Assessment of the relatedness of equivalent stimuli through a semantic differential.

A conditional discrimination establishes a relation between a set of two or more samples (e.g., Al, A2, ... An) and a set of two or more comparison stimuli (e.g., B1, B2, ... Bn), so that in the presence of sample An, selections of comparison stimulus Bn are reinforced, whereas selections of any other comparison stimulus are unreinforced. Such a conditional discrimination is conventionally designated as AB, whereas the sets of samples and comparisons are designated as A and B, respectively. Sidman and Tailby (1982) showed that conditional discriminations learned by humans are usually equivalence relations, possessing the mathematical properties of reflexivity, symmetry, and transitivity. According to Sidman and Tailby (see also Sidman, 1994, 2000), equivalence relations are symbolic. Therefore, if conditional discriminations such as AB and BC are shown to be equivalence relations, the related stimuli (An, Bn, and Cn) comprise classes of equivalent stimuli and each member of the class may be considered a symbol of the others.

Mathematically, equivalent stimuli are, by definition, equally related to each other. However, Fields and colleagues have provided evidence that stimuli that are members of equivalence classes may differ in their degree of "relatedness," as a function of several experimental parameters (e.g., Belanich & Fields, 2003; Fields, Adams, Verhave, & Newman, 1993; Fields, Landon-Jimenez, Buffington, & Adams, 1995; Fields et al., 1997).

Fields et al. (1993) suggested a procedure for investigating quantitative variations in the relatedness of equivalent stimuli. According to the authors, the relatedness of equivalent stimuli must be evaluated with methods that are alternative or complementary to the tests of emergent conditional discriminations traditionally employed. In fact, these tests involve only forced choices among discrete alternatives; consistent performances reveal that the participant established a contextualized equivalence among the related stimuli, but these performances do not permit a verification of quantitative differences in the relations. One possible strategy for assessing the relatedness of equivalent stimuli would involve measurement of the transfer of functions established between them. Many studies have shown that a function acquired by a member of an equivalence class will transfer to other class members (e.g., Barnes-Holmes, Keane, Barnes-Holmes, & Smeets, 2000; de Rose, McIlvane, Dube, Galpin, & Stoddard, 1988; de Rose, McIlvane, Dube, & Stoddard, 1988; Dougher, Augustson, Markham, Greenway, & Wulfert, 1994; Hayes, Kohlenberg, & Hayes, 1991). Variations in the amount of transfer would indicate variations in the relatedness of equivalent stimuli. This approach was first used to investigate the influence of the number of nodes on the relatedness of equivalent stimuli (Fields et al., 1993, 1995). A node is a stimulus that is related to two other stimuli in an equivalence class and, therefore, connects them. For example, given a training AB and BC, B is a node because it links A and C. Likewise, given a training AB, BC, and CD, the stimuli B and C are nodes because they link A and D. Fields and colleagues established specific functions for members of equivalence classes and showed that the degree of transfer was inversely proportional to the number of nodes between stimuli.

The present work attempted to assess the relatedness of equivalent stimuli using a semantic differential device (Osgood, Suci, & Tannenbaum, 1957). Such device was employed to investigate influences of the trial structure (Experiment 1) and also the nodal number (Experiment 2) on the transfer of functions established between equivalent stimuli. The semantic differential is a technique used to measure the meaning of "concepts" (words, locutions, pictures, figures, etc.). Simply stated, a concept is presented and participants have to assign Likert-type values ranging usually from -3 to +3 along many scales that are anchored by opposite adjectives (e.g., good and bad). Indifference related to any pair of adjectives is valuated as 0. The measurement of meaning is based on the scatter of the scale values. This assessment device allows registering, quantifying, and comparing the meanings of one or many concepts, to one or many participants, in one or many situations.

If the assumption is correct that stimulus equivalence provides the basis for semantic or symbolic meaning (Sidman, 1994, 2000), an originally meaningless stimulus that becomes equivalent to a meaningful one should acquire a similar meaning. The two experiments described here attempted to investigate the level of such transfer of meaning employing the semantic differential.

Some studies have demonstrated that Likert-type scales are efficient devices to investigate transfer of functions in equivalence classes (e.g., Barnes-Holmes et al., 2000). Thus, we expected that the semantic differential would be sensitive to changes in meaning induced by equivalent relations. Moreover, we expected that the semantic differential would provide a quantitative measure of the level of such transfer of meaning that could be used to assess the effects of training and testing parameters, such as the trial structure and the nodal number, on the relatedness of equivalent stimuli.

The two experiments in the present study employed the same generic design. First, participants of two experimental groups established three equivalence classes comprising pictures of human faces expressing emotions (presumed meaningful stimuli) and abstract pictures (presumed meaningless stimuli). Then, they evaluated some of the abstract stimuli through a semantic differential, and these evaluations were compared to the evaluations of the faces made by a control group. Faces expressing emotions were used as experimentally meaningful stimuli because they are regarded as naturally salient stimuli for humans and other primates in the communication of social and emotional signs (Parr, Winslow, Hopkins, & de Waal, 2000). As documented by Ekman and colleagues (Ekman, 1972; Ekman, Sorenson, & Friesen, 1969) and confirmed in many other studies (e.g., Dimberg, Thunberg, & Grunedal, 2002; Ohman, 2002), humans are able to produce, recognize, and interpret different facial gestures with great efficiency.

Experiment 1

For the present study, a control group and two experimental groups evaluated stimuli through a set of bipolar Likert scales. Participants in the control group received no conditional discrimination training. The semantic differential was used to evaluate abstract stimuli as well as pictures of happy, angry, and neutral human faces. Participants in the experimental groups received conditional discrimination training to establish three equivalence classes composed of pictures of faces with expressions indicative of happiness, anger, or neutrality. Each class also included three other visual stimuli that were arbitrary glyphs. Comparisons of the scale values in the semantic differential evoked by the faces and the arbitrary glyphs provided a quantitative assessment of the relatedness of equivalent stimuli. These comparisons were made when the classes were established using one of two different trial formats: simultaneous matching to sample and delayed matching to sample. These formats were used for training trials and for the derived relations test trials.

