Matching to complex stimuli under non-reinforced conditions: Errorless transfer from identity to arbitrary matching tasks

The present study investigated whether preschool children exposed to identity-matching tasks involving colour-form (CF) complex stimuli acquire arbitrary relations among those colours and forms. The children were first trained on an identity-matching task with green and yellow as samples and as comparisons (C-C task). Subsequent tests showed that the children matched: (1) samples green lambda and yellow pi, with comparisons green and yellow (CF-C), respectively; (2) samples black lambda and black pi, with comparisons green lambda and yellow pi (F-CF); (3) samples black lambda and black pi, with comparisons green and yellow (F-C); and (4) samples green and yellow, with comparisons black lambda and black pi (C-F). Other findings suggested that the F-C and C-F outcomes were likely only if the children were exposed to both CF-C and F-CF conditions. The results extend previous studies on emergent discriminations based on the elements of complex stimuli. The emergence of both form-colour and colour-form matching to sample permits an inference of symmetry, one of the properties of stimulus equivalence.     

Emergent conditional discrimination in children: Matching to compound stimuli

This study reports two experiments that first taught preschool children identity-matching to compound sample and compound comparison stimuli. A compound stimulus consisted of a colour and a form superimposed on one another. Test sessions assessed whether children related the form and colour elements of a particular compound stimulus. The test for this was matching to sample in which an arbitrary conditional discrimination was required. A majority of the children selected the correct colour comparison in the presence of each form sample. The children also showed the reverse sample-comparison relations: they matched form comparisons to the corresponding colour samples, respectively. In the context of these arbitrary relations, new colours were paired with the form elements of the samples (Experiment 1), and new form elements were paired with the colour elements of the comparisons (Experiment 2). Subsequent tests assessed whether the new stimulus elements had control over responding when presented as single samples or comparisons. Test results showed that most subjects were able to relate the new stimulus elements to the corresponding colour and form elements, respectively. The study demonstrated that matching to compound stimuli in training and testing conditionsMaygenerate conditional relations between the individual stimulus elements.     

Transfer of baseline reject control to transitivity trials and its effect on equivalence class formation

This study explored the role of baseline reject control on transitivity responding. In Experiment 1, participants learned to respond to a baseline of arbitrary AB and AC conditional relations, and then they were exposed to transitivity‐like BC and CB trials in which the correct comparison stimulus was replaced by a novel stimulus (D). Five of 10 participants selected stimulus D, but only 1 showed expansion of the baseline stimulus classes to include the D stimuli. In Experiment 2, the emergence of symmetry and transitivity from baseline relations was assessed before participants were exposed to the transitivity‐like trials. Six of 8 participants who showed emergence of equivalence relations selected the D stimuli on transitivity‐like trials and provided evidence that baseline classes expanded to include these stimuli. In Experiment 3, these 6 participants selected novel stimuli (E) in additional transitivity‐like trials, and all showed that the E stimuli had become members of the previously established classes, which now comprised 5 members. A route for the emergence of transitivity by way of the transfer of baseline between‐classes reject control is discussed.     

Reflexivity without identity matching training: A first demonstration

Until now, the equivalence property of reflexivity—matching physically identical stimuli to themselves after training on a set of arbitrary matching relations—has not been demonstrated in any animal, human or nonhuman. Previous reports of reflexivity have either implicitly or explicitly involved reinforced training on other identity matching relations. Here we demonstrate reflexivity without prior identity matching training. Pigeons received concurrent successive matching training on three arbitrary matching tasks: AB (hue–form), BC (form–hue), and AC (hue–hue with different hues in the A and C sets). Afterwards, pigeons were tested for BB (form–form) reflexivity. Consistent with the predictions of Urcuioli's ( 2008 ) theory, pigeons preferentially responded to B comparison stimuli that matched the preceding B sample stimuli in testing (i.e., BB reflexivity). A separate experiment showed that a slightly different set of arbitrary matching baseline relations yielded a theoretically predicted “anti‐reflexivity” (or emergent oddity) effect in two of five pigeons. Finally, training on just two arbitrary successive matching tasks (AB and BC) did not yield any differential BB responding in testing for five of eight pigeons, with two others showing reflexivity and one showing antireflexivity. These data complement previous findings of symmetry and transitivity (the two other properties of equivalence) in pigeons.     

Control of adolescents' arbitrary matching-to-sample by positive and negative stimulus relations.

