The synthesis of complex categories from perceptual

EUROPEAN JOURNAL OF BEHAVIOR ANALYSIS

2009, 10, 205 - 227

NUMBER 2 (WINTER 2009)

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The synthesis of complex categories from perceptual and equivalence classes: effects of training and testing parameters Lanny Fields

Queens College and the Graduate School of the City University of New York

Most real-world categories are complex since each contains some exemplars that resemble each other and others that are perceptually disparate. One example would be the many sounds of a persons’ voice when speaking and whispering, pictures of that person taken from different vantage points and in different degrees of focus, and the name of that person as written by different hands, and in different fonts. When all of these exemplars occasion the mutual selection of each other, and a function acquired by one class member generalizes to all other class members, all of the exemplars are acting as members of a complex category. A complex category can be formed by the merger of perceptual, fuzzy, and relational classes with equivalence classes. This presentation will consider how training and testing variables influence the likelihood of establishing a variety of complex categories such as linked perceptual classes, and fully elaborated generalized equivalence classes. These data provide a basis for understanding how complex categories are induced in natural settings. Keywords: Categorization, Equivalence classes, Generalized Equivalence Classes, Linked Perceptual Classes, Intermodal Perception

As an undergraduate at Columbia College, my first exposure to Psychology occurred in 1958 when I took Introductory Psychology, which used the text book Principles of Psychology, written by Keller and Schoenfeld (1950). One of the most fascinating topics in the text was their treatment of concept formation, semantic conditioning and mediated generalization. Concept formation was defined in terms of generalization among stimuli in a class and discrimination between stimuli in different classes. Semantic conditioning was even more interesting (Keller, 1943; Razran, 1939; Reiss, 1940). Using the written words URN, VASE, and EARN, Pavlovian conditioning to the written word URN resulted in more generalization of the conditional response the written word VASE, than to the written word EARN. This occurred even though URN and EARN are pronounced in the same way. How can stimuli that are physically dissimilar become related to each

other and act as a function transfer network, while stimuli that share physical similarities do not? The implication was that the sharing of a common function was the critical component; in this example, both URNS and VASES hold objects, while EARN is a verb that does not share a common function with URN or VASE. Thus, the latter words were more related to each other than the words that sounded alike but did not share a common function. In the endnotes of the chapter that discussed concept formation, Keller and Schoenfeld also mentioned that not much work had been done in the exploration of semantic conditioning but that it would seem to be of potential import. That was 1958. Little did I know that my interest then was a harbinger of a professional career and long term research interest. The more recent work on equivalence class formation initiated by Sidman(1971) launched my research regarding the determinants of per-

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ceptual classes, equivalence classes, and complex categories like those found in every day settings. I will describe some of the research that has been conducted in my laboratory, and how it can be used to account for the emergence of complex naturally occurring categories by the merger of simpler perceptual classes and equivalence classes. Along the way, I will describe experiments that disclosed training and testing variables that influenced the likelihood of forming these classes and, might well play similar roles in the emergence of complex categories in natural settings. Complex Real World Categories. In a real world setting, behavior that is appropriate for a particular situation should also be evoked by other situations that are related to the initial situation. This can occur when the situations resemble each other, and when the situations do not resemble each other but are thematically related to each other. When this is observed, we conclude that an individual is adapting effectively to the inevitable variations that are experienced in the real world. When this occurs, the set of situations that occasion the same response are said to be functioning as members of a complex category, even though the response has not been directly trained to occur in the presence of all situations. Fully Elaborated Generalized Equivalence Classes. One way of synthesizing a complex category like that mentioned above would be to combine equivalence classes and perceptual classes. This is illustrated in Figure 1 by considering a complex category of HORSE, which can consist of three perceptual classes, pictures of horses, the name “horse” written in different fonts and hands, and the name “caballo” A Naturally Occurring Category

Horse Ù Horse ÙCaballo Pics fonts fonts Figure 1.An illustration of a fully elaborated generalized equivalence class.

written in different fonts and hands, where all representation in each class are also related to the representations in the other classes. Such a category or class can be synthesized in a twostep process. Formation of Perceptual Classes. As illustrated in Figure 2, each perceptual class contains stimuli that are variants of each other and can be arrayed along a physically, psychometrically defined, or multi-dimensionally defined continuum. Because the classes contain a virtually unlimited number of exemplars, they are said to be open ended categories (Herrnstein, 1990). For descriptive purposes, the three classes are defined by the letters, A`, B`, and C`. The Perceptual Classes Horse Pics

Aa : : : Ab

Horse fonts

Ba : : : Bb

Caballo fonts

Ca : : : Cb

An Equivalence Class..

Aa====ÎBa====ÎCa

Horse pic

Horse

Caballo

A Fully Elaborated Generalized Equivalence Class Horse Pics

Horse fonts

Caballo fonts

Aa ===Î Ba ===Î Ca : : : : : : : : : Ab Bb Cb

Figure 2.The merger of perceptual and equivalence classes to form a fully elaborated generalized equivalence class.

The synthesis of complex categories from perceptual and equivalence classes

apostrophe is used to indicate a class of stimuli rather than a singular stimulus. In each class, the clearest exemplar is called an anchor stimulus (represented as a) and the most ambiguous stimulus in the class is called the boundary stimulus (represented as b). Thus, in the A` class, the anchor and boundary stimuli are represented as Aa and Ab, respectively. The perceptual classes can be formed with multiple exemplar training using simple- or conditional-discrimination paradigms. In the simple discrimination paradigm, training would involve the reinforcement of the same response in the presence of some of the stimuli in the putative classand the extinction the same response in the presence of stimuli from other classes (Cook, Wright, & Kendrick, 1990; Herrnstein & Loveland, 1964; Herrnstein, Loveland, & Cable, 1976; Hull, 1920; Markle, Tieman, 1972; Smoke, 1932; Stokes & Baer, 1977). In the conditional discrimination paradigm, training would involve the selection of some class members in the presence of a few other class membersand rejection of stimuli from other classes (Fields, Reeve, Matneja, Varelas, Belanich, Fitzer, & Shamoun, 2002; Wasserman, Kiedinger, & Bhatt, 1988; Wright, Cook, Rivera, Sands, & Delius, 1988).Tests for class formation involve the presentation of novel exemplars of the class and novel exemplars that are not from that class. Responding to the novel exemplars from the class and not responding to the novel exemplars from other classes would document the emergence of the perceptual classes. Perceptual classes can also be formed in the absence of reinforcement by conducting a forced choice generalization tests in a matching to sample trial (Reeve & Fields, 2001). Merger of Perceptual Classes via Equivalence Classes. Second, these open ended classes can be linked by the establishment of an equivalence class among one image from each of the perceptual classes: one image of a horse, one written exemplar of the word horse, one written exemplar of caballo. This could be accomplished by the training of two conditional discriminations such as PICTUREàHORSE and HORSEà CABALLO. Thereafter, the selection of stimuli from the same class in derived relations tests

