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Assessing Derived Conditional Relations Under Reinforcement Conditions.

An individual taught to relate physically dissimilar stimuli can establish new conditional relations among them without any additional training (e.g., Lazar et al. 1984; Sidman 1971; Sidman and Cresson 1973; Spradlin et al. 1973). For instance, an individual trained to select comparison stimulus B conditionally upon sample stimulus A (A-B matching) and comparison C conditionally upon sample B (B-C matching) usually perform untaught conditional relations indicative of reflexivity (A-A, B-B, and C-C), symmetry (B-A and C-B), and transitivity (A--C). The emergence of those derived relations demonstrates that stimuli A, B and C formed an equivalence class (Sidman et al. 1982; Sidman and Tailby 1982).

Derived relations are usually assessed in the absence of programmed reinforcement to ensure that testing performances is not explicitly trained. However, the lack of reinforcement during tests may be a methodological shortcoming that interferes with equivalence-class formation in some populations (Carr et al. 2000; Devany et al. 1986; Lazar 1977; Lazar et al. 1984; Maguire et al. 1994; Sidman et al. 1985, 1986; Spradlin et al. 1973). Compared to the initial baseline training, the unreinforced condition employed in testing may change considerably the sources of stimulus control (Dube and McIlvane 1996; Galvao et al. 1992; Kuno et al. 1994; Schusterman and Kastak 1993; Sidman 1994; Sidman et al. 1982), and allow the subject to discriminate the absence of reinforcement during test trials (Brino et al. 2009; Galvao et al. 2005). All these effects may interfere with the demonstration of emergent relations, especially because unreinforced test trials reproduce the same consequences the subjects experience following incorrect responses during baseline training.

Methodological strategies to assess derived performances under differential reinforcement conditions have been developed, particularly in the scope of non-human animal investigations (e.g., D'Amato et al. 1985; Hogan and Zentall 1977; Velasco et al. 2010). One strategy involves reinforcing during testing both responses consistent with the equivalence-class formation and responses inconsistent with the equivalence-class formation. For example, following the training of Al-B1 and A2-B2 baseline relations, pigeons are divided into two test groups (consistent and inconsistent). For the consistent group, reinforced relations were the symmetrical versions of the baseline relations (B1-Al and B2-A2). For the inconsistent group, reinforced relations were the opposite of the symmetrical version of the baseline relations (B1-A2 and B2-A1). Matching accuracies significantly higher for the consistent group than the inconsistent group would indicate that symmetrical responding was not a result of rapid learning due to the reinforcement employed in testing (cf. Hogan and Zentall 1977; Lionello-DeNolf and Urcuioli 2002; Urcuioli 2008).

One consequence of such a strategy, however, is that it usually requires a between-subjects design. The reinforcement of consistent (e.g., Bl--A 1 and B2--A2) and inconsistent (e.g., B1-A2 and B2-A1) relations, concurrently, for the same individual may simply merge the expected Class 1 and Class 2 into a single large class (e.g., A 1 A2B1B2). This merge could result in chance-level performances on both consistent and inconsistent test trials (but see D'Amato et al. 1985).

Velasco et al. (2010) presented an alternative strategy to assess emergent relations using a within-subject test with differential reinforcement for matching responses. With such a strategy, the reinforcement of inconsistent relations was replaced with the reinforcement of brand new relations involving novel combinations of familiar stimuli. That is, subject's performances on consistent symmetrical matching were compared to performances on novel matching that were neither consistent nor inconsistent with equivalence-class formation. One advantage of using novel relations rather than inconsistent relations to control for the effects of reinforcement during testing is to eliminate the risk of merging classes.

Thus, after pigeons had learned two independent arbitrary-matching tasks (A-B and C-D), they were given reinforced symmetry trials for half of the baseline relations (B1-Al and D1-C1). To show that accurate matching on symmetry test trials was not a result of rapid learning due to reinforcement, two novel, control relations were concurrently trained using the other baseline stimuli (D2-A2 and B2--C2). Pigeons matched at chance on both types of trials, thus, indicating no evidence for symmetry. All testing relations were then trained and a second test was given in which the symmetrical relations were B2-A2 and D2-C2 and the novel, control relations were D1-A1 and B 1-Cl. In this test, one pigeon showed clear evidence of symmetry, two pigeons showed modest evidence, and one showed no evidence.