Method

Participants

Participants were 39 undergraduates: 24 in a control group and 15 in two experimental groups, labeled "simultaneous group" (n = 8) and "delayed group" (n = 7). All participants were freshmen in an undergraduate psychology program in a Brazilian university. Their native language was Portuguese, and they were not familiar with stimulus equivalence or related phenomena and concepts.

Equipment, Setting, and Stimuli

An Apple Macintosh microcomputer Performa 6320 presented stimuli and recorded responses using the MTS software (V. 10.32; Dube & Hiris, 1997). Each trial displayed five white windows (6 cm x 6 cm) on the gray screen, one at the center and one near each of the monitor's corners. Participants responded by moving the computer's mouse to position a cursor on a window and then clicking the mouse's button.

Sessions were conducted in a 2-m x 3-m laboratory room and were approximately 40 to 50 min long. Participants of the experimental group also filled semantic differential scales in this room. The control group filled semantic differential scales in their classroom. Participation in the research was a course requirement, although students could choose not to participate. All students agreed to participate and did not receive any programmed reinforcement other than differential feedback provided in experimental trials.

Figure 1 presents the stimuli employed in the experiment. Set A comprised 12 pictures: 4 angry faces (A1), 4 neutral faces (A2), and 4 happy faces (A3). Sets B, C, and D comprised 3 abstract pictures each.

[FIGURE 1 OMITTED]

The pictures were extracted from the Pictures of Facial Affect[C] CD-ROM, purchased from Paul Ekman's website (www.paulekman.com). Several pictures of human faces depicting expressions of happiness, anger, disgust, fear, surprise, and sadness are recorded on this CD-ROM. The pictures selected for this study were judged to be expressions of happiness and anger by 100% of the judges who evaluated the faces.

Procedure

Phase 1: Establishment of equivalence classes. Each matching-to-sample trial began with the presentation of the sample stimulus in the central window. For the simultaneous group, a click on this window produced a set of three comparison stimuli, one in each of three of the peripheral windows. The other peripheral window remained blank, and the sample remained on the central window. For the delayed group, a click on the central window removed the sample and, after a delay of 2 s, produced the presentation of the three comparison stimuli. A click on the window containing the stimulus designated as correct produced a sequence of tones and a display of stars moving on the computer screen. Incorrect responses blackened the screen for 3 s. The consequence for a correct or an incorrect response ended the trial, and, after a 2-s intertrial interval, a new trial began.

Participants learned conditional discrimination AB first. Training began with a block of 36 AB trials in which samples A1, A2, and A3 were presented 12 times each, in a randomized sequence. Sample A1 could be any one of the angry faces, according to a randomized sequence. In a similar fashion, sample A2 could be any one of the neutral faces and sample A3 could be any one of the happy faces. The positions of the comparison stimuli were determined according to a randomized sequence. In the first 12 trials of this block, a written prompt appeared on the screen. The Portuguese equivalent of the phrase "When this is here" appeared above the sample, and the Portuguese equivalent of "Choose this" appeared above the correct comparison. These 12 trials were followed by 24 trials without these prompts. If the learning criterion (correct choices in all of the 36 trials) was not achieved, the block was repeated. AB teaching ended when this criterion was attained, and teaching of the AC relation began, with a similar procedure. When the participant made correct choices in all AC trials, CD training started, with a similar procedure. Each of these blocks--AB, AC, and CD--could be repeated for a maximum of three times. If the participant did not achieve criterion in three presentations of a block, she or he was dismissed.

The next block verified maintenance of the cumulative baseline (AB, AC, and BC) and mixed 12 trials of each of these conditional relations, comprising, therefore, 36 trials in a randomized sequence. This block, with a different trial sequence, was repeated (for a maximum of three times) until the participant made no more than one incorrect selection.

Cumulative baseline maintenance. When this criterion was achieved, the Portuguese equivalent of the message "The computer will no longer signal if your choices are correct or wrong" was displayed on the screen and the cumulative baseline block was repeated without differential consequences for correct and incorrect responses, until participants made no more than one error. If the participant made wrong choices in more than five trials, he or she returned to the cumulative baseline with differential consequences.

Two blocks of 24 probe trials without differential consequences tested equivalence class formation. The first block evaluated the emergence of the BD derived relation. It was followed by the cumulative baseline block without differential consequences. Finally the second probe block tested emergent conditional discrimination DB. In this arrangement, equivalence classes could be tested without the presentation of the faces. Figure 2 shows a schematic representation of the trained and tested relations in this phase.

[FIGURE 2 OMITTED]

The next phase was conducted only with participants who made no more than one error in each probe block. These participants met the criterion used to conclude that they formed happy, angry, and neutral equivalence classes. The others ended their participation.

Phase 2: Evaluation of the stimuli through the semantic differential. Participants who met the equivalence criterion were instructed to evaluate the abstract stimuli D1, D2, and D3 through the semantic differential. Each scale comprised seven intervals and was anchored in its two extremities by "polar terms" (a pair of opposite adjectives). The scales represented a series of continua, each going from an adjective to its opposite. The set of scales was printed on an A4 sheet that also depicted one of the "D" stimuli, as represented in Figure 3.

[FIGURE 3 OMITTED]

The participants received four sheets, the first one containing instructions to fill in the scales (see Appendix A). Each of the three other sheets displayed, above the set of bipolar scales, stimulus D1, D2, or D3. For all participants, the sheet immediately after the instructions displayed stimulus D2, equivalent to the neutral expression. The other sheets displayed D1 (equivalent to the angry expression) and D3 (equivalent to the happy expression) in an order that varied between participants.

Control Group. Participants of the control group received the same instructions and were asked to evaluate both the stimuli of set D and all the pictures of faces expressing emotions. The control group did not have conditional discrimination training.

