2015, 9999, 1–13

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

NUMBER

9999 (OCTOBER)

COMMON PHYSICAL PROPERTIES AMONG RELATIONAL NETWORKS IMPROVE ANALOGY APTNESS FRANCISCO J. RUIZ
UNIVERSITARIA KONRAD LORENZ FUNDACION

AND

CARMEN LUCIANO UNIVERSIDAD DE ALMER
IA

Relational frame theory (RFT) conceptualizes analogy as the establishment of a relation of coordination among common types of relations. This study provided an initial RFT analysis of analogy aptness. Twenty participants initially learned to respond to the structure of analogical tests after which they were trained on two separate relational networks, each consisting of three equivalence classes (Network: 1 F1-G1-H1, F2-G2-H2, F3-G3-H3; Network 2: M1-N1-O1, M2-N2-O2, M3-N3-O3). The node stimuli always appeared with color spots on their backgrounds (F1 and M1: yellow; F2 and M2: red; F3 and M3: blue). In the critical test, participants had to select the more correct response from two options: relating combinatorial relations of coordination with the same color in the node stimuli (e.g., relating G1H1 to N1O1) versus relating combinatorial relations with different colors in the node stimuli (e.g., relating G1H1 to N2O2). The colors of the node stimuli did not appear on the critical test. Ninety percent of participants selected the analogies with common color properties as the more correct ones. Practical implications of these findings are discussed. Key words: analogical relations, analogy aptness, arbitrary matching-to-sample, derived stimulus relations, Relational Frame Theory, relational network

Analogy is broadly described as relating two situations that share a common pattern of relations among their constituent elements (e.g., Holyoak, 2005). When information is transferred from one analog to the other, analogy can facilitate rapid understanding of one situation by reference to another. Due to this generative ability, the use of analogy has been emphasized in applied settings such as education (e.g., Bassok & Holyoak, 1989), psychotherapy (e.g., Hayes, Strosahl, & Wilson, 1999), scientific research (e.g., Hesse, 1966), politics (e.g., Blanchette & Dunbar, 2001), marketing (e.g., Capelli & Jolibert, 2009), etc.

In spite of the utility of analogy, practitioners often find that there are several alternative analogies or metaphors for a given situation, and that not all are equally effective for their specific purposes. For instance, consider an educator trying to provide an analogy to facilitate the explanation of the filter functions of the atmosphere (i.e., the atmosphere filters harmful ultraviolet light and other spatial objects from reaching the Earth). Possible analogies might consist of comparing the atmosphere to the membrane of a cell (i.e., “the atmosphere of the earth is like the membrane of a cell”) or to the spam filter of electronic mails (i.e., “the atmosphere of the earth is like the spam filter of an email system”) (i.e., the earth’s atmosphere filters harmful ultraviolet light and other spatial objects like a cell’s membrane filters substances that surround the cell, or like the spam filter blocks harmful and unwanted messages from entering electronic mail). In another example, consider the case of a behavior therapist with a client suffering from panic attacks characterized by feelings of suffocation who has significant limitations in her life because of her attempts to control them. In order to help the client to realize the consequences of trying to control

This study was done in partial fulfillment of the requirements for the Ph.D. degree granted to the first author under the supervision of the second author while he was funded by a research grant from the Junta de Andaluc
ıa, Spain (HUM1093) at the Universidad de Almer
ıa. Parts of this research were presented at the Association for Behavior Analysis Annual Convention, Phoenix, May, 2009 and at The Third World Conference on ACT, RFT and Contextual Behavioral Science, Enschede (The Netherlands), July, 2009. Correspondence concerning this article should be addressed to the first author. Francisco J. Ruiz: Fundaci
on Universitaria Konrad Lorenz, Carrera 9 bis, N° 62-43, Bogot
a (Colombia). E-mail: franciscoj.ruizj@konradlorenz. edu.co doi: 10.1002/jeab.147

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FRANCISCO J. RUIZ and CARMEN LUCIANO

the unwanted physical sensations, some analogies might relate what the client is feeling/ doing to an unrelated situation such as the quicksand metaphor (trying to control your panic attacks is like struggling in quicksand: the more you struggle, the more you sink; Hayes et al., 1999) or the wound metaphor (trying to control your panic attacks is like scratching a wound: the more you scratch, the more it itches). An important question for both the teacher and the therapist is what analogy is more effective or apt for those situations. To begin addressing this question, the present study examined some possible determinants of analogy aptness from the standpoint of relational frame theory (RFT; Hayes, BarnesHolmes, & Roche, 2001). The main idea behind RFT is that fluency and flexibility in different patterns of arbitrarily applicable relational responding, or relational framing, underlie human language and cognition abilities. RFT proposes that all patterns of relational framing are generalized operant behaviors learned through multiple exemplar training. These include relating stimuli in accordance with coordination (is, same as), distinction (is different from), opposition (is opposite to), comparison (more than, less than), hierarchy (is part of, includes), causality (if…, then), etc. Each type of relational framing is defined according to the properties of mutual entailment, combinatorial entailment, and transformation of function. Mutual entailment involves the bidirectionality of stimulus relations: if A is related to stimulus B, then B is related to A. For instance, if a person is told that Juan (A) is taller than Manuel (B), she will derive that Manuel (B) is shorter than Juan (A). Combinatorial entailment means that two or more stimuli that have acquired the property of mutual entailment can be combined: If A is related to B and B is also related to C, then A is related to C, and vice versa. In our example, if the person is also told that Manuel (B) is taller than Maria (C), she will derive that Juan (A) is taller than Maria (C) and, thus, Maria (C) is shorter than Juan (A). Lastly, transformation of function means that changing the function of one member of a relational network can also change the function of other members of the same network. For instance, if the person is told that Juan (A) is very good at playing XIP, an unknown sport, because he is very tall, she will derive that Manuel and Maria

