2015, 103, 524–541

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

NUMBER

3 (MAY)

ENHANCED EQUIVALENCE CLASS FORMATION BY THE DELAY AND RELATIONAL FUNCTIONS OF MEANINGFUL STIMULI ERIK ARNTZEN1, RICHARD K. NARTEY1, AND LANNY FIELDS2 1 OSLO AND AKERSHUS UNIVERSITY COLLEGE QUEENS COLLEGE AND THE GRADUATE SCHOOL OF THE CITY UNIVERSITY OF NEW YORK

2

Undergraduates in six groups of 10 attempted to form three 3-node 5-member equivalence classes (A!B!C!D!E) under the simultaneous protocol. In five of six groups, all stimuli were abstract shapes; in the PIC group, C stimuli were pictures with the remainder being abstract shapes. Before class formation, participants in the Identity-S and Identity-D groups were given preliminary training to form identity conditional discriminations with the C stimuli using simultaneous and 6 s delayed matching-tosample procedures, respectively. In the Arbitrary-S and Arbitrary-D groups, before class formation, arbitrary conditional discriminations were formed between C and X stimuli using simultaneous and 6 s delayed matching-to-sample procedures, respectively. With no preliminary training, classes in the PIC and ABS groups were formed by 80% and 0% of participants, respectively. After preliminary training, class formation (yield) increased with delay, regardless of relational type. For each of the two delays, yield was slightly greater after forming arbitrary- instead of identity-relations. Yield was greatest, however, when a class contained a meaningful stimulus (PIC). During failed class formation, probes produced experimenter-defined relations, participant-defined relations, and unsystematic responding; delay, but not the relation type in preliminary training influenced relational and indeterminate responding. These results suggest how meaningful stimuli enhance equivalence class formation. Key words: arbitrary conditional relations, college students, concurrent, delayed matching to sample, enhanced class formation, identity conditional relations, linear series training structure, simultaneous protocol; stimulus equivalence

The perceptually disparate stimuli in a set (represented as A, B, C, D, and E) act as members of an equivalence class when all of them become related to and interchangeable with each other. An example would be the five representations of the numeral 9 in languages not known to a subject: Cyrillic (A), Kanji (B), Urdu (C), Khmer (D), and Arabic (E). These stimuli can become interchangeable by first training a set of conditional discriminations that share particular stimuli (e.g., AB, BC, CD, and DE). If all of the untrained relations in the set then emerge without direct training (BA, CB, DC, ED, AC, BD, CE, AD, BE, AE, CA, DB, EC, EB, DA, and EA), the stimuli would be acting interchangeably and would be The authors would like to thank Peter Urcuioli and Gregory Madden for constructive and helpful comments on an earlier version of the manuscript. Part of this paper was presented in a symposium at the 7th Conference of the European Association of Behavior Analysis, Stockholm, Sweden. There is no conflict of interest to declare concerning the three authors. Correspondence regarding this article should be sent to the first author: Erik Arntzen, Department for Behavioral Science, Oslo and Akershus University College, PO Box 4 St. Olavs Plass, 0130 Oslo, Norway. (e-mail: [email protected]) doi: 10.1002/jeab.152

functioning as members of a category called an equivalence class (e.g., Fields & Verhave, 1987; Sidman, 1994). In some experiments, the to-be-formed classes consist of abstract or meaningless stimuli, and training and testing are conducted using the simultaneous protocol; that is, training all baseline relations to mastery level after which all derived-relations probes are presented on different trials within the same test. Under these conditions, the formation of equivalence classes has been found to be very unlikely, typically between 0 and 15 percent (e.g., Arntzen, Grondahl, & Eilifsen, 2010; Buffington, Fields, & Adams, 1997). Thus, the use of that protocol provides a potentially sensitive preparation for studying other variables that can enhance class formation. The stimuli in an equivalence class, however, need not all be meaningless. When at least one meaningful stimulus is included in a set of meaningless stimuli, its inclusion increases the likelihood of equivalence class formation if it has neutral or positive valence (e.g., Arntzen, 2004). For instance, in the example mentioned above, since the learner is a knowledgeable English speaker, the likelihood of class formation would be increased by the inclusion of

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MEANINGFUL STIMULI EQUIVALENCE CLASSES the English word NINE, a meaningful stimulus for this particular set, as a member of the to-be-formed class. When one of the stimuli in the set is meaningful (e.g., a picture) and the remaining stimuli are meaningless, equivalence classes are formed by 75 to 85 percent of participants (Arntzen & Lian, 2010; Fields, Arntzen, Nartey, & Eilifsen, 2012). Conversely, if the meaningful stimuli have a negative valence, eliciting, for example, feelings of disgust, pain or jealousy; then the insertion of meaningful stimuli may preclude or reduce the likelihood of equivalence class formation Other experiments have shown that there is a lower probability of class formation if at least one of the meaningful stimuli included in a tobe-formed class has a connotatively positive valence and at least one other has a connotative negative valence (Grehan, 1998; Leslie, Tierney, Robinson, Keenan, & Watt, 1993; Plaud, 1995; Watt, Keenan, Barnes, & Cairns, 1991). On the other hand, the likelihood of class formation is greatly heightened if the stimuli in a to-be-formed class have compatible connotative valences (e.g., Dickins, Bentall, & Smith, 1993). The above-mentioned class enhancement and suppression effects are typically attributed to the denotative properties (defining features) and connotative (emotive and judgmental features) properties of the meaningful stimulus (Travis, Fields, & Arntzen, 2014). Apart from these properties, however, a meaningful stimulus also occasions the production of respondents and operants (i.e., serves a number of discriminative functions), occasions the selection of other stimuli (i.e., serves conditional discriminative functions), and can act as a member of a variety of categories or stimulus classes (Fields et al., 2012). Thus, the classenhancing properties of meaningful stimuli could be attributed to any or all of these acquired behavioral stimulus control functions, independent of connotative and denotative values (Fields et al., 2012; Tyndall, Roche, & James, 2004). Initial support for this view was provided by Fields et al. (2012). Using meaningless stimuli designated as A, B, C, D, and E, some of the participants were provided with preliminary training in which the C stimuli were established as discriminanda in simple successive and simple simultaneous discrimination paradigms. A simple successive discrimination training