Data Analysis. The intervals in all of the scales received a value that varied from -3 to +3. The value of -3 was assigned to the position closest to the negative adjective, and the value of +3 was assigned to the position closest to the positive adjective. For presentation convenience, Figure 3 shows the adjectives considered negative on the left and the ones considered positive on the right, and the respective values are printed below the scales. In the sheets given to participants, the values were not printed and the position of the adjectives was randomized.

For each D stimulus, therefore, each participant made a judgment on 13 scales. Each judgment was assigned a value from -3 to +3. The 13 evaluations that a participant made for each particular stimulus were averaged, so that a mean evaluation for each stimulus was computed for each participant. The evaluations were then averaged for the participants of each group. Therefore, for each emotional expression, a mean value was obtained from the control group. For each of the D stimuli, mean values were obtained from the control group, the simultaneous group, and the delayed group.

Results and Discussion

All seven participants from the delayed group and seven out of eight participants from the simultaneous group attained criterion for equivalence class formation. For these 14 participants, the semantic differential was employed to evaluate the D stimuli in each equivalence class. Figure 4 shows the individual evaluations of the stimuli D1 and D3 made by the participants of the delayed and simultaneous groups. The medians of these individual evaluations and the medians of the evaluations of the happy and angry faces by the control group are also presented in Figure 4.

[FIGURE 4 OMITTED]

For the participants in the control group, the semantic differential was used to evaluate the pictures of faces expressing emotions and also the D stimuli. The average values of the angry and happy faces by the control group were, respectively, positive and negative. As expected, the evaluation of the D stimuli by the control group did not deviate much from neutrality. In contrast, when the D stimuli in the experimental group were considered, the picture equivalent to the angry faces (D1) received more positive evaluations and the picture equivalent do the happy faces (D3) received more negative evaluations.

The averages of all evaluations of the faces and of the equivalent pictures were submitted to an ANOVA (one-way) that found significant differences between them (p = .0083). Results were subjected to a Dunnett Multiple Comparison Test to seek differences among the values attributed to the faces by the control group and to the pictures by each experimental group separately. Differences between the evaluations of the pictures by the delayed group and the evaluations of the faces by the control group were not significant (p > .05); differences between the evaluations made by the simultaneous group and the evaluations of the faces were significant (p < .05). The statistical analyses were conducted using version 3.01 of GraphPad InStat[R] software.

Osgood et al. (1957) claimed that meaning has several dimensions, extracted through factor analysis of semantic differential data. The most salient, according to their analysis, were the evaluative, potency, and activity dimensions. Although a factor analysis was not conducted on the present data, most scales used in the present study can be perceived as being related to the evaluative dimension, that is, the extent to which stimuli were judged as positive or negative. In this regard, scales such as poor-rich, slow-fast, and dominant-submissive can be viewed as largely irrelevant for this dimension and were used mostly to mask the task so that it would not be viewed immediately as a "positive-negative" or "good-bad" evaluation. A data analysis disregarding these scales was conducted and yielded very similar data, with slightly larger absolute values. Therefore, these scales were maintained in data analysis.

The use of semantic differential scales in the present study demonstrated that abstract stimuli, originally without meaning, acquired meanings similar to those of the facial expressions with which they became related, through equivalence class formation. Happy faces and the stimuli equivalent to them were judged positively, whereas angry faces and stimuli equivalent to them were judged negatively. These data may confer external validity to stimulus equivalence as a model of meaning. Furthermore, the comparison between values attributed to the faces and to the pictures generated a quantitative assessment of transfer of functions that can be used to estimate the relatedness of these stimuli. Results revealed that "generalization or transfer of meaning" was stronger when the relations were trained with a delayed matching-to-sample procedure. These data suggest that the methodology employed here may be useful for the investigation of quantitative parameters of equivalence relations. The extent to which the meaning (evaluated by the semantic differential) of meaningful stimuli is imparted to abstract stimuli equivalent to them may be taken as a quantitative measure of the relatedness of the abstract stimuli to the meaningful ones. The second experiment described in this article used this methodology to evaluate influences of the delay parameter and the number of nodes on the relatedness of equivalent stimuli.

Experiment 2

The purpose of this study was to use the semantic differential to assess effects of nodal distance, in seven-member equivalence classes established through a linear design. The semantic differential was used to evaluate stimuli one node distant from the faces and three nodes distant from the faces. If relatedness decreases with nodal distance, this would be revealed by comparing the evaluations of the faces and of abstract stimuli distant one and three nodes from the faces.

As in the previous experiment, participants of two experimental groups received conditional discrimination training to establish three equivalence classes comprising pictures of faces expressing emotions and abstract stimuli. In this study, however, each class included seven members: the faces and six different arbitrary glyphs. Semantic differential values evoked by the faces (values from the control group in Experiment 1) were compared to values evoked by pictures after equivalence class formation, after simultaneous or delayed matching to sample.

Method

Participants

Experimental participants were 44 undergraduates: 28 in the simultaneous group and 16 in the delayed group. Their native language was Portuguese, and they were not familiar with stimulus equivalence or related phenomena and concepts.

Equipment, Setting, and Stimuli

An Apple Macintosh G4 microcomputer presented stimuli and recorded responses using the MTS software (V. 10.32; Dube & Hiris, 1997). Sessions were conducted in a 2-m x 3-m laboratory room and were approximately 40 min to 1 h long. Participants filled semantic differential scales in this room. Figure 5 presents the stimuli employed in the experiment. Set A comprised 12 pictures: 4 angry faces (A1), 4 neutral faces (A2), and 4 happy faces (A3). Sets B, C, D, E, F, and G comprised three abstract pictures each.

[FIGURE 5 OMITTED]

Procedure

The procedure of this study was similar to that of Experiment 1, except for the number of stimuli in the classes and a few differences in each of the two experimental phases.