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that contain novel stimulus combinations as samples and comparisons would document the emergence of the equivalence class. Theoretically, these two operations should result in the linkage or merger of the three perceptual classes into one large complex class like those seen in natural settings. Technically, we called these classes, fully elaborated generalized equivalence classes (Fields, & Reeve, 2001). Minimally Elaborated Generalized Equivalence Classes. The early work on generalized equivalence classes, however, did not involve classes as complex as that described above. Rather, those studies involved an equivalence class merged with the variants on only one member of the basal equivalence class (Barnes, & Keenan, 1993; Belanich, & Fields, 1999; Fields, Adams, Buffington, Yang, &Verhave, 1996; Fields & Reeve, 2001; Fields, Reeve, Adams, Brown, &Verhave, 1997; Fields, Reeve, Adams, &Verhave, 1991; Rehfeldt, 2003; Rehfeldt & Hayes, 2000). Such a class was called a minimally elaborated generalized equivalence class (Fields & Reeve, 2001). A minimally elaborated generalized equivalence class is illustrated schematically in Figure 3. The equivalence class was established by training Aa-Ba and Ba-Ca. Thereafter, the merger of the equivalence class with the perceptual class C` was measured by the presentation of two types of generalization tests: variant-to-base tests, and base-to-variant tests. In the variant-to-base generalization tests, many variants of C (represented as C```) were presented as sample stimuli with Ba or Ca of the equivalence class as comparisons. (Galizio, Stewart, & Pilgrim, 2004; Lane, Clow, Innis, &Critchfield, 1998; Rehfeldt, & Root, 2004;). In variant-to-base generalization tests, the basal members of the equivalence class (Aa or Ba) were presented as comparisons with variants presented as samples (Fields, Matneja, Varelas, &Belanich, 2003). Thus, C```-Aa probes evaluated the generalization of the CA equivalence relation, the C```-Ba probes evaluated the generalization of the symmetrical relations, the Ba-C``` probes evaluated the generalization of a baseline relations, and the Aa-C``` probes evaluated the generalization of the transitive relation. In most experiments, the variants of the

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perceptual class resulted in the selection of the members of the basal members of the equivalence classes with high and equal likelihood in variant to base tests, and the variants in the perceptual class were selected in the presence of the basal members of the equivalence classes during base to variant tests with high and equal likelihood. These results then documented the merger of an equivalence class and a perceptual class or the formation of minimally elaborated generalized equivalence classes. Retention. Very few studies have explored the stability of equivalence classes over time (Saunders, Saunders, Kirby, & Spradlin, 1990; Spradlin, Saunders, & Saunders, 1992; Saunders, Wachter, & Spradlin, 1988). Individuals with mental retardation formed equivalence classes with auditory and visual stimuli. The classes remained intact two to five months after class formation. Thus, equivalence classes appear to be stable over time. Once minimally elaborated generalized equivalence classes have been formed, to what extent are they retained over time? Only two studies have addressed this Minimally Elaborated Generalize Equivalence Class

Aa=====ÎBa====ÎCa : : : Ba----------> Ca : : : : : : : : : Ab Bb Cb Variant-to-Variant Probes A``--B`` B``--C``

Baseline

B``--A`` C``--B``

Symmetry

A``--C`` C``--A``

Transitivity Equivalence

Figure 4.The variant-to-variant tests used to track the emergence of a fully elaborated generalized equivalence class.

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called a linked perceptual class (Fields, Matneja, Varelas, Belanich, Fitzer, & Shamoun, 2002). Thus, we used this platform to identify the parameters that influenced the functionality of variant-to-variant tests, with the expectation that they could subsequently be used to track the formation of fully elaborated generalized equivalence classes. As mentioned above, a vast number of variant-to-variant tests could be conducted to document relations among the variants of stimuli in each of the classes in a linked perceptual class or in a fully elaborated generalized equivalence class. We minimized the number of such tests by the identification of three key stimuli in each perceptual class: the clearest stimulus in the class called the anchor stimulus (i.e., Aa or Ba), the most ambiguous stimulus in the class called a boundary stimulus (i.e., Ab or Bb), and a variant that was perceptually equidistant from the anchor and boundary stimulus in a class, called the midpoint stimulus, represented by m, Thus, the midpoint stimuli for the A` or B` class would be represented as Am or Bm, respectively. The anchor, midpoint, and boundary stimuli from four perceptual classes are indicated in Figure 5. By using only three variants per perceptual class, the number of variant-to-variant probes needed Linked Perceptual Class

Aa----------------------Ba : : : : Am Bm : : : : Ab Bb Variant to Variant Probes

A`-------------------BB` B`-------------------BA` Figure 5. A linked perceptual class and the variantto-variant probes needed to track class formation.

to track the formation of a linked perceptual class is large by manageable. Figure 6 provides a symbolic representation of the assignment of anchor, midpoint and boundary stimuli to classes in two domains. The anchor, midpoint and boundary stimuli in each of two domains are identified pre-experimentally by a group of independent observers. In our investigations of linked perceptual classes we used perceptual classes constructed from satellite images of four different land masses. Satellite images were used because the images were unlikely to be easily nameable. Two images were used as the endpoints of one stimulus domain, Domain-A, and were designated as the anchors of Domain-A, A1a and A2a. The other two images were used as the endpoints of a second stimulus domain, Domain-B, and were designated B1a and B2a. Many variants along each domain were created by morphing the endpoint images of that domain: A1a with A2a and B1a with B2a. This was done by the superimposition of the endpoint stimuli in a domains and then mixing the salience of each in small steps by a computer algorithm. Thereafter, the boundary stimuli for each of four classes were determined presenting the observers with one of the anchor stimuli, e.g., A1a, and all of the variants along Domain A, and asking them to identify the variant that were most distant from the anchor stimuli but was still considered to be completely related to it. That variant was identified as the boundary stimulus of perceptual class A1`, and was represented as A1b. The same was done with each of the remaining anchor stimuli which gave rise to the boundary stimuli A2b, B1b, and B2b, which were the endpoints of perceptual classes A2`, B1`, and B2`, respectively. Once the anchor and boundary stimuli were established for each class, the same observers were given the anchor and boundary stimuli for a given class, e.g., A1a and A1b, along with many variants between those endpoints and were asked to select the variant that was equidistant from the endpoints. That variant was designated as the midpoint of perceptual class A1`, and was designated as A1m. The same was done with the other classes. The same was done

The synthesis of complex categories from perceptual and equivalence classes

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Classes and Stimuli in Domains A` and B` Class 1

Class 2

A1a........A1m........A1b

A2b........A2m........A2a

B1a........B1m........B1b

B2b........B2m........B2a

a = anchor m = midpoint b = boundary

Figure 6.A schematic representation of two stimulus domains with perceptual classes at each end of each domain, with anchor, midpoint, and boundary stimuli in each perceptual class.