525

involves presenting at least two single stimuli in a random order and providing differential reinforcement for the same response in each of the stimuli. A simple simultaneous discrimination training involves the concurrent presentation of at least two stimuli and providing reinforcement for the selection of one of the stimuli on all of the trials. The remaining participants received no preliminary discrimination training. Thereafter, ABCDE equivalence classes were formed by 50% of participants who received preliminary discrimination training, whereas none of the participants formed classes without this training. By comparison, 80% of participants in a third group formed classes when the C stimuli were meaningful (familiar pictures). Using the same design, Travis et al. (2014) found that the establishment of simultaneous discriminations alone, and degree of overtraining of successive discriminations, increased the subsequent likelihood of class formation. By implication, some portion of the enhancement of equivalence class formation produced by the inclusion of a meaningful stimulus in a set of otherwise meaningless stimuli could be attributed to the simple discriminative functions served by a meaningful stimulus. That study, however, did not fully separate the classenhancing effects of preliminary training of simultaneous and successive discriminative functions alone versus together. Exploring these factors, Nartey, Arntzen, and Fields (2014) found that each alone did not enhance class formation, whereas training both discriminative functions produced an enhancement effect. Arntzen, Nartey, and Fields (2014) explored whether the conditional relational function served by a meaningful stimulus could also account for the class-enhancing effect of such a stimulus. In this experiment, participants began by learning an identity conditional discrimination using a meaningless stimulus referred to symbolically as C (i.e., a C-C relation). In one condition, the identity relation was established under a simultaneous matching-to-sample format, where the sample and comparison stimuli were concurrently present in a trial. (IdentityS). In another condition, the identity relation was established using a 6-s delay between the offset of a sample and the onset of the comparison stimuli (Identity-D). When the C stimulus was subsequently included as a

526

ERIK ARNTZEN et al.

member of a to-be-formed five-member equivalence class (i.e., ABCDE), the likelihood of class formation was greater in the Identity-D condition than in the Identity-S condition. The Arntzen et al. study did not evaluate the effects of delaying the presentation of the comparison stimuli across different types of conditional relations established in preliminary training. Thus, it is possible that if a different preliminary discrimination were trained (e.g., arbitrary conditional relation) the enhancement effect would be affected. This possibility was explored in the present experiment by varying delay values during the establishment of C-based identity relations (C– C) versus the establishment of arbitrary conditional relations (C–X). In an ABS group, all of the stimuli (A through E) were abstract shapes and no preliminary training was provided. In the PIC group, the C stimuli were familiar pictures and the remaining stimuli were abstract shapes; once again, no preliminary training was provided. In the Identity-S and IdentityD groups, pretraining established identity conditional discriminations with the C stimuli (C–C) using either a simultaneous or a 6-s delayed matching-to-sample procedure, respectively. In the Arbitrary-S and Arbitrary-D groups, separate arbitrary conditional discriminations were learned with the C stimuli (C–X) prior to class formation, again using either simultaneous or 6-s delayed matching-to-sample procedures, respectively. The participants in all groups then attempted to form five-member equivalence classes with the A, B, C, D, and E stimuli. The yields obtained in the ABS and PIC groups assessed the effect of no prior stimulus history (ABS) versus extensive (“meaningful”) stimulus history (PIC) on equivalence class formation. The other four conditions evaluated the combined and separate effects of delay and type of pretrained relation on the enhancement of equivalence class formation. We expect the PIC condition to produce a much greater yield than the ABS condition (Fields et al., 2012). The establishment of the identity conditional relation with a delay should enhance equivalence class formation more than when it is established with no delay (Arntzen et al., 2014). If delay per se is the determinant of class enhancement, the same outcomes should occur when establishing identity or arbitrary conditional relations prior to formation of the ABCDE classes. If, however, the determinant of

class enhancement is delay as well as type of relation established prior to class formation training (identity or arbitrary), different levels of enhancement should occur when delay is varied in the context of the pre-class-formation establishment of identity or arbitrary conditional relations. The effect of relational type on class enhancement might also be clarified in the present design. When equivalence classes are formed, the baseline relations and the derived relations are all arbitrary conditional relations. These relations are structurally identical to the CX relations established during Arbitrary-S and Arbitrary-D training, and differ in structure from the C-C relations established during Identity-S and Identity-D training. Based on structural similarity, the prior formation of the arbitrary conditional relations may produce a greater class enhancement effect than the preclass-formation establishment of identity conditional relations.

Method Participants Sixty students at the University of Ghana participated in the experiment. Twenty-six males and 34 females participated voluntarily in this study. Each student was given 13 dollars for participation in the experiment. They were between the ages of 19 and 28 years (M ¼ 21.5, SD ¼ 1.5), were unfamiliar with stimulus equivalence research and methodology, and were randomly assigned to one of six experimental conditions (N ¼ 10). All participants were first given an informed consent form to read. The form stated that participants were about to participate in an experiment in the field of behavior analysis that would last approximately one and a half hours and that the data collected would be anonymous. They were also informed that they were free to withdraw from the experiment at any time without any negative consequences. After reading, those who agreed by signing the forms began the experimental protocol. Apparatus Setting. The experiment took place in a lab at the Department of Psychology at the University of Ghana that measured

527

MEANINGFUL STIMULI EQUIVALENCE CLASSES approximately 5m x 5m and was furnished with tables and chairs. Hardware. An HP Compaq nc6320 laptop computer with a 1828 MHz Intel Centrino1 processor and a screen with a 16.8 in. diagonal length and a 16  9 horizontal-to-vertical ratio was used to conduct the experiment. Participants used an external mouse to control the position of the cursor throughout the experiment. Software. MTS software made by Psych Fusion Software in collaboration with the first author was used for the training and testing of conditional discriminations for all participants. The software controlled the presentation of all stimuli and also made recordings of data. Stimuli. Figure 1 shows the stimulus sets used in the experiment. The top two sections of the figure show the stimuli used as members of the equivalence classes. These consisted of 15 abstract and the 3 familiar picture stimuli. The bottom section shows the stimuli used during arbitrary matching training. The abstract stimuli were displayed in black and the

picture stimuli backgrounds.

in

color,

all

on

white

Procedure Participants were randomly assigned to six different groups. The two reference groups were labelled ABS and PIC. In the ABS group, the A through E stimuli were all abstract shapes. In the PIC group, the C stimuli were pictures and the remaining stimuli were the same abstract shapes used with the ABS group. The other four groups, which included various pretraining of the C stimuli, are presented below. Training of identity and arbitrary conditional relations. Participants were presented with the following instructions before the start of the training: A stimulus will appear in the middle of the screen. Click on this by using the computer mouse. Three stimuli will then appear in three corners of the screen. Choose one of these by using the mouse. If you choose the stimulus we have defined as correct, words like “very good”,

Fig. 1. The stimuli used as members of the equivalence classes were the abstract and familiar picture stimuli as shown in the two top sections. The bottom section shows the stimuli used during the arbitrary matching training.

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ERIK ARNTZEN et al.