In Experiment 1, four developmentally delayed adolescents were taught an A-B matching-to-sample task with nonidentical stimuli: given Sample A1, select Comparison B1; given A2, select B2. During nonreinforced test trials, appropriate matching occurred when B stimuli appeared as samples and A stimuli as comparisons, i.e., the sample and comparison functions were symmetrical (B-A matching). During A-B or B-A matching test trials in which familiar samples and correct comparisons were presented along with novel comparisons, the subjects selected the correct comparisons. In tests with familiar samples and both incorrect and novel comparisons, subjects selected the novel comparisons, demonstrating control by both positive ("matching") and negative ("nonmatching") stimulus relations in A-B and B-A arrays. In Experiment 2, 12 developmentally delayed subjects were taught a two-stage arbitrary-matching task (e.g., A-B, C-B matching). Test sessions showed sample-comparison symmetry (e.g., B-A, B-C matching) and derived sample-comparison relations (e.g., A-C, C-A matching) for 11 subjects. These subjects also demonstrated control by positive and negative stimulus relations in the derived relations.     

Accessing similarity and dimensional relations: effects of integrality and separability on the discovery of complex concepts

A series of studies investigated how stimulus integrality and separability impact the cognitive accessibility of similarity and dimensional relations. A good deal of previous work has established that stimulus integrality and separability differentially determine perception; here, the question is whether they also have differential effects on conception. Are the principles that govern perception also principles that can be readily discovered in concept learning tasks? Is a similarity-based rule especially easy to abstract from integral stimuli and a dimensionally-based rule especially easy to abstract from separable stimuli? In Experiments 1 and 2, we measured the relative ease with which the two types of rules (similarity and dimensional) are discovered by adults with the two types of stimuli (integral and separable). In experiment 1, the two rules were made redundant and we asked which rule the subjects learned. In Experiment 2, one rule was made relevant and the other irrelevant, and we compared relative speeds of learning. The results from the studies led us to conclude (a) that dimensionally based rules are more accessible from separable than from integral stimuli; (b) that similarity-based rules are more accessible from integral than from separable stimul; and (c) that, in general, subjects have a bias to access dimensional relations in this type of task. Experiment 3 pursued an additional suggestion from Experiments 1 and 2 that the dimensional relations within integral stimuli are sometimes accessible, more so when larger interstimulus differences are encountered. In confirmation, Experiment 3 demonstrated that adult subjects are more successful in applying a dimensional rule to pairs of integral stimuli that differ by a small amount if they also have exposure to pairs of integral stimuli that differ by a large amount. In a later discussion, it was argued that such a finding is consistent with the notion that the "dimensions" of integral stimuli are merely arbitrary directions in the integral stimulus space, and some relevant pilot data to that effect were presented. Finally, Experiment 4 took up a developmental issue. Young children have sometimes produced perceptual responses governed by similarity relations when presented with stimuli that are separable for adults. Will they more readily access similarity-based or dimensionally-based relations from such stimuli in the concept learning tasks here? The results showed that both kindergarteners and fifth graders more readily access the dimensional relations. A final discussion integrated the findings from the several experiments, taking up the following issues: (a) the relation between the perception and the conception of stimulus relations and (b) the nonprimacy of the dimensional axes in the integral stimulus space.     

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.     

A functional-analytic model of analogy: a relational frame analysis

The aim of this study was to explore a behavior-analytic model of analogical reasoning, defined as the discrimination of formal similarity via equivalence-equivalence responding. In Experiment 1, adult humans were trained and tested for the formation of four three-member equivalence relations: A1-B1-C1, A2-B2-C2, A3-B3-C3, and A4-B4-C4. The B and C stimuli were three-letter nonsense syllables, and the A stimulus was a colored shape. Subjects were then successfully tested for equivalence-equivalence responding (e.g., matching B1/C1 to B2/C2 rather than B3/C4). These tasks were designed such that equivalence-equivalence responding might allow subjects to discriminate a physical similarity between the relations involved. Some participants (color subjects) received only equivalence-equivalence tasks in which they might discriminate a color relation, whereas others (shape subjects) were given tasks in which they might discriminate a shape relation. A control group received both types of task. In a subsequent test for the discrimination of formal similarity, color subjects matched according to color, shape subjects matched according to shape, and the control group showed no consistent matching pattern. In Experiment 2, adult humans showed a transformation of the functions of a block-sorting task via this basic model of analogy. Empirical and conceptual issues related to these results 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.     