are probably worse at playing it because they are shorter than Juan. From an RFT perspective, analogy involves establishing a relation of coordination among common types of trained or derived relations (e.g., Lipkens, 1992; Stewart, Barnes-Holmes, Hayes, & Lipkens, 2001). For instance, if we establish relations of coordination between the Spanish words silla and estrella and the English words chair and star, then we could establish a simple analogy by deriving a frame of coordination between both trained relations (i.e., silla is to chair as estrella is to star). Many studies to date provide support for the external validity of the RFT model of analogy and analogical reasoning (e.g., Barnes, Hegarty, & Smeets, 1997; Lipkens & Hayes, 2009; Ruiz & Luciano, 2011; Stewart, Barnes-Holmes, Roche, & Smeets, 2002; see reviews in Ruiz & Luciano, 2012; Stewart & Barnes-Holmes, 2004). No RFT study to date, however, has analyzed the determinants of analogy aptness. In the study most closely related to the current one, Stewart et al. (2002) showed that relating derived relations allowed the discrimination of a physical similarity between the relations involved, which transformed the functions of a block-sorting task. For instance, participants who previously sorted a series of wooden blocks according to color instead of according to shape were exposed to an analogical test in which all trials involved the discrimination of common shapes. After that, participants changed the way they sorted the blocks (i.e., they sorted according to shape). The main requisite to establish an effective (apt) analogy is that both analogs share the same type of relations. In this sense, all analogies considered in the case of the teacher and the behavior therapist would seem equally apt because they are relationally equivalent. For instance, the analogies “the atmosphere of the earth is like the membrane of the cell” and “the atmosphere of the earth is like the spam filter of an email system” involve establishing relations of coordination between atmospheric function and cell membrane function or spam filter function, respectively. Likewise, in the case of the behavior therapist, both the quicksand and the wound metaphors contain common relationships (i.e., more attempts to control panic attacks cause more panic and unwanted, long-term effects; more struggling in quicksand causes more sinking and unwanted, long-term

3

ANALOGY APTNESS effects; more scratching a wound causes more itching and unwanted, long-term effects). This study is based on the premise that, all other things being equal, the presence of common physical properties among the networks to be related will increase the judgments of analogy aptness. From an RFT standpoint, this should occur because common physical properties would establish an additional relation of coordination between the relational networks. Taking into consideration common physical properties, differences emerge between the alternative analogies in our examples. For instance, the analogy comparing the earth’s atmosphere to a cell’s membrane might benefit from common physical properties such as the circular form of the Earth and the animal cell and that both surround what they protect. Conversely, the analogy between the earth’s atmosphere and the spam filter does not seem to share physical properties. Thus, it seems reasonable to expect that the cell analogy would be judged as more apt than the spam filter analogy. This same rationale applies to the behavior therapist example, to the extent that the sensation of suffocation is shared in the quicksand metaphor but not in the wound one. The current study, then, aimed to investigate whether relating separate relational networks with a common physical property (i.e., analogies with common physical properties) is judged as more apt than relating networks without common physical properties (i.e., exclusively relational analogies). To do so, we followed a procedure similar to the one used to model cross-domain analogies in Ruiz and Luciano (2011). Specifically, Part I of our procedure was conducted to bring participants’ behavior under control of the relevant cues in an analogical test (i.e., to establish an experimental history with the test structure that would follow training). In Part II of our procedure, we used arbitrary matching-to-sample to train two separate coordination relational networks, each with three equivalence classes (F1-G1-H1, F2-G2-H2, F3-G3-H3; and M1-N1O1, M2-N2-O2, M3-N3-O3). The node stimuli of each class (i.e., F1 and M1, F2 and M2, and F3 and M3) contained common color spots that served as common physical properties (yellow, red, and blue, respectively). In the critical test without the colors, participants were asked to choose between two combinatorial relations of coordination and a relation of distinction: One