“excellent”, and so on will appear on the screen. If you press the wrong stimulus, the word “wrong” will appear on the screen. At the bottom of the screen, the number of correct responses you have made will be counted. During some stages of the experiment, the computer will NOT tell you if your choices are correct or wrong. Please do your best to get everything right. Good luck! Participants in the Identity-S and the IdentityD groups acquired C-based identity conditional discriminations prior to the training used to establish the ABCDE equivalence classes. For the participants in the Identity-S and the Identity-D groups, the C stimuli were presented in trials that contained one sample and three comparisons, with the trials having the following content: C1/C1-C2-C3, C2/C1-C2-C3, and C3/C1-C2-C3. The stimulus that preceded the / was the sample, and the three stimuli that followed the / were the comparisons. In each trial, the bold letter–number pair represented the sample stimuli and the underlined letter–number pair represented the correct comparison. Training was conducted in blocks that contained 12 trials, with four presentations of each of the trials indicated above. Across trials the locations of the three comparisons was randomized. The 12 trials were presented in a random order without replacement. During acquisition, all trials produced programmed consequences for comparison selections. Training continued by block repetition until a participant responded with 90% accuracy (the mastery criterion) on three consecutive blocks. Once achieved, a minimum of three more blocks was administered to assure the maintenance of responding in the eventual absence of informative feedback. Across blocks, as long as mastery was maintained, the percentage of trials in a block that produced programmed consequences was systematically reduced from 75% to 25%, and then to 0% of the trials in a block. Each block was repeated with the specified level of consequences until the mastery criterion was attained for three consecutive blocks. If mastery was not achieved, the percentage of programmed consequences was increased to the previously used value for the next block. When programmed consequences were provided, a correct selection produced a screen message such as “very good” or “excellent”, while an incorrect selection produced the screen message “wrong.” On trials that did not have programmed consequences, a

selection was followed by a 2 s intertrial interval. If a trial had a programmed consequence, the latter lasted 1 s and was followed by a 1 s intertrial interval. In each block, at least 90% correct responses were required before participants could proceed to the next stage in the experiment. In the Identity-D group, all of the training parameters were just as described except that the mouse-click on the sample stimulus on each trial (the observing response) terminated the sample and initiated a fixed 6 s delay prior to presentation of the comparison stimuli. In the Identity-S group, the sample remained on as the comparison stimuli were presented following the mouse click. Participants in the Arbitrary-S and the Arbitrary-D conditions acquired the arbitrary C-based conditional discriminations (C!X, where the X stimuli are presented in the bottom row in Fig. 1) prior to the training used to establish the ABCDE equivalence classes. For the participants in the Arbitrary-S and the Arbitrary-D groups, the three C stimuli were presented as sample stimuli in the following trials: C1/X1-X2-X3, C2/X1-X2-X3, and C3/X1-X2-X3. The training parameters were the same as those used to establish the identity conditional relations. Acquisition and maintenance of baseline conditional relations. Participants assigned to the ABS or PIC groups started the experiment with this phase; as such, they were oriented to the task with a very similar version of the prior instructions. All baseline conditional discriminations were trained and tested under the simultaneous protocol (Buffington et al., 1997). Each trial began with the presentation of the sample stimulus in the middle of the screen. Mouse clicking on the sample stimulus was immediately followed by the presentation of three comparison stimuli at three of the corners of the screen, while the sample stimulus remained on the screen. A correct comparison choice removed the sample and comparison stimuli and produced the word correct,very good, super, or excellent in the middle of the screen for 1 s. An incorrect comparison choice also removed the sample and comparison stimuli but produced the word wrong on the screen for 1 s. Termination of the programmed consequences was followed by a 500-ms intertrial interval. Between trials, the mouse cursor was returned to the center of the screen.

529

MEANINGFUL STIMULI EQUIVALENCE CLASSES Baseline relations were trained using a linear series training structure represented as A!B!C!D!E. Table 1 shows each of the 12 trial types using a sample—correct comparison format. Each trial type was presented three times in each 36-trial training block. When participants satisfied the mastery criterion (same as above), they progressed to the next stage of the experiment. Failure to reach the mastery criterion meant the block was repeated until the criterion was met. During acquisition, all comparison choices produced programmed consequences. Acquisition of the baseline conditional relations was followed by four blocks of trials in which the frequency of programmed consequences was reduced (75%, 50%, 25%, and 0%), the trials with programmed consequences randomly selected in a block. Each of the four blocks was repeated until the mastery criterion was met. Tests for derived relations. After successful training of the baseline relations, emergent relations were tested in a block that contained 180 trials: 36 baseline trials, 36 symmetry trials, 54 one-node transitivity trials, 36 two-node transitivity trials, and 18

three-node transitivity trials; specifics of these trials are provided in Table 1. All trials were presented in random order without programmed consequences. Equivalence class formation was assessed in the first and second halves of the 180-trial test block. This allowed for assessment of immediate or delayed emergence of the equivalence classes (i.e., at least 90% class-consistent selections in each half of the test block for immediate emergence, and at least 90% class-consistent selections in the second half of the test block for delayed emergence). Failure of class formation was defined as less than 90% selection of class consistent comparisons in both test halves. To address concerns that the number of test trials of each type appeared at approximately the same frequency in the two test halves, these frequencies are shown for one randomly selected participant from each group in Table 2. Although each block did not necessarily contain the same number of each type of probe, the large number of trials in each half ensured the inclusion of many trials of all types. Thus, the performances engendered by each test half provided a valid measure of equivalence class formation.

Table 1 An Overview of the Experimental Phases in the Conditional Discrimination Training and Testing Experimental Phases

Acquisition of baseline relations Maintenance of baseline relations Test for derived relations All trial types presented randomly Baseline trials Symmetry trials 1 Node trials

2 Node trials 3 Node trials

Trial Types

Trials/Block

A1B1, A2B2, A3B3, B1C1,B2C2, B3C3 C1D1,C2D2, C3D3, D1E1,D2E2, D3E3 A1B1, A2B2, A3B3, B1C1,B2C2, B3C3 C1D1,C2D2, C3D3, D1E1,D2E2, D3E3

36

A1B1, A2B2, A3B3, B1C1, B2C2, B3C3 C1D1, C2D2, C3D3, D1E1, D2E2, D3E3 B1A1, B2A2, B3A3, C1B1, C2B2, C3B3 D1C1, D2C2, D3C3, E1D1, E2D2, E3D3 A1C1, A2C2, A3C3, C1A1, C2A2, C3A3, B1D1, B2D2, B3D3, D1B1, D2B2, D3B3, C1E1, C2E2, C3E3, E1C1, E2C2, E3C3, A1D1, A2D2, A3D3, D1A1, D2A2, D3A3, B1E1, B2E2, B3E3, E1B1, E2B2, E3B3 A1E1, A2E2, A3E3, E1A1, E2A2, E3A3

36

36

36

54 36 18

Note. After acquiring the baseline relations in a block(s) with 100% probability of programmed consequences, the relations were maintained in four blocks with fading of programmed consequences: 75%, 50%, 25%, and 0%. In each block, at least 34 of 36 correct responses were required before participants could proceed to the next stage in the experiment.