Phase 1: Establishment of equivalence classes. The participants of the simultaneous and delayed groups were exposed to two experimental sessions that were separated by a 10-min break. In the first session, participants learned the conditional discriminations AB, AC, CD, DE, EF, and FG in separate blocks of 36 trials each. The second session started with a cumulative baseline training block that assessed the maintenance of responding produced by the learned relations. This block presented 12 trials each, of AB, AC, CD, DE, EF, and FG relations in a randomized sequence. The block was repeated with a different sequence of trials until the participant made no more than two incorrect selections. When this criterion was achieved, the Portuguese equivalent of the message "The computer will no longer signal if your choices are correct or wrong" was displayed on the screen and the cumulative baseline block was repeated without differential consequences for correct and incorrect responses, until participants made no more than two errors. If the participant made wrong choices in more than five trials, she or he returned to the cumulative baseline training block, with differential consequences. Then, two blocks of 24 probe trials without differential consequences tested equivalence class formation. The first block evaluated the emergence of the BG derived relation. It was followed by the cumulative baseline block without differential consequences. Finally, the second probe block tested emergent conditional discrimination GB. In this arrangement, equivalence classes could be tested without the presentation of the faces. Figure 6 shows a schematic representation of the trained and tested relations in this phase.

[FIGURE 6 OMITTED]

The next phase was conducted only with participants who met the criterion for equivalence class formation: no more than two errors in each probe block. To ensure that 12 participants in each group would proceed to the next phase, more participants had to be recruited for the simultaneous group than for the delayed group (28 and 16, respectively)

Phase 2: Evaluation of the stimuli through the semantic differential. Half of the participants who met the equivalence criterion in each group were instructed to evaluate the abstract stimuli D1, D2, and D3 (one node from the faces) through the semantic differential. The other participants were instructed to evaluate stimuli F1, F2, and F3 (three nodes from the faces) through the same device.

Results and Discussion

Participants who were trained with delayed matching to sample demonstrated better performance in the probe blocks than participants submitted to simultaneous matching to sample. Thus, more participants had to be recruited for the simultaneous group. Table 1 presents, for each group, the number of participants who formed equivalence classes, who did not meet the criterion in the probe blocks, and who did not advance beyond the baseline blocks.

Table 1.

Establishment of Equivalence Classes: Number (and Percentage) of
Participants in Each Condition

Condition                                  Delayed    Simultaneous
                                            group        group

Established equivalence classes            12 (75%)    12 (43%)
Did not reach criteria in probe blocks      3 (19%)    12 (43%)
Did not reach criteria in baseline blocks   1 (6%)      4 (14%)
Total                                      16 (100%)   28 (100%)

To ensure that 12 participants formed equivalence classes in each group, 16 students had to be recruited for the delayed group and 28 for the simultaneous group. This indicates that the use of delayed matching to sample can increase probability of emergence of derived relations consistent with the formation of equivalence classes. Two recent works have presented data supporting this hypothesis. Arntzen (2006) trained AB and CB relations and verified that the probability of consistent responses in a CA test increased as a function of the delay value. Vaidya and Smith (2006) showed that consistent responses in symmetry tests occur in a higher proportion when the relations are trained with delayed matching-to-sample procedures. The data from the present study provide further support for the view that delayed matching favors the establishment of equivalence classes in a multinodal structure.

Figure 7 shows the individual evaluations of stimuli D1 and D3 (one node from the faces) made by six participants of the delayed and simultaneous groups. The medians of these individual evaluations and the medians of the evaluations of the happy and angry faces by the control group are also presented in Figure 7.

[FIGURE 7 OMITTED]

The average values of the happy and angry faces by the control group were, respectively, positive and negative. Similarly, the D stimulus equivalent to the happy faces was positively evaluated and the D stimulus equivalent to the angry faces was negatively evaluated by the two experimental groups.

Figure 8 shows the individual evaluations of stimuli F1 and F3 (three nodes from the faces) made by six participants of the delayed and simultaneous groups. The medians of these individual evaluations and the medians of the evaluations of the happy and angry faces by the control group are also presented in Figure 8.

[FIGURE 8 OMITTED]

The figure shows that F stimuli were not evaluated similarly to the faces. This is especially clear for the stimuli equivalent to the happy faces. Their evaluations were very similar to the evaluations of these stimuli made by the control group. Therefore, although the F stimuli were equivalent to the faces, their evaluation through the semantic differential approached neutrality. Evaluations of the F stimuli equivalent to the angry faces were not so clearly similar to those made by the control group. This is particularly so for the delayed group. However, evaluations of the F stimuli were clearly less similar to the evaluations of the angry faces than the evaluations of the D stimuli.

The averages of all evaluations of the faces and of the equivalent stimuli were submitted to a one-way ANOVA that found significant differences between them (p < .0001). Results were then subjected to a Dunnett Multiple Comparison Test to seek differences among the values attributed to the faces by the control group and to the D and F pictures by each experimental group separately. Differences between the evaluations of the D stimuli by the delayed group and the evaluations of the faces by the control group were not significant (p > .05); differences between all the other evaluations were significant. The statistical analyses were conducted using version 3.01 of GraphPad InStat[R] software.

General Discussion

Stimulus equivalence was proposed as a model to infer symbolic relations from observable behaviors. Experimental demonstrations that certain functions of a stimulus can transfer to equivalent stimuli are compatible with (and strengthen) the notion that, in many contexts, we react to symbols as if they were the events they refer to. Thus, a stimulus that has certain behavioral functions can be taken as a "referent," and the stimuli equivalent to it can be regarded as "symbols" that can substitute for the referent in some occasions. Generalization or the transfer of functions among equivalent stimuli has been widely demonstrated (e.g., Barnes-Holmes et al, 2000; de Rose, Mcllvane, Due, Galpin, & Stoddard, 1988; DeRose, Mcllvane, Dube & Stoddard, 1988; Dougher et al., 1994; Hayes et al., 1991). In addition to transfer of functions, a large number of experimental studies have shown a congruence between the properties of equivalence classes and symbolic relations (e.g., Barnes-Holmes et al., 2005; Bush, Sidman, & de Rose, 1989; Saunders, Saunders, Kirby, & Spradlin, 1988; Sidman & Tailby, 1982; Wulfert & Hayes, 1988).