with each of the remaining classes which gave rise to the midpoint stimuli A2m, B1m, and B2m, which were the midpoints of perceptual classes A2`, B1`, and B2`, respectively. Using variant-to-variant tests to document linked perceptual class formation. The first study of linked perceptual class formation demonstrated that variant-to-variant probes was conducted by Fields, Matneja, Varelas, Belanich, Fitzer, and Shamoun (2002). That study used the perceptual classes consisting of satellite images along with three variants per perceptual class. The procedure is represented schematically in Figure 7. Four perceptual classes were used: A1`, A1`, B1`, and B2`, The classes were linked by the establishment of conditional discriminations between the anchors of pairs of classes and the boundaries of pairs of classes., A1a-B1a, A1b-B1b, A2a-B2a and A2b-B2b, all of which are represented in the upper portion of Figure 6. Thereafter, 18 cross class variant-to-variant probes were presented to track the emergence of linked perceptual classes. Nine were in the A`-B` format and nine were in the B`-A` format, all of which are

listed in the lower portion of Figure 7. Each of these 18 probes was presented for stimuli in class 1 and class 2. For example, an Am-Bb probe for class 1 would consist of A1m as the sample with B1b and B2b as the comparisons, the class 2 probe would contain A2m as the sample with B1b and B2b as the comparisons. Performance indicative of the emergence of the linked perceptual classes would entail the selection of B1m in the former trial and B2m in the latter trial. Similar selections occasioned by all variant-to-variant tests would document the formation of two linked perceptual classes. All of the participants in that study responded in a class consistent manner to all of the variantto-variant probes thereby documenting the emergence of two linked perceptual classes. This experiment was a proof of concept for the use of variant-to-variant probes to monitor the emergence of new relations among the members of two perceptual classes that were linked by conditional discrimination training. Testing Variables and the Formation of Linked Perceptual Classes. When we considered the parameters of Fields et al (2002), it became clear that the

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outcome could have been influenced by order of presenting the variant-to-variant tests (i.e. testing schedules) and/or by the relations that were trained to link the perceptual classes. Our next step, then, involved an exploration of the effects of testing schedules on the formation of linked perceptual classes (Fields, Fitzer, Tittelbach, & Shamoun, 2005). The 18 cross class probes listed in Figure 7could have been presented in a many different orders and in different combinations, any of which could have influenced class formation. An entire battery of variant-to-variant tests can

be presented in a given number of blocks and with a corresponding number of different probe types per block. Thus, we decided to study the effect of four different testing schedules on the formation of linked perceptual classes. Each is listed in a separate column of Figure 8. The 2/9 schedule indicates the presentation of two blocks with nine different probe types per block, the 6/3 schedule indicates the presentation of six blocks with three different probe types per block, and the 18/1 schedule indicates the presentation of 18 blocks with one different probe type per block. In addi-

Linking of Perceptual Classes A` and B` A1a.......A1m.......A1b . . . A2b........A2m.......A2a | | | | | | | | | | | | B1a.......B1m.......B1b . . . B2b........B2m.......B2a Training: Aa--->Ba

&

Ab--->Bb

9 A`--->B` probes

9 B`—>A` probes

Aa---> Ba

Ba---> Aa

Am–> Ba

Bm--> Aa

Ab—> Ba

Bb---> Aa

Aa---> Bm

Ba---> Am

Am--> Bm

Bm--> Am

Ab---> Bm

Bb---> Am

Aa---> Bb

Ba---> Ab

Am--> Bb

Bm--> Ab

Ab---> Bb

Bb---> Ab

Figure 7.All 18 variant-to-variant probes that can be used to track the emergence of a linked perceptual class.

The synthesis of complex categories from perceptual and equivalence classes

tion, for the 18/1 schedule, the 18 different probes could be presented in a randomized or unsystematic order across the succession of blocks, the 18/1-RND schedule, or in a highly programmed and sequenced manner across the succession of blocks, the 18/1-PRGM schedule. Each schedule was used with a different group of participants. Participants in all groups, however, were given the same training: Aa-Ba and Ab-Bb. 2/9 ....................... Aa–--Ba

6/3 ....................... Aa–-Ba

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Figure 9 shows the effect of each schedule on the subjects in group who formed both linked perceptual classes, A1`-B1` and A2`-B2`. A similar low proportion of subjects formed linked perceptual classes when testing was conducted with the 2/9, 6/3, and 18/1-RNDschedules (see preceding paragraph). In contrast, when the 18/1-PRGM schedule was used (see preceding paragraph), close to 90% of subjects showed the emergence of the linked perceptual classes.

18 / 1-RND 18 / 1-PRGM ........................ ....................... Ba---Aa Aa–-Ba ........................ ............. Am---Ba Am--Ba Aa---Bm Am--Ba ........................ ............. Ab----Ba Ab---Ba Bm–-Ab Ab---Ba ........................ ........................ ....................... Aa----Bm Aa---Bm Am--Ba Aa---Bm ........................ ............. Am---Bm Am--Bm Bm--Am Am--Bm ........................ ............. Ab---Bm Ab----Bm Ab---Bm Am--Bb ....................... ........................ ........................ Aa---Bb Aa----Bb Aa---Bb Bb–-Ab ............. ........................ Am--Bb Am---Bb Am--Bb Ba–-Ab ............. ........................ Ab---Bb Ab----Bb Ab---Bb Ab---Bb ....................... .......................... ........................ ........................ Ba---Aa Ba----Aa Ba---Aa Ba–-Am ............. ........................ Bm--Aa Bm---Aa Bm--Aa Ab---Bm ............. ........................ Bb–-Aa Bb–--Aa Bb–-Aa Aa–-Ba ....................... ........................ ........................ Ba–-Am Ba–--Am Ba–-Am Bm--Aa ............. ........................ Bm--Am Bm---Am Bm--Am Ab---Ba ............. ........................ Bb–-Am Bb–--Am Bb–-Am Am--Bm ....................... ........................ ........................ Ba–-Ab Ba–--Ab Ba–-Ab Bb–-Am ............. ........................ Bm–-Ab Bm–-Ab Bm–-Ab Bb–-Aa ............. ........................ Bb–-Ab Bb–--Ab Bb–-Ab Aa---Bb ....................... ........................ ........................ ........................ Figure 8.Four testing schedule that can be used to assess the emergence of linked perceptual classes.

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Clearly, testing influenced the formation of linked perceptual classes. The number of test blocks and the number of different probes per test block were not critical determinants of the testing schedule effect. Rather, it was the highly serialized and programmed manner of probe sequencing that was responsible for the reliable formation of linked perceptual classes. Next, we explored the effects of a variety of training conditions on class formation (Fields, Tittelbach, Shamoun, Fitzer, Watanabe, &Matneja, 2007). Some options are illustrated in Figure 10. Two classes can be linked by the establishment of at least one cross class conditional relation. When one cross class relation is established, it can be done in at least four ways. The first involves the training of a relation between the anchor stimuli in both classes, Here, the anchor stimuli serve as samples and comparisons. This procedure is called aa training. The second involves the training of a relation between the boundary stimuli in both classes, Here, boundary stimuli serve as samples and comparisons. This procedure is called bb training. One third involves the training of a relation between the anchor stimulus in one class that is used as the sample, and the boundary stimulus from the other class which is used as the comparison. Here, stimuli that have different psychometric Figure 11 Test Schdedule effects.pzf:%sbj 2lpc in t1 by test schedule - Mon Mar 30 16:32:25 2009

100

%Subjects with 2 LPCs

90 80 70 60 50 40 30 20 10 0

2/9-RND

6/3-RND

18/1-RND

18/1-PRGM

Testing Schedule

Figure 9.The effect of four testing schedules on the percentage of participants who formed two linked perceptual classes.