530

ERIK ARNTZEN et al. Table 2 Sampling of Types of Probe Trials in Test Halves 1 and 2 First Half

Participant 4324 4344 4331 4336 4357 4322 AVG

BL 18 16 17 17 21 22 18.5

SY 20 20 19 18 17 15 18.2

1N 24 29 28 26 26 27 26.7

Second Half

2N 19 16 18 19 15 19 17.7

3N 9 9 8 10 11 7 9.0

BL 18 20 19 19 15 14 17.5

SY 16 16 17 18 19 21 17.8

1N 30 25 26 28 28 27 27.3

2N 17 20 18 17 21 17 18.3

3N 9 9 10 8 7 11 9.0

Note. BL ¼ baseline; SY ¼ symmetry; N ¼ node; AVG ¼ average.

Results Equivalence Class Formation Immediate, delayed, and overall class formation. As shown in Table 3, 20 of the 60 participants formed classes (overall yield ¼ 33.3%), 17 of whom did so in the first test half and then maintained mastery in the second test half. The three remaining participants (one each in the PIC, Identity-S, and Arbitrary-S conditions) showed delayed class formation (submastery performances in test half 1 and mastery levels of responding in test half 2). Effect of preliminary training. Figure 2 depicts the percentage of participants who formed classes in each group. No participants formed classes in the ABS condition in which the abstract C stimuli did not acquire any conditional discriminative function prior to the training used to establish the ABCDE equivalence classes. In contrast, a high proportion of participants formed the equivalence classes when the C stimulus was a meaningful picture (group PIC). The difference in these yields was significant, x2 (1) ¼ 13.33, p < .01. Pretraining either identity or arbitrary conditional discriminations improved yields relative to the ABS group. Thus, prior establishment of conditional discriminative functions for the abstract C stimulus imparted a class-enhancing property to that stimulus. However, the effects of these pretraining experiences on yields was less than that produced by using a meaningful picture as the C member of the class. Thus, the class enhancing effect of pre-class-formation establishment of C-based identity or arbitrary conditional relations with or without delay did not match that produced by the inclusion of a

meaningful stimulus as the C member of an equivalence class. Effects of delay and relational type. Of primary interest, Figure 2 shows how the likelihood of equivalence class formation was influenced separately and together by delay and type of conditional relation established during pre-class-formation C-based conditional discrimination training. With regard to delay, the likelihood of equivalence class formation increased with the increment in the value of the delay that separated the sample offset and comparison onset during pre-class formation conditional discrimination training. Regardless of type of conditional relation established prior to class formation (identity or arbitrary), the increase in delay produced the same 30% increment in likelihood of equivalence class formation. This overall effect of delay was indexed by averaging the data for both types of conditional relations. When done, yield increased from 15% under the 0 s delay condition to 45% under the 6 s delay condition, a difference that was statistically significant, x2 (1) ¼ 4.286, p ¼.038. By contrast, there was no significant effect of the type of relation learned in pretraining on class enhancement, x2 (1) ¼ .476, p ¼ .490. Participantand experimenter-defined relations during failed class formation. When a participant did not form the equivalence classes (N ¼ 40), it is possible that all of the probe trials produced unsystematic responding. It is also possible that some probes showed the emergence of experimenter-defined conditional relations, while other probes produced conditional selections of comparison stimuli

531

MEANINGFUL STIMULI EQUIVALENCE CLASSES Table 3 Accurate Selection of Class Consistent Comparisons in the Two Test Halves Condition

Participant

% correct in test half 1

% correct in test half 2

ABS

4324 4346 4326 4308 4310 4350 4347 4302 4355 4309

84 73 72 68 56 36 49 44 52 39

81 76 69 64 59 53 53 46 44 42

PIC

4344 4335 4303 4323 4319 4312 4305 4359 4317 4339

99 99 99 97 98 96 97 88 77 33

100 100 99 98 99 99 98 90 71 27

Identity-S

4331 4358 4333 4343 4337 4307 4345 4300 4342 4327

88 80 68 66 63 47 50 50 41 37

96 88 68 59 53 57 44 36 32 24

Identity-D

4336 4332 4356 4348 4306 4320 4325 4330 4328 4340

99 100 98 94 80 73 52 58 51 49

99 98 98 99 79 79 71 43 40 41 (Continued)

532

ERIK ARNTZEN et al. Table 3. (Continued)

Condition

Participant

% correct in test half 1

% correct in test half 2

Arbitrary-S

4357 4352 4353 4316 4304 4329 4314 4315 4313 4321

92 86 86 63 52 43 40 44 34 33

99 97 84 58 50 39 36 43 43 23

Arbitrary-D

4322 4311 4349 4338 4341 4351 4318 4334 4354 4301

100 99 100 98 97 70 64 56 53 52

99 100 99 99 100 66 76 70 50 51

that did not come from the same “class” as the prevailing sample stimulus. Such performances, if consistent, would document the emergence of participant-defined conditional

relations, such as C2-D3 and A1-E2. Finally, yet other probes could produce comparison selections that were unsystematic and did not indicate relational responding. To what extent,

% Participants with Class Formation

100

Arbitrary Identity

80 60 40 20

PI C

D EL A Y

SI M

A B S

0

Conditions Fig. 2. The figure shows percentage of participants responding in accordance with stimulus equivalence. ABS ¼ all stimuli were abstract shapes, SIM ¼ C stimuli were pretrained with simultaneous identity or arbitrary matching, DELAY ¼ C stimuli were pretrained with 6 s delayed identity or arbitrary matching, PIC ¼ C stimuli were pictures.