Establishing equivalence–equivalence analogical relations via tact and listener training

We investigated the role of verbal behavior on the emergence of analogy-type responding as measured via equivalence–equivalence relations. In Experiment 1, 8 college students learned to label arbitrary stimuli as, “vek,” “zog,” and “paf”, and in Experiment 2, 8 additional participants learned to select these stimuli when hearing their names in an auditory–visual matching-to-sample (MTS) task. Experimenters tested for the emergence of relational tacts (i.e., “same” and “different”) and equivalence–equivalence relations (analogy tests) via visual–visual MTS. Half of the participants were exposed to a think-aloud procedure. Even though they all passed analogy tests while tacting stimuli relationally, only participants exposed to tact training (Experiment 1) did so without the need for remediation. The results of these experiments confirm that individual discriminative and relational control of stimuli established through verbal behavior training is sufficient to produce equivalence–equivalence analogical responding, advancing the analysis of complex cognitive (problem-solving) phenomena.     

Training intraverbal bidirectional naming to establish generalized equivalence class performances

The purpose of this study was to evaluate the effects of tact and intraverbal training on the establishment of generalized equivalence classes. Seventeen college students were exposed to tact training, listener testing, and intraverbal training (A'B’ and B'C’) in two experiments. Visual–visual matching‐to‐sample and intraverbal tests measured performances consistent with the formation of equivalence classes. Generalization was assessed with four novel sets of stimuli. In the second experiment, matching‐to‐sample tests for baseline relations (AB, BC) were eliminated to control for the possibility that equivalence classes were developed through exposure to these visual stimulus–stimulus relations. Thirteen of 17 participants passed all matching‐to‐sample and intraverbal posttests. Results suggest that when trained and emergent intraverbal relations were not maintained or were faulty, participants did not respond correctly during matching‐to‐sample posttests.     

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.     

Acquisition of arbitrary conditional discriminations by young normally developing children

Three experiments investigated conditions designed to facilitate acquisition of arbitrary conditional discriminations in 3- to 6-year-old normally developing children. In Experiment 1, 6 subjects failed to master the arbitrary match-to-sample task under conditions of differential reinforcement alone, but 7 subjects did so when instructions or instructions and sample naming were added. In Experiment 2, sample naming introduced in a blocked-trial arrangement resulted in acquisition, but only when the sample name was a nonsense syllable provided by the experimenter (5 of 7 subjects) and not when the sample name was generated by the subject (0 of 5 subjects). Experiment 3 demonstrated the effectiveness of a training sequence involving thematically related stimuli as an intermediate step facilitating the transition from identity to novel arbitrary relations. The difficulties in mastering arbitrary conditional discriminations shown here imply that further analyses with young children will be particularly important in efforts to investigate the development of theoretically important stimulus relations.     

Generalization of equivalence relations from photos to objects by preschool children

Generalized equivalence classes are stimulus classes that consist of equivalent stimuli and other physically similar class‐member stimuli. The present study evaluated whether preschool children would form equivalence classes among photos of abstract objects (2D) and show equivalence generalization to the corresponding objects (3D), printed photos (2D stimuli), and to black‐and‐white drawn pictures (2D stimuli). Six typically developing children were taught arbitrary relations to establish three 3‐member equivalence classes with 2D stimuli presented on a computer screen. AB‐AC baseline relations (for half of the participants) and AB‐BC relations (for the other half) were taught using a multiple‐probe design to assess taught and tested relations. After class formation, three types of generalization probes were conducted: generalization to 3D stimuli, generalization between 2D (printed photos) and 3D stimuli, and generalization to drawn pictures (2D). All of the participants formed the equivalence classes. Two participants met the criterion for all three generalization probe types. Two participants presented mixed results across tests, and two participants did not exhibit equivalence generalization. The results demonstrated equivalence generalization from 2D to 3D stimuli in preschool children, although the variability across participants suggests that such generalization cannot be assumed a priori.     

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.     