values serve as samples and comparisons. This procedure is called ab training. Finally, a fourth involves the training of a relation between the boundary stimulus in one class that is used as the sample, and the anchor stimulus from the other class which is used as the comparison. Again, stimuli that have different psychometric values serve as samples and comparisons. This procedure is called ba training. Two classes can also be linked by the establishment of two cross class relations. One involves the training of the aa and bb conditional relations and is called aa/bb training. The other involves the training of the ab and ba conditional relations and is called ab/ba training. Six experimental groups were studied. Each of the training options mentioned above was used with participants in one group. After the formation of the cross class conditional discriminations, participants in all groups were tested for the emergence of the linked perceptual classes using the 6/3 test schedule. That schedule was used because it produced intermediate likelihoods of class formation. As such, would provide a sensitive measure of the effects of training variables on class formation. Figure 11 illustrates the results of the training variable on likelihood of forming the linked perceptual classes. The left side of the figure shows the effects of training the single relations aa, bb, ab, and ba on the formation of linked perceptual classes. The formation of linked perceptual classes is an interactive function of the value of the stimuli used in training and the behavioral functions served by each stimulus in training. Specifically, when the sample stimuli are anchors, class formation was greater if the comparsion stimuli were boundaries instead of anchors. In contrast, when the sample stimuli are boundaries, class formation was greater if the comparison stimuli were anchors instead of boundaries. Thus, there was an interaction between the value of the stimuli used as samples and comparisons (anchor or boundary) and the functions served by stimuli of the anchor and boundary stimuli (sample of comparisons). Additional research will be needed to understand the basis for this interaction of value and function.

The synthesis of complex categories from perceptual and equivalence classes

The effect of training with the two combinations of two linking relations, aa/bb and ab/ba are depicted on the right side of Figure 10. Both dual training conditions produced very similar high yields. In addition, the yields were quite similar to that produced by ab training. Thus, the yield produced by ab/ba training was driven predominantly by ab training alone. When dual training was conducted with aa and bb, we have a different story. The training of both relations produced yields that were far greater than that produced the simple summation of aa training alone and bb training alone. What accounts for this synergy is the subject of additional research. Optimizing the Formation of Linked Perceptual Classes. It would appear from the data presented above that the establishment of

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linked perceptual classes should be optimized by training with AaàBb relations and tracking for class emergence with an 18/1-PRGM testing schedule. This was evaluated by recently by Fields and Garruto (2009). As predicted, this combination of training and testing resulted in the formation of linked perceptual classes by all participants. Linked Perceptual Classes as Function Transfer Networks. As mentioned above, a wealth of data has shown that a function acquired by one member of an equivalence class generalizes to the remaining members of the equivalence class. After forming linked perceptual classes, Fields and Garruto (2009) explored whether similar results occur with linked perceptual classes. The procedures used are outlined in Figure 11.

One Linking Relation ========================= aa Training ab Training Aa : Am : Ab

Ba : Bm : Bb

bb Training Aa : Am : Ab

Ba : Bm : Bb

Aa : Am : Ab

Ba : Bm : Bb

ba Training Aa : Am : Ab

Ba : Bm : Bb

6/3 Test

Two Linking Relations ========================== aa/bb Training ab/ba Training Aa Ba Aa Ba : : : : Am Bm Am Bm : : : : Ab Bb Ab Bb Figure 10. Six training options that can be used to establish baseline relations that link two distinct perceptual classes.

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After the establishment of linked perceptual classes by training Aa-Bb, participants were divided into two experimental groups. In one group, participants were trained to make different responses to the Aa stimuli in the two linked perceptual classes. In the other group, discrimination training was conducted with the Ba stimuli. Thereafter, all of the stimuli in both classes were presented alone, without feedback in a randomized order, and many times. In all cases but one, the response trained to one stimulus in the class generalized to all of the remaining stimuli in the linked perceptual class. This occurred regardless of the class member to which the responses had been trained, which demonstrated the function transfer did not depend on the use of particular class members as the discriminative stimulus. As with other types of classes, then, linked perceptual classes also act as function transfer networks. Linked Perceptual Classes as Generalized Equivalence Classes. A linked perceptual class can be represented structurally as Ab…Am…. AaàBa…Bm…Bb. The midpoint and boundary stimuli in the A` class are linked to the midpoint and boundary stimuli in the B` class by the relation established between Aa and Ba. Technically, these two stimuli were functioning as nodes. As such, a linked perceptual class can be viewed as special case of a generalized equivalence class. Linked perceptual classes, then, are not unique; rather, they a form of generalized interactions and IE and DE.pzf:IE 6 trn cond - Sat Mar 28 12:33:56 2009

6/3 Test Schedule

% Subjects

100 80 60 40 20 0

aa

ba bb aa/bb ab Training Conditions

ab/ba

Figure 11.The effect of six training procedures to link two distinct perceptual classes on the percentage of participants who formed two linked perceptual classes.

equivalence class. Linked Perceptual Classes, Cross Modal Perception and Intersensory Integration. Linked perceptual classes were used as a vehicle to develop variant-to-variant probes. We realized, however, that linked perceptual classes represent a category that had not been studied in its own right and that had many naturally occurring exemplars. One would be the sounds made by a predator (A`), and the visual images of the predator (B`). Another would be pictures of monkeys (A`) and the sounds of the word monkey as spoken by many individuals (B`). A third would be the various X-ray images of malignant tumors (A`) and the feeling of those tumors sensed by palpation (B`). In addition, we realized that the relations among stimuli in two related perceptual classes were also being studied under the rubric of intermodal perception and intersensory integration (Bahrick& Pickens, 1994) topics studied by developmental and cognitive psychology. The procedures used to establish and measure the emergence of linked perceptual classes, then, might provide a behavioral account of intermodal perception and intersensory integration. To recapitulate, first, variant-to-variant probes that use anchor, midpoint, and boundary stimuli can be used to document the emergence of relation between the members of two perceptual classes that have become linked by conditional discrimination training. Thus, they can now be used to document the formation of fully elaborated generalized equivalence classes, as will be discussed below. Second, the formation of linked perceptual classes is influenced by the interactive effects of the values and functions of the stimuli used in the class-linking conditional discriminations and by the schedule of variant-to-variant probe presentations that is used to track class formation. Those data predicted a set of training and testing conditions that would optimize class formation, a prediction that was confirmed by subsequent research. Third, linked perceptual classes act as function transfer networks, as do other categories. Linked perceptual classes may be special form of a generalized equivalence class. Finally, linked perceptual classes may be

The synthesis of complex categories from perceptual and equivalence classes

akin to categories studied in other realms of psychology such as cross modal perception and intersensory integration. Partially Elaborated Generalized Equivalence Classes. Having developed a procedure for the measurement of variant-to-variant relations, we used the technology to study the formation of partially elaborated generalized equivalence classes. These are N-member equivalence classes that are merged with more than one perceptual classes but less than N perceptual classes (Fields & Reeve, 2001). Fields & Moss (2008) studied the formation of partially elaborated in the following manner with the use of A and B stimuli that were variants of satellite images along with C stimuli that were nonsense syllables. First a linked perceptual class (A`-B`) was established by training AaàBa and AbàBb. The emergence of the linked perceptual classes was monitored with an 18/1-PRGM testing schedule. Thereafter, a Figure conditional discrimination was established 3 Experimental Design:

between Ba and a new stimulus, C, by BaàC training. That was followed by the presentation of a 12/1-PRGM testing schedule that involved the presentation of B`-C probes, C-B` probes, A`-C probes and C-A` probes, in that order. The B`-C probes evaluated the generalization of the baseline relation, the C-B` evaluated the generalization of symmetry, the A`-C probes evaluated the generalization of the transitive relation, and the C-A` probes evaluated the generalization of the equivalence relation. Figure 14 presents the results for one representative subject where the experiment was conducted in the same session (Group 1). All A`-B` and B`-A` probes typically occasioned class consistent responding and, thus, documented the formation of the A`-B` linked perceptual classes. After Ba-C training, class consistent responding was produced by the B`-C, C-B`, A`-C and C-A` probes which demonstrated the expansion of the linked perceptual classes to partially elaborated generalized equivalence classes. 17