MEANINGFUL STIMULI EQUIVALENCE CLASSES then, do the failures of equivalence class formation reflect these three types of test performances? To qualify as a participant- or experimenterdefined relation, the same comparison stimulus had to be selected on all presentations of the same probe trial. Alternatively, if the repeated administration of a given probe produced the selection of different comparisons, that probe was said to produce an indeterminate performance. For each participant who failed to form equivalence classes, Table 4 illustrates the number of probe trials on which responding was consistent with experimenter-defined relations, participant-defined relations, and indeterminate performances during the probes that were presented in the derived relation test. For Classes 1, 2, and 3, an average of 55, 57, and 55% of probes produced class indicative performances, respectively. Thus, when aggregated across the three potential classes, 56% of the trials produced experimenter-defined relational responding. In addition, 12% of the probe trials produced participant-defined relations during the derived relations tests, but varied from 1 to 24 of such relations across participants. The remaining 27% of the probe trials produced indeterminate performances. The failure of class formation, then, could not be attributed to random or unsystematic responding alone. It is possible that the test performances produced by the participants who did not form the classes could have been influenced by the independent variables used in the present experiment. Those possibilities are shown in Table 5. The data in the first and second sections in Table 5 illustrate how preliminary training influenced the number of probes that produced experimenter-defined relations (first section) and participant-defined relations (second section). In both cases, more probes produced both types of conditional relations following the establishment of the delayed relations instead of simultaneous relations during preliminary training; this difference, however, did not reach the .05 level of significance. In addition, the type of relation established during preliminary training did not influence the prevalence of probes that produced either type of conditional relation in the derived relations tests. The third section in Table 5 indicates how preliminary training influenced the number of

533

probes that produced the combination of experimenter- and participant-defined relations. Significantly more probes produced both types of conditional relations following the formation of delayed relations instead of simultaneous relations, F(1, 24) ¼ 5.822, p ¼ .024. The type of relation established during preliminary training, however, did not influence the prevalence of probes that produced conditional relations in the derived relations tests. The bottom section of Table 5 indicates how the four preliminary training conditions influenced the number of probes that produced indeterminate relational responding. Significantly more probes produced indeterminate performances following the formation of simultaneous relations instead of delayed relations, F (1,23) ¼ 6.223, p ¼ .020. Relational type, however, did not influence the prevalence of probes that produced relationally indeterminate performances. To summarize, in addition to influencing the likelihood of equivalence class formation, preliminary training influenced the derived relations performances of the participants who did not form equivalence classes. Specifically, these performances were induced predominantly by the delays that characterized the conditional relations established during preliminary training, and much less so, if at all, by the type of conditional relation established during preliminary training. Behavioral Measures Not Influenced by Preliminary Training Trials to acquisition. Figure 3 shows the trials needed to acquire the baseline relations for the equivalence classes in each condition. Data were divided further between participants who did and did not form classes. Only two effects were significant. When we aggregated the data for the Identity-S, Identity-D, Arbitrary-S, and Arbitrary-D conditions, the participants who formed equivalence classes acquired the baseline relations in fewer trials than those who did not, t(38) ¼ −2.946, p ¼ .005). For these four conditions, the correlation between these two variables was significant, Pearson r (40) ¼ .431, p ¼ .005. Thus, acquisition speed accounted for 19% of the variance in class formation for these four conditions. In contrast, differences in speed of

Table 4

21

49 17

PIC

Id-S

4309

4317 4339

4358 4333 4343 4307 4337 4345 4300 4342 4327

45 36 28 33 32 37 26 23 23

32

4355

44 45 49 51

35 27 27 18

ABS

4324 4346 4326 4308

Cls-1: Exptr-Def.

4310 4350 4347 4302

Conditions

Participants

58 38 45 30 39 20 27 20 16

48 17

22

33

31 30 40 38

45 36 42 33

Cls-2: Exptr-Def.

48 48 39 30 34 28 24 26 16

36 20

30

25

37 24 29 27

60 51 37 35

Cls-3: Exptr-Def.

6 3 9 24 24 21 6 24 24

6 15

42

42

18 18 9 27

3 9 9 33

Participant -Def.

23 55 59 63 51 74 97 87 101

41 111

65

48

59 81 75 70

28 39 43 28

Indeterminate

(Continued)

E1A3, E3D1 C1E2 A1E3, D1B2, E1B2 A1D2, B2A3 C2D3, D2B3, E2B3, C3A2,D3C2, E3C2 B1D2, C1E3, C2E3, E2B1, B3E1, C3A2,D3A2, E3C2. C1B2, B2C1, C2D3, D2B1, D3B2, E3B1, E3C2. C2E1, D3A2 C1A3, D1B3, E1C3, A2C3, B2D1, A3E2, C3A2, D3C2 A1E3, B1E3, A2B1, B2A1, D2A1, D2E3, B3E1, D3A1

E1A3, A3E1 E1C2, A2D3, C2A1, D2A3, A3C2

B2D1 C1E2, E1B3, E2B1 B2D3, D2A3, C3D2 A1E2, B1E2, C1E2, A2E3, C2E3, E2C1, B3D2, C3D2, D3A2, E3A2, E3C2 D1A3, B2D3, C2E3, D2B3, E2A3, E3C2 A1B2, B1C3, B1D3, B2A3, B2E3, D3C2 B1E3, E1C3, D2A3 B1C3, B1E3, D1A2, E1B2, E1C2, A2D1, C2D1, C2E1, C3B2 A1E2, B1E2, C1E2, E1A3, C2A3, D2E3, E2B1, E2C1,A3D1, A3E2, C3A1, C3E2, D3B2, E3B2 A1E3, B1C2, C1E3, A2E3, B2A3, B2E3, C2A3, C2E3, D2A3, E2A3, E2D3, A3B2, D3C2, E3D2

Specific Participant Defined Relations

Number of Probes That Produced Experimenter-Defined Relations in Classes 1–3, Participant-Defined Relations, and the Symbolic Representations of the Stimuli in Each Participant-Defined Relation

534 ERIK ARNTZEN et al.

32

31

55 46 42 28

60 30 36 33 30 29 26 18

25

49 36 33 36 28

Cls-2: Exptr-Def.

30

33 34 36 34

51 35 22 12 23 28 22 18

31

51 59 42 25 29

Cls-3: Exptr-Def.

78

18 6 24 27

3 3 12 21 24 15 NA 42

45

6 15 NA 9 42

Participant -Def.

9

40 48 43 60

24 68 76 85 86 85 110 87

54

31 28 69 80 56

Indeterminate

A1D3, C1D3, D2A3, A3D1, C3D1, C3E1 D3B1, E3C1 A1D3, A1E3, A3C2, A3E2, B3A1, C3A1, D3A1, E3A1 A1D3, B1E3, C1E3, B2E3, C2A1, C2E3, C3B1, D3C1, E3B1 B1A3, C1A2, C1B2, D1A2, E1A2, E1B2, E1C2, E1D2, B2A3, C2A3, C2B3, D2A3, D23, E2A3, E2B3 E2C3, E2D3, B3A1, C3B1, D3A1, D3B1, D3C1, E3A1, E3B1, E3C1, E3D1

D1B3 A2D3 A3E2, B3D2, E3A2, E3B2 A3E2, B3A1, B3D2, B3E2, D3C1, D3A2, E3D2 B1C2, B1E3, C1E3, E1C2, C2D3, A3C2, C3A1, D3A1 A1D3, C1B3, B2D1, B2E1, C3B1. N/A A1E3, C1E3, D1E2, D1C3, B2C3, B2E3, D2A3, D2B3, E2D1, E2C3, A3D2, B3D2, D3B2, E3D1

A1E2, B1E2 A1D2, B1D2, C1D2, D2A1, D2B1 N/A A1C3, A3E1, D3C2 A1C2, B1E3, D1B2, E1B2, E1C2, E1D3, A2D3, C2E1, C2A3,C2D3, D2A3, A3C2, D3B2, E3C2 C1E2, C1A3, D1B2, D1C2, D1A3, E1C2, A2E3, C2A3, C2E3, D2A3, E2D1, E2A3, A3D1, A3C2, E3C2

Specific Participant Defined Relations

Note. The headings of columns 3–7 represent the number of probes that produced Class-1 experimenter-defined relations (column 3), Class 2 experimenter-defined relations (column 4), Class 3 experimenter-defined relations (column 5), participant-defined relations (column 6), and the number of probes that were relationally indeterminate (column 7).