of the correct options involved relating networks with a common associated color (i.e., analogy with common physical properties) and the other involved relating networks with different associated colors (i.e., exclusively relational analogy). The incorrect option was composed of a distinct (nonequivalent) network item. Consistent selection of one of the correct options would be similar to responding to the more apt analogy in the cases of the teacher and the behavior therapist. Method Participants Twenty-one undergraduates (age range ¼ 1925; 19 females, 2 males) participated in the study. They were enrolled in different courses (psychology, education, business studies, etc.) at the University of Almer
ıa. All participants were recruited through in-class announcements and on-campus flyers. None of them had previous experience with the procedures employed in this study or any previous knowledge of stimulus equivalence research/RFT literature. After Part I of training (see below), they were randomly assigned to two experimental conditions (A or B) that differed in the order in which two types of analogical tests were conducted. Upon finishing their participation, all participants received a canteen voucher exchangeable for a breakfast or snack. Design and Variables The experiment consisted of a computer task with two parts. The aim of Part I was to bring participants’ behavior under the control of the relevant cues in the analogical test that would be used at the end of the study to evaluate the effects of common physical properties on analogy aptness; the two phases of Part I are illustrated in Figure 1. Phase 1 of Part I involved training six conditional discriminations using consonant-vowel-consonant (CVC) nonsense syllables. In Phase 2, participants completed an analogical test in which they related the sameness and distinction relations trained in Phase 1 (details are provided in the Procedure section below). Following this initial training and provision of familiarity with the analogical test, Part II (Phases 3–5) involved training two separate relational networks and conducting two

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FRANCISCO J. RUIZ and CARMEN LUCIANO

Fig. 1.

Overview of the training and testing conducted in Part I.

analogical tests (Fig. 2). In Phase 3, participants were trained on six conditional discriminations using abstract shape stimuli and another six conditional discriminations using Greek letter stimuli. Stimuli in both sets were physically dissimilar (see next section) in order to avoid the establishment of relations based on nonarbitrary properties. Participants assigned to Condition A next completed the Analogical Test 1: Relating Relations of Sameness with or without Common Physical Properties. In this test, there were two correct responses in each trial: One involved relating two relational networks with common physical properties (i.e., analogies with common physical properties) and the other involved relating networks that did not share any physical property (i.e., exclusively relational analogies). After consistently responding by always selecting the same type of option, these participants received Analogical Test 2: Relating Relations of Sameness and Distinction without Common Physical Properties. In this test, they had to recognize exclusively relational analogies of sameness and distinction by matching pairs of abstract stimuli to pairs of Greek-letter stimuli and vice versa. Participants in Condition B completed these tests in reverse order. Conditions A and B were designed to control for two possibilities. First, to evaluate whether

participants in Condition A selected analogies with common physical properties in Analogical Test #1 by discriminating that both sets of stimuli shared the same type of relation and not by merely discriminating that both compounds indirectly shared a common physical property. If that were the case, participants would likely show difficulties when responding to Analogical Test #2 because it required them to relate derived relations. Also, it seems unlikely that participants in Condition B would respond to Analogical Test #1 by merely discriminating that the compound stimuli indirectly share a common physical property because they were exposed first to Analogical Test #2. Second, results in Condition A controls the possibility that participants in Condition B would select the common physical analogies only because a third response option was added in Analogical Test #1. Setting, Apparatus, and Stimuli The experiment was conducted in a laboratory consisting of two adjacent rooms (an experimental room and an observation room) of equal size (4 m x 3 m). An HP nx9010 laptop computer with a 15-in. color screen programmed with Visual Basic 6.0© was used to present visual stimuli and record participants’ responses.

ANALOGY APTNESS

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Fig. 2. Overview of the training and testing conducted in Part II. The order of the analogical tests was reversed for participants assigned to Condition B. Note that in Phases 4 and 5, the colored-dot stimuli were not presented on the screen; they are shown in the figure only to aid the reader.

The visual stimuli (see Fig. 3) were black shapes framed on a white 6  6 cm square background and presented on a general grey background (code 000000C& in Visual Basic 6.0). They consisted of nine nonsense syllables, nine abstract shapes, and nine Greek letters. Alphanumeric labels (e.g., A1, B1, C1, etc.) are used to identify the stimuli; however, these labels were not presented to the participants. The white background of stimuli F1 and M1 contained yellow spots, F2 and M2 contained red spots, and F3 and M3 contained blue spots. There were 24 versions of each of these stimuli that differed in the positions of the spots. The number of spots varied between 2 to 20 and they had different forms and sizes, with the largest

one occupying no more than a fourth part of the white background of the stimulus. Procedure Upon arriving at the laboratory, participants were told that the experiment consisted of a computer task with two parts separated by a brief break. The experimenter escorted participants to the experimental room, seated them facing the computer and left the room. Instructions were provided on the computer screen. All participants were trained and tested individually during a session that lasted 90 min, on average. The procedure consisted of the five phases described below.

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FRANCISCO J. RUIZ and CARMEN LUCIANO

Fig. 3.

Arbitrary stimuli used in the experiment.

Phase 1: Initial conditional discrimination training. The following instructions in Spanish were presented on the screen at the start of this phase: 1. 2. 3. 4. 5. 6.

A figure will appear at the top of the screen. Then, three figures will appear at the bottom of the screen. Your task is to click with the mouse on the bottom figure that goes with the upper figure. The computer will tell you if your response is right or wrong. Mistakes are normal at the beginning. Your task is to obtain as many correct responses as possible.