The results of Velasco et al. (2010) are not as robust as those normally obtained with verbally-ble humans (e.g., Lazar et al. 1984; Sidman and Cresson 1973; Sidman and Tailby 1982; Spradlin et al. 1973), but it is significant given the absence of symmetry reported in most studies with nonhuman subjects (e.g., D'Amato et al. 1985; Dugdale and Lowe 2000; Gray 1966; Hogan and Zentall 1977; Holmes 1979; Lionello-DeNolf and Urcuioli 2002; Lipkens et al. 1988; Richards 1988; Rodewald 1974; Sidman et al. 1982). Such a finding also suggests the potential applicability of our testing strategy in studies with symbolic disabled individuals. Before that, however, this strategy should be tested first with verbally able individuals in order to confirm its effectiveness in demonstrating equivalence-class formation.

The present study had two related aims: (1) replicate Velasco et al.'s (2010) strategy with a population that is known to respond in accordance with equivalence-class formation and (2) check whether or not the results of the present procedure aligns with the results usually obtained with the traditional unreinforced tests. If the answer is to be affirmative, such a strategy could be seen as a reliable method to be used in both basic and applied researches with populations for which the suspension of reinforcement clearly produces impediments.

Experiment 1

Experiment 1 was conducted with four college students to test the procedure effectiveness in demonstrating symmetry. The training and testing was conducted in two phases. Both training and testing phases were conducted under reinforcement conditions. Students were first taught eight conditional relations (Al-Bl; A2-B2; A3-B3, A4-B4 and C1-D1; C2-D2; C3-D3; C4-D4), concurrently (see Fig. 1). Then, during the test, four symmetrical relations (Bl-A1; B2-A2; D1-C1; D2-C2) and four novel relations (B3-C3; B4-C4; D3-A3; D4-A4) were reinforced concurrently (see Fig. 1). If baseline conditional discriminations were symmetrical, then accuracies in testing should be higher on the symmetrical trials than the novel trials.

[FIGURE 1 OMITTED]

Method

Participants

Three 20-year-old women (DMP, NAS and ACV) and one 21-year-old man (PRR) served as volunteers. They were drawn from journalism and biology undergraduate courses. An informed consent term has been appropriately obtained from all participants that also reported no familiarity neither with the experimental analysis of behavior nor with similar types of experiment.

Setting and Apparatus

The research was conducted in a room containing four experimental stations separated from each other by an opaque divider. More than one subject participated simultaneously and, therefore, they were instructed not to talk while in the room. Each experiment station was equipped with a microcomputer, an LCD video monitor, a mouse and an earphone. Software specially developed for this study controlled experimental contingencies and recorded data. Sixteen colored visual stimuli (developed by Dube and Hiris 1999) were randomly assigned to four four-stimulus sets (Fig. 2). The assignment of stimuli to the sets was counterbalanced across participants, such that stimuli assigned to Sets 1 and 2 for half of participants were respectively assigned to Sets 3 and 4 for the other half of participants, and vice-versa.

[FIGURE 2 OMITTED]

Procedure

All participants were exposed to two experimental phases, that is, baseline training and symmetry test. In both phases, participants were exposed to a 0-s delay arbitrary matching-to-sample task. Each trial began with the onset of the sample on the center of the screen. A response to the sample, accomplished by moving the cursor over the stimulus and pressing the left mouse button, turned it off and simultaneously produced four different comparison stimuli, one in each corner of the screen. A response to the comparison arbitrarily set as the correct one turned all stimuli off, produced a "beep" in the earphones, and increased by the value of one a counter located at the center-top portion of the screen. A response to any of the other three stimuli, that is, an incorrect response, turned all stimuli off and ended the trial. Between every two trials, there was a 0.5-s intertrial interval (ITI), during which the screen remained blank. There were no scheduled consequences for responses during the ITI.