Although the results of stimulus equivalence studies have been robust and consistent, only a few investigations have assessed the symbolic character of equivalent stimuli through instruments that are not components of the equivalence model itself. One such instrument is the semantic differential. In the present study, the generalization of functions from faces expressing emotions to arbitrary stimuli equivalent to them was evaluated through a semantic differential. This methodology contributed to an external validation of stimulus equivalence as a model of meaning and permitted us to evaluate to what extent abstract stimuli ("symbols") acquire properties of meaningful stimuli ("referents").

The referents simulated in this study were members of perceptual classes (e.g., Fields, Matneja, Varelas, Belanich, Fitzer, & Shamoun, 2002; Fields & Moss, 2008; Fields et al., 2002). The stimuli designated as Al, A2, and A3 were not individual stimuli; rather, each comprised four pictures of faces, with each face belonging to a different person. The common feature of the faces in each category was the emotional expression, which was an angry expression in A1, a neutral one in A2, and a happy one in A3. Perceptual classes were used to ensure that abstract stimuli would be equivalent to a particular emotional expression and not to idiosyncratic aspects of a particular face.

Experiment 1 was conducted to examine whether the level of transfer of functions is influenced by the delayed presentation of the comparison stimuli in a matching-to-sample training. In effect, the results showed that transfer was more robust when classes were formed after a delayed matching-to-sample training. As mentioned, Arntzen (2006) and Vaidya and Smith (2006) provided evidence that delayed matching to sample can increase the probability of emergence of derived relations consistent with equivalence class formation. To explain such results, Arntzen argued that delayed matching to sample requires the emission (or evokes) precurrent behaviors and these behaviors would favor the establishment of derived relations. Vaidya and Smith considered that the emission of precurrent behaviors would have at least a complementary or facilitating function in this process. Precurrent behaviors are any responses that increase the probability of reinforcement for a subsequent behavior (Skinner, 1968), without being themselves required by the reinforcement contingencies. Then, we could hypothesize that during the interval between sample removal and presentation of the comparisons, the participant has to do something to increase the probability of making the correct choice--something that helps him or her "remember" the absent sample. Any precurrent behavior emitted in this situation would constitute an additional effort relative to what one has to do during simultaneous matching to sample. This additional effort during the training would facilitate the establishment of derived relations demonstrated in the tests.

The hypothesis that the participant should emit precurrcnts during the delay could also explain part of the data obtained with the semantic differential. The emission of precurrents should strengthen the learned relations. Stronger relations should generate higher transfer of functions that would be reflected in the evaluation of the stimuli. However, this effect seems to occur only with the stimuli "closer" to the faces in the nodal chain (e.g., the "D" stimuli), as verified in Experiment 2.

Experiment 2 manipulated delayed matching and the number of nodes between faces and abstract pictures. As documented in many other studies (e.g., Bentall, Jones, & Dickens, 1998; Fields et al., 1995; Kennedy, 1991; Spencer & Chase, 1996), the increase in the number of nodes negatively affected the formation of equivalence classes. In the present study, however, the nodal effect on the establishment of equivalence was much less pronounced when the relations were established by the delayed matching-to-sample procedure. But, even for participants from the delayed and simultaneous groups who demonstrated consistent performances in the tests for emergent relations, the nodal effect could be observed in the subsequent transfer test. For both groups, the evaluations of the pictures one node from the faces were similar to the evaluations of the faces (the delayed group assigned average values closer to the values assigned to the faces than the simultaneous group), whereas the evaluations of the pictures three nodes from the faces were not similar. These results support the claim by Fields et al. that the relatedness of two members of an equivalence class is an inverse function of the number of nodes comprised in the relation.

The goals of both experiments presented in this study can be articulated around a proposal to investigate quantitative properties of equivalence relations. According to Belanich and Fields (2003), the strength of the relations among equivalent stimuli can be assessed by requiring new performances that depend on class integrity. The present investigation is aligned with this suggestion. Results show that a 2-s delay can enhance and that nodal distance can decrease transfer of functions between equivalent stimuli, supporting the idea that the relatedness of stimuli can vary as a function of the experimental parameters employed. The semantic differential was sensitive to both manipulations. Tests of emergent relations conducted with matching-to-sample procedures could not reveal such differences: Matching tests can reveal the presence of an emergent relation but not any possible difference in the degree of relatedness. Different degrees of relatedness can be revealed, however, by other measures, such as latency (Fields & Moss, 2008) or transfer of functions (Fields & Watanabe-Rose, 2008). The methodology described here seems to be very sensitive to revealing such effects. It showed that relatedness varies as a function of delay and nodal distance and could possibly be used to study other parameters.

References

ARNTZEN, E. (2006). Delayed matching-to-sample: Probability of stimulus equivalence as a function of delays between sample and comparison stimuli during training. The Psychological Record, 56, 135-167.

BARNES-HOLMES, D., KEANE, J., BARNES-HOLMES, Y., & SMEETS, P. M. (2000). A derived transfer of emotive functions as a means of establishing differential preferences for soft drinks. The Psychological Record, 50, 493-511.

BARNES-HOLMES, D., STAUNTON, C., WHELAN, R., BARNES-HOLMES, Y., COMMINS, S., WALSH, D., ET AL. (2005). Derived stimulus relations, semantic priming, and event-related potentials: Testing a behavioral theory of semantic networks. Journal of the Experimental Analysis of Behavior, 84, 417-433.

BELANICH, J., & FIELDS, L. (2003). Generalized equivalence classes as response transfer networks. The Psychological Record, 53, 373-413.

BENTALL, R. P., JONES, R. M., & DICKINS, D. W. (1998). Errors and response latencies as a function of nodal number in five-member equivalence classes. The Psychological Record, 48, 93-115.

BUSH, K. M., SIDMAN, M., & DE ROSE, T. (1989). Contextual control of emergent equivalence relations. Journal of the Experimental Analysis of Behavior, 51, 29-45.