Discrimination Training to Aa ------------------------------------------

Linked Perceptual Class

3J || A1b……A1m…..A1a  B1b.….B1m…...B1a

Aa-------------Ba : : : : Ab Bb

7J || A2b……A2m…..A2a  B2b.….B2m…...B2a

Discrimination Training to Ba -----------------------------------------3J || A1b……A1m…..A1a  B1b.….B1m…...B1a 7J || A2b……A2m…..A2a  B2b.….B2m…...B2a

Figure 12. The structures of linked perceptual classes and the stimuli to which responses are trained prior to the measurement of response transfer to the members of linked perceptual classes.

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Partially Elaborated Generalized Equivalence Class Aa------------Ba-------------Ca : : : : Ab Bb Figure 13. Strategy for the expansion of linked perceptual classes to partially elaborated generalized equivalence classes.

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Figure 15 presents the results for one representative subject where the experiment was conducted in two sessions separated by one week (Group 2). The first session involved the establishment of the linked perceptual classes. The second session began with Ba-C training and subsequence testing for the expansion of the linked perceptual classes to partially elaborated generalized equivalence classes. These participants formed the A`-B` linked perceptual classes. After Ba-C training, class consistent responding was produced by the B`-C, and C-B` probes but not for the A`-C and C-A` probes. These results then demonstrated the generalization of baseline relations and symmetrical relations, but no emergence of the nodally mediated transitive or equivalence relations between the A-based variants and the C stimuli. For these participants, then, the linked perceptual classes did not expand to form partially elaborated generalized equivalence classes.

The failure of class expansion could have been caused a breakdown or inactivation of the A-B relations that linked the A and B classes. This possibility was evaluated with a third group that replicated Group 2 in all regards but one. At the start of the second session, subjects were presented with a block of the Aa-Ba and Ab-Bb baselines under extinction conditions, along with their symmetrical counterparts, Ba-Aa and Bb-Ab. The rationale for this intervention is that the presentation of the baselines and symmetry probe would determine whether the class linking relations were retained, and if so, should prime the expansion of the linked perceptual classes to partially elaborated generalized equivalence classes. Thereafter, the participants were presented with the C-based emergent relations probes, B`-C, C-B`, A`-C, and C-A`, in that sequence. The results of this procedure are shown in Figure 16 for a representative subject. In the Figure 8.

TF2657

Linked Perceptual Class

Percentage Correct

A`-B`

B`-C C-B'

A'-C C-A'

Class

100 75

1

50 25 0

aa ma ba am mmbm ab mb bb

A`-B` Percentage Correct

B`-A`

Generalized Equivalence Class

aa ma ba am mmbm ab mb bb

B`-A`

a m b a m b

a m b a m b

B`-C C-B'

A'-C C-A'

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2

50 25 0

aa ma ba am mmbm ab mb bb

aa ma ba ammmbm ab mb bb

a m b a m b

a m b a m b

Probes Figure 14.Performances evoked by variant-to-variant tests during the formation of linked perceptual classes, and their expansion to partially elaborated generalized equivalence classes, where the entire experiment is conducted in a single session.

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The synthesis of complex categories from perceptual and equivalence classes

first session, after the establishment of theAa-Ba and Ab-Bb relations, all of the variant-to-variant probes evoked class consistent responding which documented the formation of the linked perceptual classes. When the Aa-Ba and Ab-Bb, Ba-Aa and Bb-Ab trials were presented at the start of the second session, all produced 98% class consistent responding. At the least, the baseline relations used to establish the A`-B` linked perceptual classes were intact. Thereafter, the participants were presented with the B`-C, C-B`, A`-C and C-A` probes, and all evoked class consistent responding. These performances documented the immediate expansion of the linked perceptual classes to partially elaborated generalized equivalence classes. To conclude, the expansion of a linked perceptual class to a partially elaborated generalized equivalence class requires the active status of the relations that link the separate classes that

are components of the linked perceptual class, at the time of expansion. That was the case in Groups 1 and 3 and was not the case in Group 2. It would appear that a priming process was responsible for the expansion of the linked perceptual classes to partially elaborated generalized equivalence classes. It is also possible that the same outcome would have occurred with the presentation of any of the relation in the linked perceptual class at the start of session 2 in Group 3. The outcome of such an experiment would provide a substantial amount of information about the processes responsible for the emergence of partially elaborated generalized equivalence classes. Partially elaborated generalized equivalence classes in higher education. To date, the only other study to study partially elaborated generalized equivalence classes used academically relevant college level course content instead of meaningFigure 9.

TF2664

Linked Perceptual Class

Percentage Correct

A`-B`

B`-C C-B'

A'-C C-A'

Class

100 75

1

50 25 0

aa ma ba am mmbm ab mb bb

A`-B` Percentage Correct

B`-A`

Generalized Equivalence Class

aa ma ba am mmbm ab mb bb

B`-A`

a m b a m b

a m b a m b

B`-C C-B'

A'-C C-A'

100 75

2

50 25 0

aa ma ba am mmbm ab mb bb

aa ma ba ammmbm ab mb bb

a m b a m b

a m b a m b

Probes Figure 15. Performances evoked by variant-to-variant tests during the formation of linked perceptual classes, and their expansion to partially elaborated generalized equivalence classes. In this condition, the linked perceptual classes were formed in one session, and the expansion of class membership was conducted a week later.

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less class members (Fields, Travis, Yadlovker, Roy, de Aguiar-Rocha, & Sturmey, 2009). In that study, four equivalence classes were established, each for a different type of interaction: no interaction, a cross over interaction, a divergent interaction, and a synergistic interaction. For each class, the type of interaction was represented by a graph (A), a textual description of the graph (B), the written names of the type interaction (C), and a generic definition of the interaction (D). Using computer based training and testing, four 2-node 4-member equivalence classes were formed by training AB, BC, and CD relations which yielded equivalence classes with nodal structures of AàBàCàD. Thereafter, a paper and pencil test was presented to evaluate generalization to novel graphs and descriptions. These were variants of A and B, respectively. All participants responded cor-

rectly to the novel tests. The variants of A and B, novel graphs and descriptions, occasioned the mutual selection of each other in A`-B` and B`-A` tests, the correct names of the interactions and the definitions of the interactions, in A`-C, A`-D, B`-C, and B`-D probes, and their symmetrical counterparts, C-A`, D-A`, C-B`, and D-B` probes. In addition to recognizing novel representations of academically based material, these performances demonstrated the emergence of partially elaborated generalized equivalence classes: A``--B``--C—D. Fully Elaborated Generalized Equivalence Classes. The experiments described thus far, involved the establishment of classes that were precursors to fully elaborated generalized equivalence classes. In 2008, we studied the formation of fully elaborated generalized equivalence classes by the expansion of linked Figure 12.