Participants underwent training on six different, arbitrary conditional discriminations (A1-B1, A1-C1, A2-B2, A2-C2, A3-B3, and A3C3) using a simultaneous matching-to-sample procedure (Sidman & Tailby, 1982). Training trials were as follows: a sample (e.g., A1) appeared in the center of the upper third of the screen. One second later, three comparisons (e.g., B1, B2, B3) appeared in line horizontally in the lower third of the screen. Participants responded by clicking on one of the comparisons with the mouse. Immediately after responding, all the stimuli were removed from the screen. Correct responding (i.e., B1 after A1) was followed by the word “CORRECTO” (i.e., correct) in white capital letters, centered on the screen. Incorrect responses were followed by the word “MAL” (i.e., wrong). Feedback remained on the screen

for 2 s, after which the screen became blank for another 2 s and a new training trial followed. The training sequence was as follows. First, A1-B1 was trained until the participant emitted two consecutive correct responses. Then, a new relation was trained (e.g., A2-B2) followed by a 4-trial block of the two relations (two trials per relation), until achieving 100% correct responses. Next, A3-B3 and A2-C2 were trained in the same way and were followed by a mixed block with each of these two relations. Subsequently, two 4-trial, mixed blocks containing all four previous relations (i.e., A1-B1, A2-B2, A3-B3, A2-C2) were presented. When participants responded correctly to two consecutive blocks, A3-C3 and A1-C1 were trained in the same way (i.e., first separately and then in a 4trial mixed block). Finally, several consecutive mixed blocks followed until participants responded correctly to two of each one: (a) 4-trial blocks with A3-B3, A1-C1, A2-C2 and A3-C3; (b) 4-trial blocks with A1-B1, A2-B2, A1-C1 and A3C3; and, finally, (c) 6-trial blocks with all six trained relations. Then, a written message appeared on the screen informing participants that no feedback would appear during the next trials, and two 6-trial blocks (one trial per each A-B and A-C relation) started. If a participant produced 100% correct responses in both blocks, the next phase commenced; otherwise, the same two 6-trial blocks were presented with feedback as retraining and then participants had to repeat the test. Phase 2. Relating trained relations test. The aim of this phase was to evaluate the discrimination of the relevant features of the analogical

ANALOGY APTNESS test that would later be conducted in Phases 4 and 5. This phase consisted of eight randomly presented trials: four similar-similar trials and four different-different trials. A typical trial was as follows: A compound stimulus with a previously trained relation (e.g., A1B1) was framed in a dark rectangle and appeared in the center of the upper third of the screen as a sample. One second later, two compound stimuli with other previously trained relations (e.g., A2B2 and A2B3), framed like the sample, appeared in a row in the lower third of the screen, one on the left and the other one on the right (positions changed randomly). Participants had to press the “Z” or the “M” keys to choose, respectively, the comparison on the left or the comparison on the right. If the sample stimulus was a trained relation of sameness (e.g., A1B1), then participants had to choose another trained relation of sameness (e.g., A2B2). The four similar–similar trials are illustrated in the top row of Phase 2 in Figure 1. If the sample compound stimulus was a trained relation of distinction (e.g., A1B2), then participants had to choose another trained relation of distinction (e.g., A2B3); see the bottom row of Phase 2 in Figure 1. The mastery criterion was to respond correctly to all eight trials. The following instructions appeared on the screen at the beginning of this phase: 1. 2.

3. 4. 5.

6. 7.

Two joint figures will appear at the top of the screen. Then, two joint figures will appear at the bottom left of the screen and another two joint figures will appear at the bottom right of the screen. Pay attention to both figures at the top. Pay attention to both figures at the bottom left and to both figures at the bottom right. Your goal is to select one of the two joint figures at the bottom of the screen that you think goes with the joint figures at the top. To choose the figures at the bottom left, press the “Z” key. To choose the figures at the bottom right, press the “M” key. Your goal is to obtain as many corrects as possible, but… THE COMPUTER WILL NOT SAY WHETHER OR NOT YOU ARE DOING WELL.

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Every incorrect response was followed by the presentation on the screen of the following instructions: You are going to return to the previous task. The computer will not tell you whether your response is right or wrong. Please pay attention to the screen in order to obtain as many correct responses as possible. Then, a retraining block of 12 trials (two trials of each relation trained in Phase 1; e.g., A1-B1 relation) commenced as in Phase 1. However, in this case, if the participant responded to the trial correctly, the following occurred: The two incorrect comparisons (e.g., B2 and B3) were removed from the screen and the sample and correct comparison stimuli (e.g., A1 and B1) moved towards the center of the screen and were framed into a dark rectangle to form a compound stimulus (i.e., A1B1). This process took about 7 s. If participants responded correctly to all trials, they were reintroduced to the Relating Trained Relations Test. If participants responded incorrectly to one trial of this retraining block, all stimuli were removed from the screen and participants were exposed to further training with feedback as in Phase 1. Once they passed this block, they were returned to the block with movement feedback. No more than 10 attempts to pass the Relating Trained Relations Test were permitted. Phase 3. Conditional discrimination training with abstract shapes and Greek letters. As shown in Figures 2 and 3, abstract figures and Greek letters were used to form three separate 3-member equivalence classes (Abstract shapes: F1-G1-H1, F2-G2-H2, F3-G3-H3; Greek letters: M1-N1-O1, M2-N2-O2, M3-N3-O3). First, participants were trained on the six relations using abstract shape stimuli, followed by training on the six relations using the Greek letter stimuli. Afterwards, participants received several mixed blocks of training trials. The backgrounds of sample stimuli F1 and M1 had yellow spots, F2 and M2 had red spots, and F3 and M3 had blue spots. The version of each stimulus presented was randomized across trials (see the Settings, Apparatus, and Stimuli section). Conditional discrimination training with the abstract shape stimuli was conducted in the sequence shown (left to right) in the top row of Figure 2. Afterwards, conditional