Each session for either training or test consisted of 192 trials presented in a semi-random order within blocks of 48 trials according to the following criteria: 1) each comparison location was scheduled to receive 12 correct comparisons; 2) the presentation of correct comparisons in the same location did not repeat more than twice consecutively; and 3) a given conditional relation did not repeat more than twice consecutively.

At the beginning of the experiment, each participant was given the following written instruction in Portuguese soon after they were placed in front of the computer running the experimental task: "This study is not about intelligence testing, and does not aim to evaluate any aspect of your intellectual abilities. At the end, you will receive a full explanation on its purpose. For now, please, do not talk while in the experimental room. An image will appear in the center of the computer monitor. Your task is to click on this image using the mouse. Then, other four different images will appear, one in each corner of the screen. Your task is to select one of those images using the mouse. During the task, sometimes you will receive points, sometimes not. Your goal in this task is to earn the maximum number of points you can. Now, please, repeat the instructions you just read to me." Once the subject could repeat the instruction, the experiment started.

Baseline Training Eight conditional relations were concurrently trained in two independent matching tasks. On half of the trials, participants were trained to match B comparisons to A samples (A--B matching). On the remaining trials, they were trained to match D comparisons to C samples (C--D matching). Each reinforced sample-comparison matching is shown in Table 1 ("Training" column). Each 48-trial block comprised six trials for each conditional relation. Training sessions lasted until participants reached 100 % accuracy in two consecutive blocks within the same session. However, training session lasted until the completion of all four programmed trial blocks, even when the participant met the accuracy criterion in either the second or the third block.

Symmetry Test Participants were tested for symmety with samples from the baseline being used as comparisons, and vice-versa. Test performances were differentially reinforced. On half of the trials, reinforced sample-comparison relations were the symmetrical versions of half of the baseline relations (see Table 1, "Symmetrical" column). That is, responses to Al and A2 comparisons were reinforced after B1 and B2 samples, respectively, (B--A matching); and responses to C 1 and C2 comparisons were reinforced after D1 and D2 samples, respectively, (D--C matching). To control for the use of reinforcement on symmetry test trials, reinforcement was also provided for correct choices on four novel relations (see Table 1, "Novel" column). These relations were formed from the remaining baseline relations. That is, responses to C3 and C4 comparisons were reinforced after B3 and B4 samples, respectively, (B--C matching); and responses to A3 and A4 comparisons were reinforced after D3 and D4 samples, respectively, (D--A matching). Note that in the novel trials only stimuli from a same set (see Fig. 2) were paired to each other to prevent the merging of potential classes. Thus, the reinforced novel relations are neither consistent nor inconsistent with equivalence-class formation. Symmetrical and novel relations were concurrently reinforced until a participant met 100 % accuracy in two consecutive 48-trial blocks within the same session. As in baseline training, testing session continued until the completion of all four programmed trial blocks, even when the accuracy criterion was met in either the second or the third block.
Table 1 Summary of procedure for Experiment 1

Training     Testing

           Symmetrical   Novel
A1-B1          B1-A1
A2-B2          B2-A2
A3-B3                    B3-C3
A4 B4                    B4-C4
C1-D1          D1-C1
C2-D2          D2-C2
C3-D3                    D3-A3
C4-D4                    D4-A4

Note. The alphanumeric element to the left of each
dash represents the sample; that to the right
represents the correct comparison (S+). The incorrect
comparisons (S-) Were omitted for clarity.


Results Baseline Training Baseline relations composed of Set-1 and Set-2 stimuli were grouped for analysis because they were used to form the symmetrical relations in the testing phase. Similarly, baseline relations composed of Set-3 and Set-4 stimuli were analyzed together because their stimuli were rearranged to form the novel relations.