4301

Arb-D

4351 4318 4334 4354

34 46 35 31

42 44 34 29 17 23 22 15

Arb-S

4353 4316 4304 4329 4314 4315 4313 4321

43 42 36 30 25

25

Id-D

4306 4320 4325 4330 4328

Cls-1: Exptr-Def.

4340

Conditions

Participants

Table 4. (Continued)

MEANINGFUL STIMULI EQUIVALENCE CLASSES 535

536

ERIK ARNTZEN et al. Table 5 Effect of Pre-training on Average Number of Probes Producing Participant-, Experimenter- or the Experimenter and Participant-Defined Relations, and Probes Producing Indeterminate Relational Performances, for Those who Did Not Form Classes Delay (sec)

Response pattern

Relational type

0

6

Average

Exp-defined

Identity Arbitrary

87.4 96.6 92.0

109.4 107.5 108.5

98.4 102.1

Identity Arbitrary

17.1 15.7 16.4

30.6 23.4 27.0

23.9 19.6

Identity Arbitrary

104.5 112.3 108.4

140.0 130.9 135.6

122.3 121.7

Identity Arbitrary

73.0 67.8 70.4

40.0 49.8 44.9

56.5 58.8

Average Part-defined Average Exp and Part-defined Average Indeterminate Average Note. Numbers in bold indicate significant differences.

meaningfulness of the C-stimuli in the to-beformed equivalence classes. In addition, the acquisition of the baseline relations after preliminary training was also

900

Yes 600

No

300

*

* PI C

0

A B S Id en tit yS Id en tit yA D rb itr ar yA S rb itr ar yD

Mean Trials to Bsl Acquisition

acquiring the baseline relations for the equivalence classes was not influenced by the presence or absence of preliminary training, by type of preliminary training, or by the

Groups Fig. 3. The figure shows the mean number of trials to criterion for baseline for each group. Standard error of the means are on each data bar. ABS ¼ all abstract group; PIC ¼ C-stimuli as pictures. Identity-S and Identity-D groups indicate identity conditional discriminations with the C stimuli using simultaneous or 6 s delayed matching-to-sample procedures, respectively. Arbitrary-S and Arbitrary-D groups indicate arbitrary conditional discriminations with simultaneous or 6 s delayed matching-to-sample procedures, respectively. Yes indicates class formation and No indicates no class formation. * ¼ no participants responded in accordance with stimulus equivalence.

MEANINGFUL STIMULI EQUIVALENCE CLASSES compared with baseline acquisition when a meaningful picture was used as the C stimulus in each of the to-be-formed classes, as in the PIC condition. For participants who went on to form the equivalence classes, significantly fewer trials were needed to acquire the baseline relations in the preliminary training groups than in the PIC group, t(16) ¼ 1901, p ¼ .015. For participants who did not go on to form the equivalence classes, the difference was not significant, t (30) ¼ −1.502, p ¼ .079. Finally, the acquisition of the baseline relations after preliminary training was also compared to baseline acquisition when no preliminary training was conducted, as in the ABS condition. For participants who did not form the equivalence classes, there was no significant difference in the number of trials needed to acquire the baseline relations, t (37) ¼ -.640, p ¼.411. Response speed. The strength of a stimulus– stimulus relation can be measured using response speed—the reciprocal of the time that separates the response to the sample stimulus and the selection of a comparison stimulus (e.g., Imam, 2001; Reilly, Whelan, & Barnes-Holmes, 2005; Spencer & Chase, 1996). Figure 4 shows response speed for the last five baseline trials at the end of training, and the first five trials in each of the two derived relations test halves; data are separated into trials in which correct and incorrect responses

537

were made. Data were averaged across participants, groups, and regardless of class formation because none of these factors had systematic effects on response speed. The introduction of the novel relations in the derived relations test block slowed down response speed, regardless of the correctness of responding. Additional testing resulted in an increase in response speed for trials that produced correct responding but not to the level seen during baseline training. In contrast, response speed produced by incorrect responding returned to the level produced by the same type of trials during training. When correct choices were made, response speed was faster than for incorrect responses at the end of baseline, t(5) ¼ 7.319, p ¼ .001, and during the first, t(5) ¼ 3.773, p ¼ .013, and second halves of derived relations testing, t (5) ¼ 7.172, p ¼ .001. Relative to baseline, response speed was significantly slower during the first test half, t (22) ¼ 5.877, p < .0001, and the same was true in the second test, but only for correct responses, t(10) ¼ 5.245, p < .0001. Finally, response speeds were faster during the second half of the test than during the first part, t(22) ¼ −4.761, p < .0001. This was so for trials that occasioned correct selections and for those that occasioned incorrect selections

Discussion Bsl

Response Speed (s)

0.5

Test half 1

Test half 2

0.4 0.3 0.2 0.1 0.0

C

I

C

I

C

I

Type of Responses Fig. 4. Average comparison-response speed (i.e., 1/ latency) during baseline and in the first and second half of the test for emergent relations; error bars show standard error of the mean. Data are aggregated across groups and separated by correct (C) and incorrect (I) responses.