TF2819

Linked Perceptual Class

Percentage Correct

A`-B`

B`-C C-B'

A'-C C-A'

Class

100 75

1

50 25 0

aa ma ba am mmbm ab mb bb

A`-B` Percentage Correct

B`-A`

Generalized Equivalence Class

aa ma ba am mmbm ab mb bb

B`-A`

a m b a m b

a m b a m b

B`-C C-B'

A'-C C-A'

100 75

2

50 25 0

aa ma ba am mmbm ab mb bb

aa ma ba ammmbm ab mb bb

a m b a m b

a m b a m b

Probes Figure 16. Performances evoked by variant-to-variant tests during the formation of linked perceptual classes, and their expansion to partially elaborated generalized equivalence classes. In this condition, the linked perceptual classes were formed in one session, and the expansion of class membership was conducted a week later. Expansion, however, was conducted after confirmation of the baselines for the linked perceptual classes at the start of the second session.

The synthesis of complex categories from perceptual and equivalence classes

perceptual classes (Fields & Moss, 2008). Figure 17 depicts the stimuli used in the experiment. They were created using morphing technology and are in three domains with separate perceptual classes at each end of each domain. The images represent the anchor, midpoint and boundary stimuli in each class. In general, the experiment involved the formation of linked perceptual classes, which were then expanded to fully elaborated generalized equivalence classes, as depicted in Figure 18. The experiment was conducted in two training phases and nine test phases. Figure 19shows the results of that experiment for one representative participant. Data for Classes 1 and 2 are presented in the left and right hand portions Domain A

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of the Figure. The testing phases are portrayed in the rows numbers 1-9. The types of cross class probes presented in the testing phases are listed as column headers. After training AaàBa and AbàBb, all six participants passed A`-B` tests (Row 1) and then the B`-A` tests (Row 2), which documented to formation of the A`B` linked perceptual classes. The experiment continued with the training of BaàCa and BbàCb relations (indicated by the horizontal dashed line). All participants then passed the subsequently presented A`-C` tests (Row 3) and then the C`-A` tests (Row 4). These were generalization tests of transitivity and of equivalence which demonstrated the expansion of the linked perceptual classes to fully elaborated generalDomain B

Domain C

_1a

_1m

_1b

_n

_2b

_2m

_2a

Figure 17. The stimuli used to form fully elaborated generalized equivalence classes.

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ized equivalence classes. These tests, however, did not provide a comprehensive evaluation of the formation of fully elaborated generalized equivalence classes since the emergence of relations among the B` and C` classes had not been tested. Thus, next phase involved the presentation of A`-B` probes along with B`-C` probes (Row 5), all of which evoked class consistent responding. These performances demonstrated the maintenance of the A`-B` linked perceptual class and the emergence of B`-C` cross class relations needed to more fully document the existence of the fully elaborated generalized equivalence classes. Thereafter, the participants were presented with B`-A` and C`-B` probes (Row 6), all of which evoked class consistent responses. The B`-A` probes demonstrated the maintenance of the previously emergent relations, while the C`-B` probes demonstrated the immediate emergence of the last set of new relations needed to fully document the fully elaborated generalized equivalence class. At this stage of the experiment, then, the perfor-

A Linked Perceptual Class Aa-------------Ba : : : : : : Ab Bb

A Fully Elaborated Generalized Equivalence Class Aa-------------Ba-----------Ca : : : : : : : : Ab Bb Cb Figure 18. A schematic representation of the expansion of linked perceptual class to a fully elaborated generalized equivalence class.

mances produced by all of the variant-to-variant probes documented the emergence of fully elaborated generalized equivalence classes. The maintenance of the A`-C` and C`-A` relations were confirmed with re-exposure to the A`-C` and C`-A` probes (Rows 7 and 8). Finally, all variant-to-variant probes were presented in a single test block (Row 9), and all evoked class consistent responding. These performances demonstrated that the intactness of fully elaborated generalized equivalence classes when challenged by the presentation of all probes in the same test block. The six participants exposed to the above mentioned procedureformed the A`-B` linked perceptual classes. Of those, only five then showed the expansion to fully elaborated generalized equivalence classes. The results for the latter participant are presented in Figure 20. After forming the A`-B` linked perceptual classes, and learning the B`-C` relations, this participant responded inconsistently to some of the A`-C` and C`-A` probes (Rows 3 and 4). These performances indicated questionable emergence of generalized transitive and equivalence relations between the members of the C` and A` classes.The A`-B` and B`-A` probes (Rows 5 and 6) evoked class consistent responding documented the maintenance of the A`-B` linked perceptual classes. The B`-C` and C`-B` probes (Rows 5 and 6) evoked class consistent responding which documented the emergence of B`-C` linked perceptual classes. Finally, reexposure to the generalization tests of transitivity (Row 7) and equivalence (Row 8) confirmed a complete weakening of these relations. Thus, even though two linked perceptual classes were formed (A`-B` and B`-C`) and the classes were linked by common nodal stimuli, transitive and equivalence relations did not emerge between the A` and C` classes. One possible reason for this failure is that an essentially complex to simple protocol was used for training and testing. After training Aa-Ba and Ab-Bb, variant-to-variant tests were conducted to document the emergence of the A`-B` classes. After the subsequent training of Ba-Ca and Bb-Cb, no tests were conducted to document the emergence of B`-C` classes.

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The synthesis of complex categories from perceptual and equivalence classes

Participant 16

B`C`

C`B`

A`C`

C`A`

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

aa ma ba am mm bm a mb b bb

100 75 50 25 0

a maa ba am mm bm a mb b bb a maa ba am mm bm ab mb bb aa ma ba am mm bm a mb b bb a maa ba am mm bm a mb b bb

Class 2

A`B`

100 75 50 25 0

a maa ba am mm bm a mb b bb a maa ba am mm bm ab mb bb

% Correct Responding

B`A`

B`A`

B`C`

C`B`

A`C`

C`A`

Row

1 2 3 4 5 6 7 8 9

a maa ba am mm bm a mb b bb a maa ba am mm bm ab mb bb

Class 1 A`B`

conducted in an essentially complex-to-simple sequence. Perhaps, fully elaborated generalized equivalence classes could be established more efficiently by addressing each of these components of training and testing. As noted above, ab training optimized the formation of linked perceptual classes. Thus, fully elaborated generalized equivalence classes might be established by the linking of perceptual classes through the training ofAa-Bb to form the A`-B` classes and Ba-Cb to form the B`-C` classes. In addition, the order of training and testing could be done in a simple to complex manner. Specifically, after Aa-Ba training, the A`-B` probes could be presented to assess the generalization of the baseline relations, followed by the B`-A` probes to assess the generalization of the symmetrical properties of the A`-B` relations. After Ba-Cb training, B`-C` probes could be presented to assess the generalization of the baseline relations, followed by C`-B` probes to assess the

a maa ba am mm bm a mb b bb a maa ba am mm bm ab mb bb aa ma ba am mm bm a mb b bb

Rather, the participants were immediately presented with A`-C` and C`-A` to document the generalization of transitive relations and equivalence relations, and the emergence of the fully elaborated generalized equivalence classes. This analysis suggests that the likelihood of forming fully elaborated generalized equivalence classes might be enhanced by the use of a simple to complex strategy wherein, B`-C` and C`-B` probes should presented prior to the A`-C` and C`-A` probes. This possibility can be evaluated in a future research project. Extensions and Implications. Fields and Moss (2008) used only one a myriad of protocols that could have been used to establish fully elaborated generalized equivalence classes. In that study, the classes were established using aa/bb training to form A`-B classes (Aa-Ba and Ab-Bb) and the B`-C` classes (Ba-Ca and BbCb).In addition, there were many redundancies in the testing procedure. Finally, testing was

Cross Class Probes Figure 19. Data depicting the results of variant-to-variant tests conducted to track the emergence of fully elaborated generalized equivalence classes for one participant whose test performances documented class formation.