Results Baseline Training Baseline relations composed of Set-1 and Set-2 stimuli were grouped for analysis because they were used to form the symmetrical relations in the testing phase. Similarly, baseline relations composed of Set-3 and Set-4 stimuli were analyzed together because their stimuli were rearranged to form the novel relations.

Symmetry Test The right portion of the graphs in Fig. 3 shows accuracy over 48-trials blocks of the symmetry test when the reinforced matching was either symmetrical (filled circles) or novel (open circles) concerning the baseline relations. All participants performed well above chance on the symmetrical matching in the first 48-trial block (ranging from 83 % to 100 %) and matched at 100 % accuracy from the second block onwards. In contrast, accuracy levels on the novel matching were around chance in the first trial block for Participants NAS and ACV (42 % correct), and slightly above chance for Participants DMP and PRR (67 % and 63 % correct, respectively). For participants DMP and NAS, performance accuracy on the novel matching abruptly increased to 100 % correct, while for ACV and PRR it increased gradually. In accordance with symmetry, performance accuracies on test sessions were clearly higher on the symmetrical matching than on the novel matching for all participants.

[FIGURE 3 OMITTED]

Experiment 2

Experiment 2 was conducted with the other four college students to test the effectiveness of the procedure in demonstrating transitivity. Training and testing were conducted in two phases under reinforcement conditions. During the first phase, students were trained on 16 baseline conditional relations (four A--B; four B--C; four D--E; four E--F), concurrently (see Fig. 4). During the testing phase, four transitive relations (A 1--C 1; A2--C2; D1--F1 ; D2--F2) and four novel relations (A3--F3; A4--F4; D3--C3; D4--C4) were reinforced, concurrently (see Fig. 4). Evidence of transitivity would be indicated by higher accuracies on the transitive trials than on the novel trials, especially earlier on testing.

[FIGURE 4 OMITTED]

Method

Participants Two 21-year-old women (MGC and TBN) and two 20-year-old men (JOK and TSG) served as volunteers. They were drawn from journalism and history undergraduate courses. An informed consent term has been appropriately obtained from all participants that also reported no familiarity neither with the experimental analysis of behavior nor with similar types of experiment.

Setting and Apparatus

Setting and apparatus were the same as in Experiment 1. Twenty-four colorful visual stimuli were randomly assigned to four six-stimulus sets (Fig. 2). The assignment of stimuli to the sets was counterbalanced across participants, such that stimuli assigned to Sets I and 2 for half of participants were respectively assigned to Sets 3 and 4 for the other half of participants, and vice-versa.

Procedure

Each participant was exposed to two experimental phases (baseline training and transitivity test). The parameters of the matching-to-sample task described in Experiment I were kept identical in Experiment 2.

Baseline Training Participants were concurrently trained for sixteen baseline conditional relations, divided into two groups of interconnected matching tasks. In one group, B and C comparisons were conditionally related to A and B samples, respectively (A--B and B--C matching). In the other group, E and F comparisons were conditionally related to D and E samples, respectively (D--E and E--F matching). The sixteen sample-comparison matching reinforced in baseline are shown in Table 2 ("Training" column). Each 48-trial block comprised three trials for each conditional relation presented in a semi-random order according to the same criteria previously described in Experiment 1. Because the number of trials of each conditional relation in a block was only a half the number of trials in Experiment 1, participants were trained in Experiment 2 until they reached 100 % accuracy in all four (instead of two) 48-trial blocks in a session.
Table 2 Summary of procedure for Experiment 2

                    Testing

Tranning           Transitive   Nonel
A1-B1      B1-C1      A1-C1
A2-B2      B2-C2      A2-C2
A3-B3      B3-C3                A3-F3
A4-B4      B4-C4                A4-F4
D1-E1      E1-F1      D1-F1
D2-E2      E2-F2      D1-F1
D3-E3      E3-F3                D3-C3
D4-E4      E4-F4                D4-C4

Note. The alphanumeric clement to the left
oleach dash represents the sample; that to
the tight represents the correct comparison
(S+). Incorrect comparisons (S-) were
omitted Ibr clarity