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FRANCISCO J. RUIZ and CARMEN LUCIANO

discrimination training with the Greek letter stimuli commenced in the sequence shown in the second row of Figure 2. After the performance criterion was achieved on the latter relations, a 6-trial block with the abstract shapes was conducted (one trial per relation). After correctly responding on all of these trials, a 6-trial block with the Greek letter stimuli was conducted (one trial per relation). Correct responding on all trials of the latter block was followed by a written message on the screen that informed participants that no feedback would be presented during the upcoming trials. These consisted of a 12-trial block that intermixed trials with the abstract stimuli and trials with the Greek letter stimuli. Participants had to respond correctly to all trials in order to pass on to the next phase; otherwise, the same 12-trial block with feedback was presented until they produced a block with 100% correct responses. Then, they returned to the 12-trial block without feedback. Participants assigned to Condition A completed Phases 4 and 5 in that order; participants assigned to Condition B completed these phases in reverse order. Phase 4. Analogical test 1: Relating relations of sameness with or without common physical properties. The question asked in this test was what relations would participants select as the more correct response option: combinatorial relations of sameness involving relational networks that shared physical properties (i.e., analogy with common physical properties; e.g., yellow – N1O1, see Phase 4 in Fig. 2) or combinatorial relations of sameness involving relational networks that did not share any physical property (i.e., exclusively relational analogy; e.g., blue – N3O3). The trial format was the same as in Phase 2 except that a third comparison was added in the center of the screen, in line with the other two. The following instructions were presented on the screen at the start of this phase: 1. 2.

3. 4.

Two joint figures will appear at the top of the screen. Then, two joint figures will appear at the bottom left of the screen, another two at the center and, finally, another two joint figures at the bottom right of the screen. Pay attention to both figures at the top. Pay attention to both figures at the bottom left, to both at the bottom center, and to both at the bottom right.

5.

6. 7. 8.

Your goal is to select one of the two figures at the bottom of the screen that you think goes with the joint figures at the top. To choose the figures at the bottom left, press the “Z” key. To choose the figures at the bottom center, press the “V” key. To choose the figures at the right bottom, press the “M” key. Your goal is to obtain as many correct responses as possible, but… THE COMPUTER WILL NOT SAY WHETHER OR NOT YOU ARE DOING WELL. VERY IMPORTANT: THERE MIGHT BE MORE THAN ONE CORRECT RESPONSE. YOUR OBJECTIVE IS TO SELECT THE MOST CORRECT ONE.

This phase consisted of the random presentation of two 3-trial blocks; the stimuli presented in the two blocks were the same but the trial sequence and stimulus presentations were randomized. The sample was always a compound stimulus with a combinatorial relation of sameness established with abstract shapes (e.g., G1H1) and the comparisons were three compound stimuli from the Greek letters: one combinatorial relation of sameness with a node stimulus with the same color associated as the node of the sample compound stimulus (e.g., N1O1); one combinatorial relation of sameness with a different color in the sample stimulus from the sample compound (e.g., N3O3); and a combinatorial relation of distinction (e.g., N1O2). Colors did not appear in the test trials, they are shown in Figure 2 only to aid the reader in discriminating which comparison stimulus had and did not have common node stimuli. The mastery criterion was to respond consistently (e.g., select comparisons indicative of a combinatorial relation of sameness) in all 6 trials of the test. If this was not achieved, a retraining sequence was introduced after completion of this test. Specifically, the retraining sequence was: (a) Phase 1: One 12-trial block without feedback (two trials per relation) using CVC stimuli; (b) Phase 2: Relating Trained Relations Test; (c) Phase 3: One 12-trial block without feedback with each conditional discrimination involving the abstract shape stimuli and Greek letter stimuli; and (d) Combinatorial Relations Test with the abstract shape and with the Greek letter stimuli. The aim of this last test

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ANALOGY APTNESS was to evaluate the emergence of the combinatorial relations between the training stimuli in each set. Participants completed a 6-trial block with the same format used during conditionaldiscrimination training but without feedback. Each trial of this block evaluated a combinatorial relation with the abstract stimuli (G1-H1, G2-H2, G3-H3) or a combinatorial relation with the Greek letter stimuli (N1-O1, N2-O2, N3O3). As in Phase 3, the abstract shape and Greek letter stimuli never appeared together on the same trial. The mastery criterion was 100% correct responses. Incorrect responding was followed by a 12-trial block of mutual entailment (symmetry) relations (G1-F1, H1-F1, G2F2, H2-F2, G3-F3, H3-F3, N1-M1, O1-M1, N2M2, O2-M2, N3-M3, O3-M3). Responding correctly on all trials was followed by a 6-trial block of combinatorial relations. If participants responded incorrectly on a mutual entailment trial, further training with the abstract shape and Greek letter stimuli was reintroduced as when responding incorrectly in Phase 3. Then, the mutual entailment test was reintroduced and followed by the combinatorial relations test. Participants who did not respond correctly to three combinatorial or to three mutual entailment tests were excluded from further participation. When participants fulfilled the retraining criterion, they returned to Phase 4 testing. The maximum number of attempts allowed to pass this analogical test was three. If participants did not show a consistent pattern of responding within three exposures, they proceeded to Phase 5 (Condition A) or were informed that the experiment had concluded (Condition B). Phase 5. Analogical test 2: Relating relations of sameness and distinction without common physical properties. The question asked in this test was: Would participants derive exclusively relational analogies of sameness and distinction between the abstract shape and the Greek letter stimuli? As illustrated at the bottom of Figure 2, this phase consisted of the random presentation of six trials using the same basic format and instructions as in Phase 2. There were three similar–similar trials (e.g., G1H1/N3O3, N1O2) and three distinction–distinction trials (e.g., G1H2/N1O1, N1O3). The mastery criterion was to respond correctly to all 6 trials. If this criterion was not met after 6 trials, the test was presented up to two more times. Participants who did not pass this test within the three attempts