DE ROSE, J. C, MCILVANE, W. J., DUBE, W. V., GALPIN, V. C., & STODDARD, L. T. (1988a). Emergent simple discriminations established by indirect relations to differential consequences. Journal of the Experimental Analysis of Behavior, 50, 1-20.

DE ROSE, J. C, MCILVANE, W. J., DUBE, W. V., & STODDARD, L. T. (1988b). Stimulus class formation and functional equivalence in moderately retarded individuals' conditional discrimination. Behavioral Processes, 17, 167-175.

DIMBERG, U., THUNBERG, M., & GRUNEDAL, S. (2002). Facial reactions to emotional stimuli: Automatically controlled emotional responses. Cognition & Emotion, 16, 449-471.

DOUGHER, M., AUGUSTSON, E., MARKHAM, M., GREENWAY, D., & WULFERT, E. (1994). The transfer of respondent eliciting and extinction functions through stimulus equivalence classes. Journal of the Experimental Analysis of Behavior, 62, 331-351.

DUBE, W., & HIRIS, J. (1997). Matching to Sample Program (Version 11.08) [Computer software]. Waltham, MA: E. K. Shriver Center for Mental Retardation.

EKMAN, P. (1972). Darwin and facial expression: A century of research in review. New York: Academic Press.

EKMAN, P., SORENSON, E. R., & FRIESEN, W. V. (1969). Pan-cultural elements in facial displays of emotion. Science, 164, 86-88.

FIELDS, L., ADAMS, B. J., VERHAVE, T., & NEWMAN, S. (1993). Are Stimuli in equivalence classes equally related to each other? The Psychological Record, 43, 85-105.

FIELDS, L., LANDON-JIMENEZ, D. V., BUFFINGTON, D. M., & ADAMS, B. J. (1995). Maintained nodal-distance effects in equivalence classes, Journal of the Experimental Analysis of Behavior 64, 129-145.

FIELDS, L., MATNEJA, P., VARELAS, A., BELANICH, J., FITZER, A, & SHAMOUN, K. (2002). The formation of linked perceptual classes. Journal of the Experimental Analysts of Behavior, 78, 271-290.

FIELDS, L., & MOSS, P. (2008), Formation of partially and fully elaborated generalized equivalence classes. Journal of the Experimental Analysis of Behavior, 90, 135-168.

FIELDS, L., REEVE, K. E., MATNEJA, P., VARELAS, A., BELANICH, J., FITZER, A., & SHAMOUN, K. (2002). The formation of a generalized categorization repertoire: Effect of training with multiple domains, samples, and comparisons. Journal of the Experimental Analysis of Behavior, 78, 291-313.

FIELDS, L., REEVE, K. F., ROSEN, D., VARELAS, A., ADAMS, B. J., BELANICH, J., & HOBBIE, S. A. (1997). Using the simultaneous protocol to study equivalence class formation: The facilitating effects of nodal number and size of previously established equivalence classes. Journal of the Experimental Analysis of Behavior, 67, 367-389.

FIELDS, L., & WATANABE-ROSE, M. (2008). Nodal structure and the partitioning of equivalence classes. Journal of the Experimental Analysis of Behavior, 89, 359-381.

HAYES, S. C., KOHLENBERG, B. S., & HAYES, L. J. (1991). The transfer of contextual control over equivalence classes through equivalence classes: A possible model of social stereotyping. Journal of the Experimental Analysts of Behavior, 56, 505-518.

KENNEDY, C. H. (1991). Equivalence class formation influenced by the number of nodes separating stimuli. Behavioural Processes, 24, 219-245.

OHMAN, A. (2002). Automaticity and the amygdale: Nonconscious responses to emotional faces. Current Directions in Psychological Science, 11(2), 62-66.

OSGOOD, C. E., SUCI, G. I., & TANNENBAUM, P H. (1957). The measurement of meaning. Urbana,: University of Illinois Press.

PARR, L. A., WINSLOW, J. T., HOPKINS, W. D., & DE WAAL, F. B. M. (2000). Recognizing facial cues: Individual discrimination by chimpanzees (Pan troglodytes) and rhesus monkeys (Macaca mulatto). Journal of Comparative Psychology, 114, 47-60.

SAUNDERS, R. R., SAUNDERS, K. J., KIRBY, K. C., & SPRADLIN, J. E. (1988). The merger and development of equivalence classes by unreinforced conditional selection of comparison stimuli. Journal of the Experimental Analysis of Behavior, 50, 145-162.

SIDMAN, M. (1994). Equivalence relations and behavior: A research story. Boston: Authors Cooperative.

SIDMAN, M. (2000). Equivalence relations and the reinforcement contingency. Journal of the Experimental Analysis of Behavior, 74, 127-146.

SIDMAN, M., & TAILBY, W. (1982). Conditional discrimination vs. matching-to-sample: An expansion of the testing paradigm. Journal of the Experimental Analysis of Behavior, 37, 261-273.

SKINNER, B. F. (1968). The technology of teaching. New York: Prentice-Hall.

SPENCER, T. J., & CHASE, P. N. (1996). Speed analyses of stimulus equivalence. Journal of the Experimental Analysis of Behavior, 65, 643-659.

VAIDYA, M., & SMITH, K., N. (2006). Delayed matching-to-sample training facilitates derived relational responding. Experimental Analysis of Human Behavior Bulletin, 24, 9-16.

WULFERT, E., & HAYES, S. C. (1988). Transfer of a conditional ordering response through conditional equivalence classes. Journal of the Experimental Analysis of Behavior, 50, 125-144.

Appendix A

Instructions for the Participants

The instructions for the participants, translated into English, are reproduced in Figure Al.

[FIGURE A1 OMITTED]

INSTRUCTIONS

You will find a picture on the top of each of the following sheets. Your task is to mark wit an X the location of the picture in scales limited to opposite adjectives. Each scale represents an continuum from one adjective to its opposite. Thus, you will find, for example, the pair beautiful/ugly and will have to judge, based on this pair of adjectives, a figure like:

Appendix B

Individual evaluations

The values assigned to the individual evaluations by each participant of the experimental groups are reproduced in Tables B1, B2, B3, B4, B5, and B6.