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Lanny Fields

generalization of the symmetrical properties of the B`-C` relations. Thereafter, introduce A`-C ` probes could be introduced to assess the generalization of the transitive relation between stimuli in the A` class and the C` class. Finally, the C`-A ` probes could be introduced to assess the generalization of the equivalence relations between stimuli in the C` class and the A` class. Fields & Moss (2008) induced fully elaborated generalized equivalence classes by the expansion of linked perceptual classes. It should also be possible to form fully elaborated generalized equivalence classes by starting with the establishment of a basal equivalence class, and then introducing variant to variant tests to evaluate the emergence of relations among all of the perceptual classes that were nominally linked via equivalence. If successful, these outcomes would demonstrate that the formation of fully elaborated generalized equivalence classes is not dependent on a narrow range of training

Participant 21

Class 1 B`A`

B`C`

C`B`

A`C`

C`A`

100 75 50 25 0

B`C`

C`B`

A`C`

C`A`

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

100 75 50 25 0

aa ma ba am mm bm ab mb bb aa ma ba am mm bm ab mb bb a maa ba am mm bm ab mb bb

100 75 50 25 0

aa ma ba am mm bm a mb b bb

100 75 50 25 0

a maa ba am mm bm ab mb bb aa ma ba am mm bm ab mb bb

100 75 50 25 0

a maa ba am mm bm a mb b bb

100 75 50 25 0

a maa ba am mm bm a mb b bb

100 75 50 25 0

Row

1 2

100 75 50 25 0

100 75 50 25 0

aa ma ba am mm bm ab mb bb

Class 2 B`A`

100 75 50 25 0

100 75 50 25 0

% Correct Responding

A`B`

3 4 5 6 7 8 9 a maa ba am mm bm a mb b bb a maa ba am mm bm a mb b bb a maa ba am mm bm a mb b bb

A`B`

and testing protocols, but rather would be a general behavioral phenomenon. The complex categories experienced in real world settings can be simulated by laboratory created linked perceptual classes, partially elaborated generalized equivalence classes, and fully elaborated generalized equivalence classes. The experiments described above identified some parameters that influenced the formation of these classes. As such, they may also account for the emergence of the complex categories observed in real world settings, and might also provide a behavior analytic account of processes such as intersensory integration and cross modal perception. Summary. Complex categories can be established by the merger of equivalence classes and perceptual or open ended classes. This requires the presentation of variant-to-variant probes that use anchor, midpoint, and boundary stimuli from perceptual classes to document the

Cross Class Probes Figure 20. Data depicting the results of variant-to-variant tests conducted to track the emergence of fully elaborated generalized equivalence classes for one participant whose test performances documented a failure of class formation.

The synthesis of complex categories from perceptual and equivalence classes

emergence of relations among the members of all of the perceptual classes that are linked common membership with the equivalence classes. The variant-to-variant probes were developed while forming linked perceptual classes. Along the way, we found that the likelihood of forming the linked perceptual classes was influenced by the interactive effects of the values and functions of the variants used in the class-linking conditional discriminations and by the schedule of variant-to-variant probe presentations that was used to track class formation. Those data predicted a set of training and testing conditions that would optimize class formation; that prediction was confirmed by subsequent research. Furthermore, these class act as function transfer networks, as do other categories. A formal analysis suggests that a linked perceptual class is a special form of a generalized equivalence class. In addition, the relations among the members of linked perceptual classes are akin to relations studied under the rubrics of cross modal perception and intersensory integration. Thus, the variables that influence the formation of linked perceptual classes may also account for the latter phenomena. Finally, the information gained while studying the formation of linked perceptual classes was used to expand them to fully elaborated generalized equivalence classes. The variables responsible for the formation of these classes then may provide a behavior analytic account of the formation of complex categories the influence our behavior in real world settings. References Adams, B. J., Fields, L., &Verhave, T. (1993). Formation of generalized equivalence classes. The Psychological Record, 43, 553-566. Augustson, E. M., &Dougher, M. J. (1997). The transfer of avoidance functions through stimulus equivalence classes. J Behav Therap Exp Psychiatry, 28, 181-191. Bahrick, L. E., & Pickens, J. N. (1994). Amodal relations: The basis for intermodal perception and learning in infancy. In D. J. Lewkowicz& R. Likliter (Eds.), The development of intersensory perception: Comparative

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perspectives (pp. 205-234). Englewood, NJ: Erlbaum. Barnes, D., & Keenan, M. (1993). A transfer of functions through derived arbitrary and non arbitrary stimulus relations. Journal of the Experimental Analysis of Behavior, 59, 61-82. 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. Belanich, J. & Fields, L. (2003). Generalized equivalence classes as response transfer networks. The Psychological Record, 53, 373-413. Belanich, J., & Fields, L. (1999). Tactual equivalence class formation and tactual-tovisual cross-modal transfer. The Psychological Record, 49, 75-92. Cook, R. G., Wright, & Kendrick, D.F. (1990). Visual categorization by pigeons. In In M. L. Commons, R. J. Herrnstein, S. M. Kosslyn, & D. B. Mumford (Eds.),Quantitative analyses of behavior: Behavioral approachs to pattern recopgnition and concept formation, pp. 187-214. Hillsdale, NJ: Erlbaum. Dougher, M. J., Auguston, E., Markham, M. R. Greenway, D. E.,& Wulfert, E. (1994). The transfer of emotional respondent eliciting and extinction functions through stimulus equivalence classes. Journal of the Experimental Analysis of Behavior, 62, 331-351. Fields, L. & Verhave, T. (1987). The structure of equivalence classes. Journal of the Experimental Analysis of Behavior, 48, 317-332. Fields, L., & Garruto, M. (2009). Linked perceptual classes: Formation and response transfer. Journal of the Experimental Analysis of Behavior, 91, 225-251. Fields, L., & Moss, P. (2008).The formation of partially elaborated and fully elaborated generalized equivalence classes. Journal of the Experimental Analysis of Behavior, 90, 135-168. Fields, L. & Reeve, K. F. (2001). A methodological integration of generalized equivalence classes, natural categories, and cross modal perception. The Psychological Record,