None of the participants responded in accordance with stimulus equivalence when all of the class members were abstract stimuli (ABS group), whereas 80% of participants did when the middle node was a meaningful picture and the other class members were abstract stimuli (PIC group). These findings are similar to those reported by others (Fields et al., 2012). This experiment also demonstrated that class enhancement was directly related to the delay that separated the termination of sample stimuli and the presentation of the comparison stimuli in the identity and arbitrary relations that were established prior to class formation. In contrast, the enhancement of class formation was influenced only slightly by the type of relation established with the C stimuli prior to class formation: Perhaps there was somewhat

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ERIK ARNTZEN et al.

greater enhancement by the prior establishment of C-based arbitrary relations than identity relations. In addition, none of the pre-classformation operations enhanced class formation as much as the inclusion of a meaningful stimulus in the to-be-formed class. Finally, for the participants who did not form classes, the number of probes that produced participantand experimenter-defined relations in the derived relations tests, as well as those producing indeterminate performances, were influenced by the delay that characterized the relations established in preliminary training and but not by the type of relation established during preliminary training. Fields et al. (2012) and Travis et al. (2014) have shown that likelihood of equivalence class formation increases by the prior acquisition of simultaneous and successive discriminative functions. In addition, Travis et al. (2014) showed that class enhancement was a positive function of the amount of pre-class-formation overtraining of simple successive discriminations. The present experiment showed that the establishment of identity or arbitrary conditional relations on a delayed basis also enhanced the likelihood of subsequent equivalence class formation. Taken together, these data support the more general view that enhancement of class formation produced by the inclusion of a meaningful stimulus may reflect the stimulus control functions served by a meaningful stimulus rather than, or in addition to its denotative and connotative properties. The results of the present experiment replicated and extended the findings reported by Arntzen et al. (2014). In both experiments, the likelihood of equivalence class formation was a direct function of the delay that separated the sample and comparisons in the previously established identity conditional relations. Thus, the present experiment replicated the main finding of Arntzen et al. (2014). Because that experiment did not explore the effect of delay using arbitrary instead of identity conditional relations, its findings could not be used to determine whether the effect of delay on class enhancement was limited to identity relations alone, or whether it was a more general effect. The present experiment addressed that issue, and demonstrated that increases in delay had a similar class enhancing effect regardless of the type of relation that was established prior to class formation training. Thus, the class

enhancing effect of delay was not restricted to the establishment of a particular type of conditional relation. Nedelcu, Fields, and Arntzen (2015) reported that the prior establishment of a single arbitrary conditional relation (e.g., C-X) produced a small increment in the likelihood of forming new equivalence classes that consisted of stimuli represented by the letters A, B, C, D, and E. That conditional relation was also established using a simultaneous matching-tosample paradigm. The present experiment, then, replicated the findings reported by Nedelcu et al. (2015) thereby demonstrating the reliability of the finding. Because all the relations involved in equivalence class formation were arbitrary relations, we postulated that the prior training of arbitrary relations would enhance subsequent equivalence class formation relative to the prior formation of identity relations. Clearly that was not the case; the prior establishment of arbitrary relations produced no significant increment in class formation relative to the prior formation of identity relations. Thus, formal similarity between the type of relation established prior to class formation and the relations included in subsequently formed equivalence classes was not responsible for inducing class enhancement. These results also imply that the class-enhancing property of a meaningful stimulus cannot be attributed to types of relational functions served by meaningful stimuli. The empirical outcome also implies that the processes that induce a class-enhancing property to stimuli was active during the pre-class-formation establishment of identity and arbitrary relations. Additional research will be needed to identify those processes. Delay and Working Memory In the simultaneous matching- to-sample procedure used to establish the baseline relations, the sample and comparison stimuli in a trial were concurrently present, and likelihood of class formation was relatively low. In comparison, likelihood of class formation was much higher when the 6 s delay separated the offset of the sample stimuli and onset of the comparison stimuli used during baseline training. These results raise a question regarding the enhancement effects of delays

MEANINGFUL STIMULI EQUIVALENCE CLASSES between the 0 s and 6 s values used in the present experiment and the invocation of working memory (see Baddeley, 2007 on details about working memory) as a process involved in the enhancement of equivalence class formation. In a typical preparation (e.g., Drover, 2014; Fassihi, Akrami, Esmaeili, & Diamond, 2014), working memory is studied by the presentation and termination of one stimulus for X s, which is followed by the presentation of a second stimulus T s after the termination of the X stimulus. Finally, a participant has to respond in a manner that indicates the first presented stimulus. When the value of T is varied, in general, high levels of response accuracy occur when delay intervals are in the 6 s range and remain relatively high as delay interval declines to about 3 s, after which level of recall drops substantially. Thus, there is a 2-point correlation between accuracy of responding in the working memory experiments and likelihood of class formation in the present experiment. These results, then, suggest that working memory might influence equivalence class formation. The validity of such a correspondence can be evaluated by studying class formation after the training of baseline relations with delays ranging between 6 s and 0 s. If working memory is a determinant of class formation, we would expect to find high yields using delays in baseline training as small as 3 s and substantial declines with delays below 3 s. Additional research will be needed to assess these predictions. A positive outcome would extend the conceptual linkage between factors that influence equivalence class formation and working memory. Stimulus-control Topography and Failed Class Formation The preliminary training procedures used in the present experiment induced responding in the derived relations tests that were controlled by relations among stimuli, some of which were consistent with the experimenter-defined classes, and others that were relationally controlled but not by the two stimuli from the same experimenter-defined class. These phenomena could be accounted for by a consideration of Stimulus Control Topography Coherence Theory (Mcllvane & Dube, 1992). According to this theory, when conditional discrimination training

539

is conducted, the contingencies of reinforcement can establish a variety of forms of stimulus control, some of which are relational but are not consistent with the experimenter defined stimulus–stimulus relations; each form of control is referred to as a stimulus control topography (SCT). Fields, Garruto, and Watanabe (2010) showed that 16 SCTs could emerge during the establishment of an arbitrary conditional relation trained with trials that contained two comparison stimuli. Two of these STCs are conditional relations that contain stimuli from the same experimenter-defined sets, such as X1-Y1 or X2Y2, and conditional relations that contain stimuli from different experimenter-defined sets such as X1-Y2 or X2-Y1. In that study, the authors documented the transient emergence of up to five SCTs during the course of acquiring arbitrary conditional relations. After acquisition, all of the SCTs that emerged during training could resurge during tests for the emergence of novel conditional relations. These processes are probably reflected in the emergence of the different patterns of responding noted in Table 4 for the participants who did not form the equivalence classes, but rather showed the presence of experimenter-defined conditional relations on some trials (of the form X1-Y1) and the presence of participantdefined conditional relations on other trials (of the form X1-Y2). Stimulus control topography and response speed. A stimulus control topography analysis is also relevant to the interpretation of the response speed data obtained in the present experiment. Specifically, response speed decreased at the start of testing compared to response speed during baseline training, and then became faster later in testing. These outcomes replicated previously reported results (Arntzen, Braaten, Lian, & Eilifsen, 2011; Arntzen & Hansen, 2011). In all three experiments, the slowing of response speed with the introduction of testing could have been due to the novelty of the derived relations probes administered at the start of testing. During the course of testing, the probes were repeated a number of times and became familiar. Thus, the subsequent increase in response speed could be attributed to an acquired familiarity with the probes when presented later in testing. Furthermore, response speed was much faster for correct than incorrect responses. This disparity could reflect the influence of the number of