ended their participation in the study. Participants in Condition B proceeded to Phase 4. Results Part I Table 1 shows the number of trials participants completed and their percentage of correct responses across the initial conditional discrimination training conducted in Part I. There were considerable differences in the number of trials needed to meet the mastery criterion, ranging from 79 trials for P17 to 324 for P5 (M ¼ 191.4; SD ¼ 74.4) and percent correct choices ranged from 69% for P3 to 97% for P17 (M ¼ 80.6%, SD ¼ 7.9). No statistically significant differences were found between Conditions A and B (number of trials: U ¼.46, p ¼.58; percentage of correct responses: U ¼ 45.5, p ¼.52). Twenty of the 21 participants passed the Relating Trained Relations test (Phase 2); P11 was dismissed from further participation because she did not respond correctly within the 10 allowed attempts. None of the participants that passed this test did so on the first attempt (see Table 1). The mean number of attempts was 5.3 (SD ¼ 2.7), and there were no statistically significant differences between conditions (U ¼ 39, p ¼.44). Part II All 20 participants who passed the previous test completed conditional discrimination training with the abstract shape stimuli and Greek letter stimuli in Phase 3 (see Table 1), requiring between 181 trials for P14 to 316 trials for P21 (M ¼ 212.4, SD ¼ 33.4) and with accuracies across this phase from 75% correct for P21 to 98% correct for P10 and P14 (M ¼ 93.4%, SD ¼ 5.1). There were no statistically significant differences between conditions either in the number of trials (U ¼ 29, p ¼ .12) or in the percentage of correct responses (U ¼ 40.5, p ¼ .48). Analogical Test 1: Relating relations of sameness with or without common physical properties. Table 1 shows that 14 of the 20 participants showed a completely consistent pattern of responding in the first analogical test (6 of 10 in Condition A, 8 of 10 in Condition B). In all 14 cases, participants related relations of sameness that shared common physical properties (i.e., analogies with common physical

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FRANCISCO J. RUIZ and CARMEN LUCIANO Table 1 Training trials needed to meet the mastery criterion, and the percentage correct responses in Parts I and II. Part I

Part II

Training Trials

Training Trials

Cond.

(% Correct)

Attempts

(% Correct)

Phase 4†

Phase 5

P1 P2 P3

A B A B A

P6

B

P7

A

P8

B

P9 P10 P11 P12 P13 P14 P15

A B A B A B A B

P17

A

184 (97%) 280 (93%) 194 (94%) 12 (100%) 200 (93%) 188 (96%) 12 (100%) 232 (88%) 12 (100%) 198 (95%) 12 (100%) 214 (92%) 12 (100%) 185 (97%) 205 (98%) -213 (93%) 190 (96%) 181 (98%) 208 (94%) 12 (100%) 12 (100%) 197 (96%) 12 (100%) 12 (100%) 196 (96%) 12 (100%) 12 (100%) 12 (100%) 236 (94%) 12 (100%) 12 (100%) 218 (91%) 12 (100%) 12 (100%) 211 (90%) 12 (100%) 316 (75%) 12 (100%) 12 (100%)

100% 100% 83.3% 100% 100% 83.3% 100% 83.3% 100% 83.3% 100% 50% 100% 100% 100% -100% 100% 100%

P16

2 3 2 1 2 7 1 8 1 9 3 8 4 4 10 -3 6 7 5 4 1 4 1 1 2 1 1 1 10 1 1 5 2 1 4 2 5 2 1

100% 100% 100%

P4 P5

181 (76%) 234 (79%) 300 (69%) 12 (100%) 107 (90%) 324 (75%) 30 (93%) 267 (70%) 12 (100%) 212 (76%) 12 (100%) 276 (73%) 12 (100%) 106 (92%) 173 (76%) 196 (79%) 149 (84%) 95 (89%) 150 (83%) 167 (80%) 12 (100%) 12 (100%) 91 (92%) 12 (100%) 12 (100%) 79 (97%) 12 (100%) 12 (100%) 12 (100%) 191 (83%) 12 (100%) 12 (100%) 249 (71%) 12 (100%) 12 (100%) 174 (83%) 12 (100%) 299 (76%) 12 (100%) 27 (96%)

