training. The 2 participants who failed categorization tests in Experiment 1 passed these tests in Experiment 2, although none of the participants passed the tests for functional classes. The results of the current study did not unequivocally support the naming hypothesis. Future research should therefore evaluate other possible sources of control that aid in stimulus categorization.     

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

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

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.     

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

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

The transfer of specific and general consequential functions through simple and conditional equivalence relations

The purpose of this study was to examine the transfer of consequential (reinforcement and punishment) functions through equivalence relations. In Experiment 1, 9 subjects acquired three three-member equivalence classes through matching-to-sample training using arbitrary visual forms. Comparison stimuli were then given conditioned reinforcement or punishment functions by pairing them with verbal feedback during a sorting task. For 8 of the 9 subjects, trained consequential functions transferred through their respective equivalence classes without additional training. In Experiment 2, transfer of function was initially tested before equivalence testing per se. Three of 4 subjects showed the transfer without a formal equivalence test. In Experiment 3, 3 subjects were given training that gave rise to six new three-member conditional equivalence classes. For 2 of the subjects, the same stimulus could have either a reinforcement or punishment function on the basis of contextual cues that defined its class membership. Experiment 4 assessed whether equivalence training had established general or specific consequential functions primarily by adding novel stimuli in the transfer test. Subjects treated even novel feedback stimuli in the transfer test as consequences, but the direction of consequential effects depended upon the transfer of specific consequential functions through equivalence relations.