Extending sequence-class membership with matching to sample

Three normal adults were first trained to point sequentially to each member of several pairs of visual stimuli. This baseline training established one class of stimuli to which subjects responded first, and another class of stimuli to which they responded second. Then, in a matching-to-sample procedure, baseline-sequence stimuli served as samples and new visual stimuli served as comparisons. Subjects were trained to choose one group of new comparisons when the sample was a "first" stimulus from the sequence baseline, and to choose the other new comparison stimuli when the sample was a "second" from the sequence baseline. When the new stimuli were then presented as pairs in the posttest, two subjects pointed to them in sequences predictable on the basis of the stimulus-class membership established during matching to sample. The failure of one subject to demonstrate sequential transfer was shown to be a consequence of the failure of the matching-to-sample procedure to establish stimulus classes. The production of sequences that were not directly trained suggested an empirical approach to the analysis of simple grammatical behavior.     

Effectiveness and persistence of precurrent mediating behavior in delayed matching to sample and oddity matching with children.

Two kinds of mediating behavior were compared with respect to their effectiveness in variable-delay matching-to-sample and oddity-matching tasks. Each of four 5-year-old children was trained to emit either differential or common mediating responses. The differential mediating response consisted of pressing a specific computer key corresponding to either of two possible sample stimuli (a red or a green square). The common mediating response consisted of pressing one of the two response keys regardless of the sample. The differential-response subjects did not show the typical, delay-related decrease in matching-to-sample performance that characterized the behavior of common-response subjects. An oddity-matching task was then introduced, and subjects were instructed to use the mediating keys however they preferred, including not at all. Differential-response subjects continued to respond on the originally trained mediating keys in response to sample presentation and later reversed their choice responding, thus accommodating the oddity-matching requirements. Common-response subjects continued to emit the previously trained mediating response and experienced limited success in oddity matching. Results were interpreted in terms of stimulus control, instructional control, and experimental history.     

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

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

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.     

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.     

The development of derived stimulus relations through training in arbitrary-matching sequences

Five-year-old children were taught three-stage sequences of arbitrary matching: A-C, B-C, A-D; A-C, B-D, B-C; or A-C, A-D, B-C. Each stage refers to a sample-comparison relation between stimuli. Unreinforced test probes revealed untrained arbitrary matches (B-D, A-D, and B-D, respectively), derivable by substitution of stimuli with a common sample or comparison function. Additional probes revealed further untrained sample-comparison relations derivable by substitution and identity, including the commuted relations D-B, D-A, and D-B, respectively. These processes may have relevance to conceptual and verbal behavior.     

SPELLING AND EMERGENT PICTURE-PRINTED WORD RELATIONS ESTABLISHED WITH DELAYED IDENTITY MATCHING TO COMPLEX SAMPLES

Students with academic deficits learned delayed matching-to-sample tasks that used complex sample stimuli, each consisting of a picture and a printed word. A touch to the sample complex removed it from the computer display and produced either picture comparisons or a choice pool of letters. If the comparisons were pictures, selecting the picture identical to the preceding sample was reinforced. If the letters appeared, letter-by-letter construction of the preceding printed word sample was reinforced. The procedure engendered new constructed-response spelling performances and arbitrary relations among pictures and printed words in matching to sample. The emergence of relations among different sets of printed words (paired with the same pictures) suggested classes of equivalent stimuli. Outcome tests involving spoken words as sample stimuli suggested expansion of subjects' spelling repertoires and stimulus 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.     

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.     

THE FORMATION OF VISUAL STIMULUS EQUIVALENCES IN CHILDREN

Four normal children were presented a series of matching-to-sample tasks, using five sets of visual stimuli designated A, B, C, D, and E. Stimulus equivalences were established by matching stimuli from one set to those from another set. Each set consisted of three stimuli, so matching set A to set D meant that each stimulus in set A served as a sample with all three stimuli in set D as comparisons. Subjects were first taught AD and DC matching and were then able to perform AC/CA matching without additional training. After ED was taught directly, CE/EC and AE/EA performances emerged. Following CB training, three new equivalences were demonstrated: AB/BA, EB/BE, and DB/BD. Oral naming of each stimulus showed that subjects had not assigned a common label to stimuli in the same class, indicating that naming is not necessary for the formation of stimulus equivalences. The absence of response mediation suggests that matching to sample can form direct stimulus-stimulus associations. The data also provide support for the notion that generative performances are outcomes of existing stimulus-control relationships.     

Equivalence relations and the reinforcement contingency

Where do equivalence relations come from? One possible answer is that they arise directly from the reinforcement contingency. That is to say, a reinforcement contingency produces two types of outcome: (a) 2‐, 3‐, 4‐, 5‐, or n‐term units of analysis that are known, respectively, as operant reinforcement, simple discrimination, conditional discrimination, second‐order conditional discrimination, and so on; and (b) equivalence relations that consist of ordered pairs of all positive elements that participate in the contingency. This conception of the origin of equivalence relations leads to a number of new and verifiable ways of conceptualizing equivalence relations and, more generally, the stimulus control of operant behavior. The theory is also capable of experimental disproof.