Table B1.

Individual Evaluations: D Stimulus From the Happy Class by the Two
Experimental Groups

                                 Delayed group

                     jay  raq  mar  cha  mat  tan  gab

Sad-happy             3    3    0    3    3    3    2
Tense-relaxed         0    3   -2    3    3    3    2
Rough-smooth          1    3    3    0    3    0    2
Slow-fast             1    3    0    0   -1    3   -1
Ugly-beautiful        3    3    1    3    3    3    3
Heavy-light           1    3    2    3    3    3    3
Negative-positive     2    3    0    3    3    3    3
Passive-active        1    3    0    3    0    3    0
Hard-soft             1    3   -2    0    1    3   -2
Bad-good              1    3    0    3    3    3    2
Unpleasant-pleasant   2    3    0    3    3    3    2
Poor-rich             0    0    1    0    0    0    0
Submissive-dominant  -1    3    0    0   -1    0    0

                            Simultaneous group

                     kat  tha  dor  ium  mar  ari  fab

Sad-happy             3    3    0    0    2    3    1
Tense-relaxed         3    3    0   -3   -2    3    0
Rough-smooth          3    2    3    3    3    3   -1
Slow-fast             0    2    0    3    0    0   -2
Ugly-beautiful        2    3    0    2    2    3    0
Heavy-light           3    3    2    1    2    3    1
Negative-positive     3    3    0    0    0    3    0
Passive-active        0    2   -3    3    0    0   -1
Hard-soft             3    2   -2   -3   -3    3   -1
Bad-good              3    3    0    0    0    2    0
Unpleasant-pleasant   2    3    0    0    1    3    1
Poor-rich             0    1   -2    3    0    0    0
Submissive-dominant   0    1   -3    3    0    0   -1

Table B2.

Individual Evaluations: D Stimulus From the Angry Class by the Two
Experimental Groups

                              Delayed group

                     jay  raq  mar  cha  mat  tan  gab

Sad-happy             3    1    1    0   -2    0    3
Tense-relaxed        -3   -2    0   -3   -3   -3   -3
Rough-smooth         -3    3    0    0   -3   -3    2
Slow-fast             0   -3   -2    0    2    3    3
Ugly-beautiful       -3    1    1    0   -3   -3    0
Heavy-light          -1    3   -1    0   -3   -3   -2
Negative-positive    -3    0    2   -3   -3   -3   -3
Passive-active        0    3   -1    3   -3    3    0
Hard-soft            -3   -2    3    0    2   -3   -3
Bad-good             -3   -2    2   -3   -1   -3   -3
Unpleasant-pleasant  -3    1    2   -3   -3   -3   -2
Poor-rich             0    2    0    0    0    0    0
Submissive-dominant  -2    2   -1    1    3    3    2

                            Simultaneous group

                     kat  tha  dor  ium  mar  ari  fab

Sad-happy             0   -3   -3    0    1   -2    1
Tense-relaxed        -3   -3   -2    2   -1    3    0
Rough-smooth         -2   -1    0    3    0   -3    2
Slow-fast             2   -1   -2   -3    0    3    1
Ugly-beautiful       -2   -3    0    1    1   -3    1
Heavy-light          -3   -3   -1   -2    0    3   -1
Negative-positive    -3   -3    0    2    0   -3    1
Passive-active        2    0    1    2    0    3    2
Hard-soft            -2   -3   -1    2    0   -3    0
Bad-good             -3   -3    0    0    0   -1    1
Unpleasant-pleasant  -2   -3    2    0    0   -3    0
Poor-rich             0   -1    1    3    0    0   -1
Submissive-dominant   3   -2   -1    3    0    2    0

Table B3.

Individual Evaluations: D Stimulus From the Happy Class by Six Members
of Each Experimental Croup

                           Delayed Group

                     car  gis  tia  dan  tan  cal

Sad-happy             3    3    2    3    3    3
Tense-relaxed         3    3    2    3    3    3
Rough-smooth          3    2    2    0    3    0
Slow-fast             2    0   -2    0    2    0
Ugly-beautiful        2    2    2    0    3    1
Heavy-light           2    3    3    0    1    1
Negative-positive     3    3    2    0    3    3
Passive-active        2    0    0    0   -3    0
Hard-soft            -1    0   -2    0    3    0
Bad-good              0    0    2    1    3    3
Unpleasant-pleasant   3    3    3    1    3    3
Poor-rich             2    0    0    0    0    0
Submissive-dominant   2    1    0    0    0    3

                         Simultaneous Group

                     ela  sam  pat  lar  mar  nai

Sad-happy             3    2    0   -1    3    1
Tense-relaxed         3    0    3    3   -1    3
Rough-smooth          2    2    2    3    0    2
Slow-fast             3    2   -2   -3    2    2
Ugly-beautiful        3    2    0    1    3    2
Heavy-light           3    3    0    3    1    3
Negative-positive     3    3    1    1    1    0
Passive-active        3    0    2   -3    2    2
Hard-soft             2    0   -2    2    0    0
Bad-good              3    0    1    2    1    0
Unpleasant-pleasant   3    1    2    3    2    1
Poor-rich             3    0    0   -2    0   -1
Submissive-dominant   0    0    2   -3    3    0

Table B4.