Transitivity Test Participants were given a transitivity test in which both transitive and novel matching were concurrently reinforced. Transitive relations comprised stimuli from Sets 1 and 2 that had been related to a common nodal stimulus during the baseline training (see Table 2, "Transitive" column). That is, responses to Cl and C2 comparisons were reinforced after Al and A2 samples, respectively, (A--C matching); and responses to F I and F2 comparisons were reinforced after D 1 and D2 samples, respectively, (D--F matching). Novel matching involved stimuli from the Sets 3 and 4 that had not been previously related to any common nodal stimulus (see Table 2, "Novel" column). In this case, responses to F3 and F4 comparisons were reinforced after A3 and A4 samples, respectively, (A--F matching); and responses to C3 and C4 comparisons were reinforced after D3 and D4 samples, respectively, (D--C matching). Note that in the novel test trials only stimuli from a same set (see Fig. 2) were paired to each other to prevent the merging of potential classes. Thus, the reinforced novel relations are neither consistent nor inconsistent with equivalence-class formation. Testing sessions were conducted until participant met 100 % accuracy in two consecutive trial blocks within the same session. Nonetheless, the session continued until the completion of all four programmed trial blocks, even if the participant reached the accuracy criterion in earlier blocks.

Results

Baseline Training Fig. 5 (left portion of the graphs) shows matching accuracy for each participant over all 48-trial blocks of the baseline training. Throughout training sessions, matching accuracies on the Set-1 and Set-2 baseline relations (filled circles) did not differ from that on the Set-3 and Set-4 baseline relations (open circles) for all participants. On average, participants required 24 48-trial blocks (ranging from 12 to 48) to acquire both groups of baseline relations to a criterion of 100 % accuracy in a session.

[FIGURE 5 OMITTED]

Transitivity Test The right portion of the graphs in Fig. 5 shows individual matching accuracy over 48-trial blocks of the transitivity test, when the conditional relations were either transitive (filled circles) or novel (open circles) with respect to the baseline. In general, matching accuracies on the transitive relations were higher than on the novel relations from the beginning of and throughout the test sessions for all four participants, despite some variability among participants.

JOK and TSG matched well above chance-level on the transitive relations in the first 48-trial block (92 % and 96 % correct, respectively), reaching 100 % accuracy on the second block. Regarding the novel relations, JOK performed 75 % and 100 % correct in the first and second blocks, respectively. TSG, in turn, performed below chance-level (42 % correct) on the novel relations in the first block, and reached 100 % accuracy after five blocks. MGC's accuracy on the transitive relations increased from 79 % to 100 % along the first three blocks, while, on the novel relations, it took eight blocks to increase accuracies from 42 % to 100 %. Finally, in contrast to all other three participants, TBN performed considerably below chance-level (21 % correct) with respect to the transitive relations and slightly below chance (42 % correct) with respect to the novel relations, in the first 48-trial block. TBN's accuracies on both transitive and novel relations gradually increased without much distinction across eight blocks.

Discussion

Several studies have shown that having learned a certain number of conditional relations verbally able humans can show derived matching performances in accordance with equivalence-class formation (e.g., Devany et al. 1986; Lazar et al. 1984; Sidman and Cresson 1973; Sidman et al. 1985; Sidman and Tailby 1982; Spradlin et al. 1973). Assessing reflexivity, symmetry and transitivity (i.e., equivalence) in the absence of reinforcement is important to demonstrate an emergent relational performance. Nonetheless, it has been argued that unreinforced test trials can disturb the sources of stimulus control precluding the demonstration of equivalence-class formation in certain population (Dube and McIlvane 1996; Galva() et al. 1992; Kuno et al. 1994; Sidman et al. 1982). Moreover, it is worth mentioning that the unreinforced test trials reproduce the same consequences the subjects experience following incorrect responses during baseline training.