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stimulus control topographies that influenced responding on trials that were terminated with correct and incorrect selections (Mcllvane & Dube, 1992). Specifically, it is plausible to assume fast response speeds occurred on trials that produced correct responding because responding was determined by only one stimulus control topography. Conversely, the slower response speeds that occurred on trials that produced incorrect responding were determined by a variety of conflicting stimulus control topographies. Finally, because there were no systematic differences in the patterns of response speed across the conditions in the present experiment, it is plausible to conclude that the parameters that influenced the likelihood of equivalence class formation in the present experiment did not influence the mix of stimulus control topographies that controlled response speed. While speculative, these assumptions could be assessed empirically by measuring the stimulus control topographies active on all trials during the derived relations tests (Fields et al., 2010). References Arntzen, E., (2004). Probability of equivalence formation: Familiar stimuli and training sequence. The Psychological Record, 54, 275–291. Retrieved from http://thepsychologicalrecord.siuc.edu/index.html Arntzen, E., Braaten, L. F., Lian, T., & Eilifsen, C. (2011). Response-to-sample requirements in conditional discrimination procedures. European Journal of Behavior Analysis, 12, 505–522. Retrieved from http://www. ejoba.org/ Arntzen, E., Grondahl, T., & Eilifsen, C. (2010). The effects of different training structures in the establishment of conditional discriminations and the subsequent performance on the tests for stimulus equivalence. The Psychological Record, 60, 437–462. Retrieved from http://thepsychologicalrecord.siuc.edu/index.html Arntzen, E., & Hansen, S. (2011). Training structures and the formation of equivalence classes. European Journal of Behavior Analysis, 12, 483–503. Retrieved from http:// www.ejoba.org/ Arntzen, E., & Lian, T. (2010). Trained and derived relations with pictures as nodes. The Psychological Record, 60, 659–677. Retrieved from http://thepsychologicalrecord.siuc.edu/index.html Arntzen, E., Nartey, R. K., & Fields, L. (2014). Identity and delay functions of meaningful stimuli and enhanced equivalence class formation. The Psychological Record, 64, 349–360. 10.1007/s40732-014-0066-3 Baddeley, A. (2007). Working memory, thought, and action. New York, NY: Oxford University Press. Buffington, D. M., Fields, L., & Adams, B. J. (1997). Enhancing equivalence class formation by pretraining of other equivalence classes. The Psychological Record, 47, 69–96. Retrieved from http://thepsychologicalrecord. siuc.edu/index.html

Dickins, D. W., Bentall, R. P., & Smith, A. B. (1993). The role of individual stimulus names in the emergence of equivalence relations: The effects of interpolated paired-associates training of discordant associates between names. The Psychological Record, 43, 713– 724. Drover, J. D. (2014). Timing over tuning: Overcoming the shortcomings of a line attractor during a working memory task. PLoS Computational Biology, 10, e1003437. 10.1371/journal.pcbi.1003437 Fassihi, A., Akrami, A., Esmaeili, V., & Diamond, M. E. (2014). Tactile perception and working memory in rats and humans. Proceedings of the National Academy of Science USA, 111, 2331–2336. 10.1073/pnas.1315171111 Fields, L., Arntzen, E., Nartey, R. K., & Eilifsen, C. (2012). Effects of a meaningful, a discriminative, and a meaningless stimulus on equivalence class formation. Journal of the Experimental Analysis of Behavior, 97, 163–181. 10.1901/jeab.2012.97-163 Fields, L., Garruto, M., & Watanabe, M. (2010). Varieties of stimulus control in matching-to-sample: A kernel analysis. The Psychological Record, 60, 3–26. Retrieved from http://thepsychologicalrecord.siuc.edu/ Fields, L., & Verhave, T. (1987). The structure of equivalence classes. Journal of the Experimental Analysis of Behavior, 48, 317–332. 10.1901/jeab.1987. 48-317 Grehan, P. M. (1998). Depressed subjects’ formation of mood congruent and incongruent equivalence relations. Unpublished doctoral dissertation. Hofstra University, Hempstead, New York. Imam, A. A. (2001). Speed contingencies, number of stimulus presentations, and the nodality effect in equivalence formation. Journal of the Experimental Analysis of Behavior, 76, 265–288. 10.1901/ jeab.2001.76-265 Leslie, J. C., Tierney, K. J., Robinson, C. P., Keenan, M., & Watt, A. (1993). Differences between clinically anxious and non-anxious subjects in a stimulus equivalence training task involving threat works. The Psychological Record, 43, 153–161. Retrieved from http://thepsychologicalrecord.siuc.edu/index.html Mcllvane, W. J., & Dube, W. V. (1992). Stimulus control shaping and stimulus control topographies. The Behavior Analyst, 15, 89–94. Retrieved from http:// www.abainternational.org/TBA.asp Nartey, R. K., Arntzen, E., & Fields, L. (2014). Enhancement of equivalence class formation by pre-training discriminative functions. Learning & Behavior. 10.3758/s13420014-0158-6 Nedelcu, R. I., Fields, L., & Arntzen, E. (2015). Conditional discriminative functions of meaningful stimuli and enhanced equivalence class formation. Journal of the Experimental Analysis of Behavior, 103, 349–360. 10.1002/ jeab.141 Plaud, J. J. (1995). The formation of stimulus equivalences: Fear-relevant versus fear-irrelevant stimulus classes. The Psychological Record, 45, 207–222. Retrieved from http://thepsychologicalrecord.siuc.edu/index. html Reilly, T., Whelan, R., & Barnes-Holmes, D. (2005). The effect of training structure on the latency of responses to a five-term linear chain. The Psychological Record, 55, 233–249. Sidman, M. (1994). Equivalence relations and behavior: A research story. Boston, MA: Authors Cooperative.

MEANINGFUL STIMULI EQUIVALENCE CLASSES Spencer, T. J., & Chase, P. N. (1996). Speed analysis of stimulus equivalence. Journal of the Experimental Analysis of Behavior, 65, 643–659. 10.1901/ jeab.1996.65-643 Travis, R. W., Fields, L., & Arntzen, E. (2014). Discriminative functions and over-training as class-enhancing determinants of meaningful stimuli. Journal of the Experimental Analysis of Behavior, 10.1002/jeab.91 Tyndall, I. T., Roche, B., & James, J. E. (2004). The relation between stimulus function and equivalence class

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formation. Journal of the Experimental Analysis of Behavior, 81, 257–266. 10.1901/jeab.2004.81-257 Watt, A., Keenan, M., Barnes, D., & Cairns, E. (1991). Social categorization and stimulus equivalence. The Psychological Record, 41, 33–50. Retrieved from http:// thepsychologicalrecord.siuc.edu/index.html Received: October 4, 2014 Final Acceptance: March 24, 2015

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