ASSOCIATIVE SYMMETRY,ANTISYMMETRY, AND A THEORY OF PIGEONS' EQUIVALENCE‐CLASS FORMATION

Five experiments assessed associative symmetry in pigeons. In Experiments 1A, 1B and 2, pigeons learned two‐alternative symbolic matching with identical sample‐ and comparison‐response requirements and with matching stimuli appearing in all possible locations. Despite controlling for the nature of the functional stimuli and insuring all requisite discriminations, there was little or no evidence for symmetry. By contrast, Experiment 3 demonstrated symmetry in successive (go/no‐go) matching, replicating the findings of Frank and Wasserman (2005). In view of these results, I propose that in successive matching, (1) the functional stimuli are stimulus‐temporal location compounds, (2) continual nonreinforcement of some sample‐comparison combinations juxtaposed with reinforcement of other combinations throughout training facilitates stimulus class formation, (3) classes consist of the elements of the reinforced combinations, and (4) common elements produce class merger. The theory predicts that particular sets of training relations should yield “antisymmetry”: Pigeons should respond more to a reversal of the nonreinforced symbolic baseline relations than to a reversal of the reinforced relations. Experiment 4 confirmed this counterintuitive prediction. These results and other theoretical implications support the idea that equivalence relations are a natural consequence of reinforcement contingencies.     

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.     

Emergent identity matching after successive matching training, I: reflexivity or generalized identity

This research investigated the source of an ostensible reflexivity effect in pigeons reported by Sweeney and Urcuioli (2010). In Experiment 1, pigeons learned two symmetrically reinforced symbolic successive matching tasks (hue-form and form-hue) using red-green and triangle-horizontal line stimuli. They differed in their third concurrently trained baseline task: form-form matching with stimuli appearing in the symbolic tasks (triangle and horizontal) for one group versus hue-hue matching with stimuli not appearing in the symbolic tasks (blue and white) for the other. During subsequent nonreinforced probe tests, all pigeons in the former group and most pigeons in the latter group responded more to the comparisons on matching than on nonmatching red-green probes. In Experiment 2, the latter group was tested on nonreinforced form-form probes. One of the 4 pigeons responded significantly more to the comparisons on matching than on nonmatching triangle-horizontal probes. These data are consistent with generalized identity and at least one other interpretation of the reflexivity results and question the functional stimulus assumption of Urcuioli's (2008) stimulus-class theory.     

An analysis of emergent simple discrimination in children

In Experiment 1 eight five-year-old children received an arbitrary matching-to-sample task with sample stimuli A1 and A2 and comparison stimuli B1 and B2. This task was mixed with a simple, two-choice discrimination task with stimuli A1 and A2. In subsequent tests with B1 and B2 presented alone, the number of responses to B1 was greater when it had been paired with the correct stimulus of the simple discrimination task than when it had been paired with the incorrect stimulus. In Experiment 2 incorrect comparisons were omitted during the matching-to-sample task. Eight children were taught to point to either A1 or A2 first, and to either B1 or B2 second. Eight other children were taught to point to either B1 or B2 first, and to either A1 or A2 second. The effect of Experiment 1 was replicated with the first but not with the second group. The results of both experiments suggest that the functions of S+ and S- in a simple discrimination task can transfer to test stimuli if the training stimuli precede the test stimuli during paired presentations.     

ELECTROPHYSIOLOGICAL CORRELATES OF STIMULUS EQUIVALENCE PROCESSES

Research reported here concerns neural processes relating to stimulus equivalence class formation. In Experiment 1, two types of word pairs were presented successively to normally capable adults. In one type, the words had related usage in English (e.g., uncle, aunt). In the other, the two words were not typically related in their usage (e.g., wrist, corn). For pairs of both types, event‐related cortical potentials were recorded during and immediately after the presentation of the second word. The obtained waveforms differentiated these two types of pairs. For the unrelated pairs, the waveforms were significantly more negative about 400 ms after the second word was presented, thus replicating the “N400” phenomenon of the cognitive neuroscience literature. In addition, there was a strong positive‐tending wave form difference post‐stimulus presentation (peaked at about 500 ms) that also differentiated the unrelated from related stimulus pairs. In Experiment 2, the procedures were extended to study arbitrary stimulus—stimulus relations established via matching‐to‐sample training. Participants were experimentally näive adults. Sample stimuli (Set A) were trigrams, and comparison stimuli (Sets B, C, D, E, and F) were nonrepresentative forms. Behavioral tests evaluated potentially emergent equivalence relations (i.e., BD, DF, CE, etc.). All participants exhibited classes consistent with the arbitrary matching training. They were also exposed also to an event‐related potential procedure like that used in Experiment 1. Some received the ERP procedure before equivalence tests and some after. Only those participants who received ERP procedures after equivalence tests exhibited robust N400 differentiation initially. The positivity observed in Experiment 1 was absent for all participants. These results support speculations that equivalence tests may provide contextual support for the formation of equivalence classes including those that emerge gradually during testing.