The present study tested an alternative methodological strategy to evaluate derived relations under differential reinforcement condition. Basically, the procedure exposes participants to a continuous reinforcing sequence of training and testing of conditional relations in a matching-to-sample task. In baseline, conditional relations were trained to a high accuracy level. In tests, stimuli from baseline were re-arranged so that the reinforced relations were either symmetrical (or transitive) or novel concerning the baseline. By comparing the acquisition of both sets of relations by the same participant, symmetry and transitivity may be noticed.

Testing data for all four participants of Experiment 1 clearly showed higher levels of accuracy on the symmetrical matching trials than on the novel matching trials. In Experiment 2, all but one participant (TBN) demonstrated higher accuracies (or faster acquisition) on transitive matching compared to novel, control matching.

These results indicate symmetry and transitivity in the conditional discriminations of verbally competent humans, in accordance with well-established findings in the literature (e.g., Devany et al. 1986; Sidman and Cresson 1973; Sidman and Tailby 1982). The fact that one participant in Experiment 2 did not exhibit evidence of transitivity also reveals parallels with previous studies that showed that, even in humans, the emergence of conditional relations can be delayed, dependent on remediating procedures, or it may never be obtained (e.g., Lazar 1977; Lazar et al. 1984; Sidman et al. 1985; Spradlin et al. 1973).

One may argue, however that the differences in the matching accuracies observed on symmetrical and novel test trials (Experiment 1) were not due to symmetry. Another feature was also coincident with the symmetrical or novel status of the relations assessed during the testing condition. The stimuli presented on the symmetrical trials had been presented in close temporal proximity and within the "bounds" of a trial during training, whereas the stimuli presented in the novel trials never appeared in close temporal proximity to each other and never within the "bounds" of a trial. In other words, it is possible that the lower accuracy observed in the novel relations could have been due to the absence of paring between their component stimuli during the baseline training. Nonetheless, if this were the case, we would expect no difference in matching accuracies between transitive and novel relations in Experiment 2 because the stimuli component of both these sets of relations were never presented in close temporal proximity or within the same trial in baseline training. In contrast, the results of Experiment 2 were consistent with transitivity just like the results of Experiment I were consistent with symmetry.

One important feature of the present testing procedure is to avoid a possible negative effect of reinforcing both consistent and inconsistent matching responses within-subjects. The reinforcement of inconsistent matching might merge the expected classes into a single larger class, thus, resulting in chance-level performances in both types of trials, a fact that vanishes any possible comparison among them.

Demonstration of equivalence-class formation in verbally able adults is robust in the literature, and that is the reason why the present study was carried out with such a population. Since our results conform to those arising from the traditional unreinforced tests, the present study certifies a powerful strategy to be used with population whose behavior may be disrupted by the suspension of reinforcement in test trials (e.g., language-disabled individuals). In the applied field, the present testing strategy can contribute to the development of behavioral techniques to teach and test complex and relational repertoires for students with deficits in the symbolic functioning. The replication of the present study with children diagnosed with autism is an ongoing project in our lab.

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Saulo Missiaggia Velasco * Gerson Yukio Tomanari

S. M. Velasco * G. Y. Tomanari DepartamentO de Psicologia Experimental, Universidade de Sao Paulo, Brazil, Avenida Professor Mello Moraes, 1721, Cidade Universitaria, Sao Paulo, SP 05508-030, Brazil e-mail: saulomv@usp.br

Author Note This research was supported by Doctoral Grant (CNN 142544/2005-1) to the first author, and Researcher Grant (CNN 302640/ 2007-0) and Research Support (CNN, Edital Universal, 471953/2004-0) to the second author. Both authors are members of the National Institute of Science and Technology on Behavior, Cognition and Teaching, supported by FAPESP (Grant #08/57705-8) and CNPq (Grant #573972/ 2008-7). There is no conflict of interest to declare concerning both authors. The authors express their acknowledgments to Alex Wahl, Paula Braga-Kenyon, and Shawn Kenyon for their comments on an earlier version of this manuscript. Correspondence must be sent to either Saulo M. Velasco, e-mail: saulovelasco@gmail.com or Gerson Y. Tomanari, email: tomanari@usp.br.
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Date:Sep 1, 2014
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