Individual Evaluations: D Stimulus From the Angry Class by Six Members
of Each Experimental Group

                           Delayed Group
                     car  gis  tia  dan  tan  cal

Sad-happy             0   -3   -3   -1   -3    0
Tense-relaxed        -2   -2   -2   -3   -3   -3
Rough-smooth          2   -1   -2    0   -3    0
Slow-fast            -2    0   -1    0   -2    0
Ugly-beautiful       -1    0    3    0   -3    0
Heavy-light          -1   -1   -2    0   -3    0
Negative-positive     2   -2   -3    0   -3   -3
Passive-active       -3    0   -3    2    3    3
Hard-soft            -2    0   -2    0   -3    0
Bad-good              0    0   -2   -2   -3   -3
Unpleasant-pleasant  -1   -1   -1   -2   -3   -3
Poor-rich            -1    0    1    0    0    0
Submissive-dominant  -1    0    2    1    3    3

                          Simultaneous Group

                     ela  sam  pat  lar  mar  nai

Sad-happy             2   -2    0    0   -3    0
Tense-relaxed         3    0   -2   -3    0    0
Rough-smooth          2    0   -2   -2    0    0
Slow-fast             0    2   -1    3   -2    0
Ugly-beautiful        2    1    0   -2   -2    0
Heavy-light           1    0    0   -3    0    0
Negative-positive     2   -3    2   -2   -2   -2
Passive-active        2    0    2    3    0    2
Hard-soft             2    0   -2   -3    0    0
Bad-good              2   -2   -2   -2    0   -2
Unpleasant-pleasant   2   -1   -2   -2   -2   -2
Poor-rich             1    0    0    0   -2    0
Submissive-dominant   0    0    2    3   -2    0

Table B5.

Individual Evaluations: F Stimulus From the Happy Class by Six Members
of Each Experimental Group

                                Delayed Group

                     kle  fad  jer  dig  gla  dan

Sad-happy            -1   -1    1    3   -2    1
Tense-relaxed        -1   -1    0    1   -2    1
Rough-smooth          2   -1    0    3   -2   -1
Slow-fast            -2    0    0    0   -3   -1
Ugly-beautiful        2    1   -1    1   -1   -1
Heavy-light          -1    0   -1    2   -3    1
Negative-positive    -1   -1    0    3   -2    1
Passive-active       -1    0    0   -2   -3   -1
Hard-soft            -2    0   -1    2   -2   -1
Bad-good              0    0    0    2   -1    0
Unpleasant-pleasant   0    0    1   -3    0    1
Poor-rich             0    0    0    0   -2   -1
Submissive-dominant  -1   -1   -1   -2    2   -1

                         Simultaneous Group

                     jul  and  ari  ira  fla  rai

Sad-happy             1    0    2   -3    2    1
Tense-relaxed         1    2    2   -3   -2    1
Rough-smooth          0    0    2    2    0    0
Slow-fast             1   -1    0   -3    0    0
Ugly-beautiful       -1    2    2   -1   -3   -1
Heavy-light           1    0    2   -2   -2    0
Negative-positive     1    3    2   -2    0    0
Passive-active        0    0    0    2    3    0
Hard-soft             1   -1    2   -3   -3   -1
Bad-good              2    2    2   -1    0    0
Unpleasant-pleasant   2    3    2   -3   -2    2
Poor-rich             2    0    0   -1    0    0
Submissive-dominant   0    2    1   -2    3    1

Table B6.

Individual Evaluations: F Stimulus From the Angry Class by Six Members
of Each Experimental Group

                            Delayed Group

                     kle  fad  jer  dig  gla  dan

Sad-happy             1   -1   -3   -2    1   -1
Tense-relaxed        -1    0   -1   -2    2    1
Rough-smooth          0    0   -1   -2   -2    0
Slow-fast            -3    1    0   -3   -2   -2
Ugly-beautiful       -1    1   -3   -3   -1   -1
Heavy-light          -2    1   -3   -2   -2    1
Negative-positive     0    0   -1   -2   -2   -1
Passive-active       -2    1   -1   -2   -2   -2
Hard-soft            -3   -1   -1   -2    0    1
Bad-good              0    0    0   -2    0    2
Unpleasant-pleasant   0    1   -1   -2    1    1
Poor-rich             0    0    0    0   -1    0
Submissive-dominant  -1   -1   -1    2   -1   -1

                         Simultaneous Group

                     jul  and  ari  ira  fla  rai

Sad-happy            -2   -2   -2    1    0    1
Tense-relaxed        -2   -3   -3    1    2    0
Rough-smooth         -2   -1   -2    1    3   -1
Slow-fast             2   -3    0   -3    0    0
Ugly-beautiful        1    0   -2    2    2    1
Heavy-light          -2   -1   -2    2    2    1
Negative-positive    -2   -1   -2    2    0    0
Passive-active        2   -1    0   -3   -2   -1
Hard-soft            -2   -1   -2   -3    2   -2
Bad-good             -2    0   -1    3    0    0
Unpleasant-pleasant  -1   -2   -2    3    2    0
Poor-rich             1    0    0    3    2    1
Submissive-dominant   3   -3    1    3    0    1

Renato Bortoloti

Universidade Federal do Para

Julio C. de Rose

Universidade Federal de Sao Carlos 

Renato Bortoloti (now at Universidade Federal de Sao Carlos), Programa de Pos-Graduacao em Teoria e Pesquisa do Comportamento; Julio C. de Rose, Departamento de Psicologia.

This study is based on part of a dissertation submitted by the first author to the Graduate Program in Theory and Research on Behavior, Universidade Federal do Para, in partial fulfillment of the requirements for a doctoral degree. The first author was supported by a graduate fellowship from the Brazilian National Council for Scientific and Technological Development (CNPq), and the second author was supported by a research productivity grant from CNPq. The research was conducted with support by the State of Sao Paulo Foundation for Support of Research (FAPESP), Grant 03/09928-4. Preparation of the manuscript was also supported by a FAPESP postdoctoral fellowship for the first author, Grant 07/51120-5. We thank Olavo de Faria Galvao, William J. McIlvane, and Deisy G. de Souza for contributions and encouragement for this research; we also thank Lanny Fields for his thoughtful suggestions on the manuscript.

Correspondence concerning this article should be addressed to Julio C. de Rose or Renato Bortoloti, both at Departamento de Psicologia, Universidade Federal de Sao Carlos, Caixa Postal 676, 13565-905, Sao Carlos, SP. Electronic mail may be sent via Internet to [e-mail] or [e-mail].