Participant

P18

B

P19

A

P20

B

P21

A

100% 100% 100% 100% 100% 100% 100% -100% 100% 100% 50% 66.6% 33.3% 50% 66.6% 33.3% 50% 50% 100% 83.3% 100% 66.6% 83.3% 100% 100% 83.3% 100%

100% 100%

83.3% 100% 83.3% 100%

100% 83.3% 100% 83.3% 100%

† Participants in Condition A completed Phase 4 first and Phase 5 second; the order was reversed in Condition B. Note. Within participants’ Part I data, the first row indicates the number of trials completed in Part I and the second row indicates retraining conducted in Part II. Results of analogical tests conducted in Phase 4 are shown as the percentage of trials on which the relation of sameness comparison selected had, during training, shared a common physical property with the sample (e.g., G1H1–N1O1 in Fig. 2). Phase 5 results show the percentage of trials on which the participant selected the comparison compound stimulus with same relation as the sample stimulus.

properties). Two other participants (P18 and P21) made this same relational response on five of six analogical test trials and, after retraining, chose the sameness comparison that shared common physical properties on six of six retest trials.

Of the remaining participants who responded less consistently in the first analogical test, two (P17 and P19) consistently chose the common-properties comparison stimulus in the third retest. Lastly, P15 and P16 did not show any consistent pattern of responding in any of

ANALOGY APTNESS their three Phase-4 analogical tests. Thus, 18 of the 20 participants eventually passed the test by showing a consistent pattern of responding by selecting analogies with common physical properties as more correct than exclusively relational analogies, 14 without retraining. Analogical Test 2: Relating relations of sameness and distinction without common physical properties. Eleven of the twenty participants passed this test on the first exposure by consistently selecting the comparison compound stimulus with the same relation as the sample stimulus (5 of 10 participants in Condition A, 6 of 10 in Condition B). All of the remaining 9 participants passed the test on their first retesting. Discussion The aim of the current study was to provide the first RFT experimental analysis of analogy aptness. Specifically, this study analyzed whether, all things being equal, analogies with common physical properties are judged as more apt than exclusively relational analogies (i.e., without common physical properties). After training in the analogical test format, 20 participants underwent training in two separate relational networks, each containing three 3member equivalence classes. The node stimuli of these equivalence classes contained colored spots that were subsequently used as relevant physical properties. Then, participants were randomly assigned to Condition A or Condition B, which only differed in the presentation order of the analogical tests. In the critical test, participants had to select the more correct response out of two options: one relating derived relations of sameness between two networks with a common physical property (i.e., analogy with common physical properties), and the other relating derived relations of sameness between two networks that did not share any physical property (i.e., exclusively relational analogy). An additional analogical test required participants to relate combinatorial relations of sameness and distinction without common physical properties (i.e., exclusively relational analogies). The results showed that 18 out of 20 participants (9 per condition) consistently selected analogies with common physical properties over those that were exclusively relational. Fourteen of these 18 participants passed

11

this test on their first attempt (78%). Additionally, all 20 participants passed the Test for Relating Relations of Sameness and Distinction without Common Physical Properties, 11 of them on their first attempt (55%). Together, 8 of the 18 participants (44%) passed both tests on their first attempt, without retraining and the Combinatorial Relations Test. Importantly, most of the failures (52%) in the analogical tests were due to only one error (i.e., participants responded correctly to five out of six trials). Thus 75% of the participants performed perfectly or almost perfectly in the analogical tests. Some possible limitations of the current study are worth noting. The procedure of Part I (Phases 1 and 2) can be substantially improved. On the one hand, a good number of participants had difficulties in the training of conditional discriminations with CVC (Phase 1) whereas they did not have them with abstract shapes and Greek letters (Phase 3). The use of English nonsense syllables as arbitrary stimuli with Spanish speakers might provide an explanation. Alternatively, participants may have performed better in Phase 3 because they benefited from the practice afforded in Phase 1. On the other hand, participants also experienced difficulties in solving the Relating Trained Relations Test (Phase 2). Indeed, none of the participants passed this test on the first attempt as opposed to the 50% of participants who passed it with exactly the same procedure in Experiment 2 of Ruiz and Luciano (2011). One difference between studies is that the participants in Ruiz and Luciano experiment were previously exposed to an analogical reasoning test and this might have facilitated participants’ analogical repertoire. In any case, it is worth noting that the aim of Part I was only to bring participants’ behavior under the control of the relevant cues of the analogical test format. Therefore, the results from this phase do not affect the conclusions reached about participants’ performance in the final analogical tests. A more relevant limitation is that many participants were exposed to the Combinatorial Relations Test after responding incorrectly on one trial in the critical analogical tests. Although no explicit feedback was provided on combinatorial test trials, it could be argued that relating stimuli in this fashion might inherently provide