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51, 67-88. Fields, L. & Watanabe, M. (2008). Relatedness of stimuli in equivalence classes: Effects of contingencies and nodal structure. Journal of the Experimental Analysis of Behavior, 89, 359-382. Fields, L., Adams, B. J., Buffington, D. M., Yang, W., & Verhave, T. (1996). Response transfer between stimuli in generalized equivalence classes: a model for the establishment of natural kind and fuzzy superordinate categories. The Psychological Record, 46, 665-684. Fields, L., Fitzer, A., Tittelbach, D., & Shamoun, K. (2005). The effect of testing variables on the formation of linked perceptual classes. Journal of the Experimental Analysis of Behavior, 84, 243-269. 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. (2003). Effect of variant-to-base and base-to-variant test formats on membership in generalized equivalence classes. The Psychological Record, 53, 287-311. Fields, L., Matneja, P., Varelas, A., Belanich, J., Fitzer, A., &Shamoun, K. (2002). The formation of linked perceptual classes. Journal of the Experimental Analysis of Behavior, 78, 271-290. Fields, L., Newman, S., Adams, B. J., &Verhave, T. (1992). The expansion of equivalence classes through simple discrimination training and fading. The Psychological Record, 42, 3-15. Fields, L., Reeve, K. F., Adams, B. J., & Verhave, T. (1991). Stimulus generalization and equivalence classes: a model for natural categories. Journal of the Experimental Analysis of Behavior, 55, 305-312. Fields, L., Reeve, K. F., Adams, B. J., Brown, J. L., & Verhave, T. (1997). Predicting the extension of equivalence classes from primary generalization gradients: The merger of equivalence classes and perceptual classes. Journal of the Experimental Analysis of Behav-

ior, 68, 67-91. Fields, L., Reeve, K.F., Matneja, P., Varelas, A., Belanich, J., Fitzer, A., & Shamoun, K. (2002). The formation of generalized categorization repertoires: Effect of multiple domain, sample, and comparison training. Journal of the Experimental Analysis of Behavior, 78, 291-313. Fields, L., Tittelbach, D., Shamoun, K., Fitzer, A., Watanabe, M., & Matneja, P. (2007). The effect of training variables on the formation of linked perceptual classes. Journal of the Experimental Analysis of Behavior, 87, 97-119. Fields, L., Travis, R., Yadlovker, D. E., Roy, D., de Aguiar-Rocha, L., & Sturmey, P. (2009). Equivalence class formation: A method for teaching statistical interactions. Journal of Applied Behavior Analysis, 42, 575-593. Fields, L., Landon-Jimenez, D.V. Buffington, D. M., & Adams, B.J. (1995). Maintained nodal distance effects after equivalence class formation. Journal of the Experimental Analysis of Behavior, 64, 129-146. Galizio, M., Stewart, K.L., & Pilgrim, C. (2004). Typicality effects in contingencyshaped generalized equivalence classes. Journal of the Experimental Analysis of Behavior, 82, 253-273. Herrnstein, R. J. (1990). Levels of stimulus control: A functional approach. Cognition, 37, 133-166. Herrnstein, R. J., & Loveland, D. H. (1964). Complex visual concept in the pigeon. Science, 146, 549-551. Herrnstein, R. J., Loveland, D. H., & Cable, C. (1976). Natural concepts in pigeons. Journal of Experimental Psychology: Animal Behavior Processes, 4, 285-301. Hull, C. L. (1920). Quantitative aspects of the evolution of concepts. Psychological Monographs, (Whole 123). Keller, F. S., &Schoenfeld, W. N. (1950). The Principles of psychology. New York: AppletonCentury-Crofts. Keller, M. (1943). Mediated generalization of a conditioned galvanic skin response. American Journal of Psychology, 56, 438-448. Lane, S. D., Clow, J. K., Innis, A., & Critch-

The synthesis of complex categories from perceptual and equivalence classes

field, T. S. (1998). Generalization of crossmodal stimulus equivalence classes: Operant processes as components in human category formation. Journal of the Experimental Analysis of Behavior, 70, 267-280. Mackay, H., & Fields, L. (2009). Syntax, Grammatical Transformation, and Productivity: A Synthesis of Stimulus Sequences, Equivalence Classes, and Contextual Control. In R.A. Refeldt and Y. Barnes-Holmes (Eds.), Derived Relational Responding: Applications for Learners with Autism and Other Developmental Disabilities (pp. 209-236). New Harbinger: London. Markle, S. M., Tieman, P. W. (1972). Some principles of instructional design at higher cognitive levels. Ehrenwirth- Verlag, Berlin, Germany. Razran, G. H. S. (1939). A quantitative study of meaning by a conditioned salivary technique (semantic conditioning). Science, 90, 89-90. Reeve, K. F., & Fields, L. (2001). Effect of number of forced-choice primary generalization test trials on the establishment of perceptual classes along a single dimension. Journal of the Experimental Analysis of Behavior, 76, 95-114. Rehfeldt, R.A. (2003). Establishing contextual control over generalized equivalence relations. The Psychological Record, 53, 415-428. Rehfeldt, R. A.,& Hayes, L. J. (2000). The long-term retention of generalized equivalence classes. The Psychological Record, 50, 405-428. Rehfeldt, R. A., & Root, S. (2004). The generalization and long-term retention of equivalence relations in adults with mental retardation. The Psychological Record, 54, 173-186. Reiss, B. F. (1940). Semantic conditioning involving the galvanic skin reflex. Journal of Experimental Psychology, 26, 238-240. Roche, B., & Barnes, D. (1997). A transformation of respondently conditioned stimulus function in accordance with arbitrarily applicable relations. Journal of the Experimental Analysis of Behavior, 67, 275-301. Saunders, R. R., Saunders, K. J., Kirby, K. C., & Spradlin, J. E. (1990). Long term stabil-

227

ity of equivalence relations in the absence of training or practice. American Journal of Mental Retardation, 95, 291-303. Saunders, R. R., Wachter, J. A., & Spradlin, J. E. (1988). Establishing auditory stimulus control over an eight-member stimulus class via conditional discrimination procedures. Journal of the Experimental Analysis of Behavior, 49, 95-115. 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. Sidman, M. (1971).Reading and auditoryvisual equivalences. Journal of Speech and Hearing Research, 14, 5-13. Sidman, M. (1994). Equivalence relations and behavior: A research story. Boston: Authors Cooperative. Smoke, K. L. (1932). An objective study of concept formation. Psychological Monographs, 42, whole no. 191. Spradlin, J. E., & Saunders, R. R. (1986). The development of stimulus classes using match-to-sample procedures: Sample classification versus comparison classification. Analysis and Intervention in Developmental Disabilities, 6, 41-58. Spradlin, J. E., Saunders, K. J., & Saunders, R. R. (1992). The stability of equivalence classes. In S. C. Hayes & L. B. Hayes (Eds.), Understanding verbal relations (pp. 29-42). Reno NV: Context Press. Stokes, T.F., & Baer, D.M. (1977). An implicit technology of generalization1. Journal of Applied Behavior Analysis, 10, 349–367. Wasserman, E. A., Kiedinger, R. E., & Bhatt, R. S. (1988). Conceptual behavior in pigeons: Categorization of both familiar and novel examples from four classes of natural and artificial stimuli. Journal of Experimental Psychology: Animal Behavior Processes, 3, 235-246. Wright, A. A., Cook, R. G., Rivera, J. J., Sands, S. F., & Delius, J. D. (1988). Concept learning by pigeons: Matching-to-sample with trial-unique video picture stimuli. Animal Learning and Behavior, 16, 436-444.