12

FRANCISCO J. RUIZ and CARMEN LUCIANO

reinforcement (e.g., Barnes-Holmes, Hayes, Dymond, & O’Hora, 2001; Luciano, ValdiviaSalas, Berens, Rodr
ıguez-Valverde, Ma~ nas, & Ruiz, 2009; Rodr
ıguez-Valverde, Luciano, & Barnes-Holmes, 2009; T€ orneke, 2010). If so, subsequent analogical test performances may not have involved relating completely derived relations. Nevertheless, the general conclusion of this study holds because prior to the combinatorial relations tests, participants most often selected analogies with common physical properties as more correct than exclusively relational analogies. The main limitation of the current study is that it does not specify the mechanism by which common physical properties affect the derivation of analogies. Two alternatives seem feasible to explain the current results. On the one hand, participants could have first recognized both analogies as correct and then, in the context of choosing the more correct one, discriminated the common physical properties of both relational networks. On the other hand, attending to the common physical properties could have facilitated the derivation of the analogies. Further research may explore this issue. One option in this respect is to measure participants’ response latency because if common physical properties facilitate analogy derivation, then participants should more quickly recognize analogies with common physical properties than exclusively relational analogies. In conclusion, the current study is the first RFT analysis of analogy aptness and provides strong experimental evidence supporting the idea that, all things being equal, analogies between domains that share physical properties are considered to be more apt. This finding has important implications in applied areas in which analogies are frequently used, such as education and psychotherapy. For instance, the results of the current study suggest that the cell analogy and the quicksand metaphor would be judged as more apt than the spam filter analogy and the wound metaphor, respectively, given the presence of common physical properties among the relational networks involved. References Barnes, D., Hegarty, N., & Smeets, P. M. (1997). Relating equivalence relations to equivalence relations: A

relational framing model of complex human functioning. The Analysis of Verbal Behavior, 14, 1–27. Barnes-Holmes, D., Hayes, S. C., Dymond, S., & O’Hora, D. (2001). Multiple stimulus relations and the transformation of stimulus functions. In S. C. Hayes, D. Barnes-Holmes, & B. Roche (Eds.), Relational frame theory. A post-Skinnerian account of human language and cognition (pp. 51–71). New York: Kluwer Academic. Bassok, M., & Holyoak, K. J. (1989). Interdomain transfer between isomorphic topics in algebra and physics. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 153–166. Blanchette, I., & Dunbar, K. (2001). Analogy use in naturalistic settings: The influence of audience, emotion, and goals. Memory & Cognition, 29, 730–755. Capelli, S., & Jolibert, A. (2009). Metaphor’s validity in marketing research. Psychology & Marketing, 26, 1079–1090. Hayes, S. C., Barnes-Holmes, D., & Roche, B. (Eds.) (2001). Relational frame theory. A post-Skinnerian account of human language and cognition. New York: Kluwer Academic. Hayes, S. C., Strosahl, K. D., & Wilson, K. G. (1999). Acceptance and commitment therapy. An experiential approach to behavior change. New York: Guilford. Hesse, M. (1966). Models and analogies in science. Notre Dame, IN: Notre Dame University Press. Holyoak, K. J. (2005). Analogy. In K. J. Holyoak, & R. G. Morrison (Eds.), The Cambridge handbook of thinking and reasoning (pp. 117–142). New York: Cambridge University Press. Lipkens, R. (1992). Analogical reasoning as arbitrarily applicable relational responding. Unpublished doctoral dissertation, University of Nevada, Reno. Lipkens, R., & Hayes, S. C. (2009). Producing and recognizing analogical relations. Journal of the Experimental Analysis of Behavior, 91, 105–126. Luciano, C., Valdivia-Salas, S., Berens, N. S., Rodr
ıguezValverde, M., Ma~ nas, I., & Ruiz, F. J. (2009). Acquiring the earliest relational operants. Coordination, difference, opposition, comparison, and hierarchy. In R. A. Rehfeldt & Y. Barnes-Holmes (Eds.), Derived relational responding. Applications for learners with autism and other developmental disabilities (pp. 149–170). Oakland, CA: New Harbinger. Rodr
ıguez-Valverde, M., Luciano, C., & Barnes-Holmes, D. (2009). Transfer of aversive respondent elicitation in accordance with equivalence relations. Journal of the Experimental Analysis of Behavior, 92, 85–111. Ruiz, F. J., & Luciano, C. (2011). Cross-domain analogies as relating derived relations among two separate relational networks. Journal of the Experimental Analysis of Behavior, 95, 369–385. Ruiz, F. J., & Luciano, C. (2012). Relacionar relaciones como modelo anal
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afora [Relating relations as a functional-analytic model of analogy and metaphor]. Acta Comportamentalia, 20, 5–31. 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, 5–22. Stewart, I., & Barnes-Holmes, D. (2004). Relational frame theory and analogical reasoning: Empirical

ANALOGY APTNESS investigations. International Journal of Psychology and Psychological Therapy, 4, 241–262. Stewart, I., Barnes-Holmes, D., Hayes, S. C., & Lipkens, R. (2001). Relations among relations: Analogies, metaphors, and stories. In S. C. Hayes, D. Barnes-Holmes, & B. Roche (Eds.), Relational frame theory. A post-Skinnerian account of human language and cognition (pp. 73–86). New York: Kluwer Academic. Stewart, I., Barnes-Holmes, D., Roche, B., & Smeets, P. M. (2002). A functional-analytic model of analogy: A

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relational frame analysis. Journal of the Experimental Analysis of Behavior, 78, 375–396. T€ orneke, N. (2010). Learning RFT. An introduction to relational frame theory and its clinical implications. Oakland, CA: New Harbinger. Received: August 28, 2014 Final Acceptance: February 26, 2015