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Response transfer between stimuli in generalized equivalence classes: a model for the establishment of natural kind and fuzzy superordinate categories.

An equivalence class consists of a finite number of perceptually disparate stimuli represented symbolically by letters such as A, B, C, and D. After some stimulus pairs are linked by training, the remaining stimulus pairs occasion class-consistent performances in emergent relations tests (Sidman & Tailby, 1982). A generalized equivalence class consists of some stimuli that are perceptually disparate (A, B, C, and D) and other stimuli that resemble one of the disparate stimuli (Adams, Fields, & Verhave, 1993a). These other stimuli are called variants. To determine whether a set of stimuli constitutes a generalized equivalence class, two types of tests must be conducted. (a) Emergent relations tests are used to determine whether the disparate stimuli are functioning as members of an equivalence class. In these tests, the disparate stimuli are used as the samples and comparisons. For example, after training AB, BC, and CD with stimulus sets 1 and 2, a DA equivalence test would contain D1 or D2 as a sample with A1 and A2 as comparisons. Selection of the class-consistent comparison would indicate class formation. (b) Generalization tests of emergent relations are used to determine the class membership of each variant. For example, using a generalization test of DA equivalence, each variant would be presented as a sample with A1 and A2 as comparisons. Comparison selection would indicate class membership for the particular variant. If D2 was selected in the presence of a given variant, that variant would be functioning as a member of Class 2. To confirm such a class assignment to a variant, similar performances would have to be observed in the presence of all generalization tests of emergent relations (variants of D as the sample with A1/A2, B1/B2, and C1/C1 as the comparison pairs). To date, a number of experiments have demonstrated the establishment of generalized equivalence classes (Adams et al., 1993a; Barnes & Keenan, 1993; DeGrandpre, Bickel, & Higgins, 1992; Fields, Adams, Brown, & Verhave, 1993; Fields, Reeve, Adams, & Verhave, 1991).

Many experiments have shown that equivalence classes act as effective transfer networks (Sidman, 1990). For example, the discriminative (de Rose, McIlvane, Dube, Galpin, & Stoddard, 1988; de Rose, McIlvane, Dube, & Stoddard, 1988), conditional reinforcing and aversive (Hayes, Devaney, Kohlenberg, Brownstein, & Shelby, 1987; Hayes, Kohlenberg, & Hayes, 1991), and conditional emotional stimulus functions (Dougher, Augustson, Markham, Greenway, & Wulfert, 1994; Watt, Keenan, Barnes, & Cairns, 1991) acquired by one stimulus in an equivalence class transferred to the remaining members of the same class.

In addition to stimulus functions, an equivalence class can also act as a transfer network for new responses. After training an individual to make a particular response in the presence of one member of an equivalence class, the remaining class members will evoke the same response. This has been demonstrated with a wide range of response topographies that includes rate (Barnes & Keenan, 1993; Catania, Horne, & Lowe, 1989), repetitive key pressing (Fields, Adams, Verhave, & Newman, 1993), vocal naming (Sidman, 1971), word spelling with anagram blocks (Mackay & Sidman, 1984), clapping and waving (Hayes et al., 1987), and sequential responding to a set of concurrently presented discriminative stimuli (Green, Sigurdadottir, & Saunders, 1991; Lazar & Kotlarchyk, 1986; Wulfert & Hayes, 1988).

Only one study has measured the transfer of responding trained to one stimulus in an equivalence class to a single variant of another stimulus in the same class (Barnes & Keenan, 1993). Equivalence classes that contained three consonant-vowel-consonant trigrams were established by training AB and AC. Then, a unique response was trained to each of the B stimuli. Each response was then evoked by the class-related C stimulus and by a variant of that C stimulus which consisted of the same consonants with a different vowel (e.g., DAX and DUX). These data provide a demonstration of response transfer to a single variant of a class member. No study has yet demonstrated the transfer of responding from one member of an equivalence class to a broad range of dimensional variants of another member of the same class. That is the purpose of the current experiment. In addition, such a demonstration would strengthen the procedurally based account of the development of natural kind (Gelman & Markman, 1986) and fuzzy superordinate categories (Rosch & Mervis, 1975) proposed by Adams et al. (1993a).

In this experiment, two 4-member equivalence classes were formed using nonsense words as three of the stimuli in each class. The fourth stimulus in each class was either a short or a long line. After classes were formed, generalization tests of emergent relations were conducted to identify the range of intermediate line lengths (variants) that functioned in the same manner as the members of each equivalence class. A unique response was then trained to one stimulus in the class, and response transfer tests were conducted with other class members and all of the line variants. Finally, we measured the extent to which the performance occasioned by each variant in the generalization tests of emergent relations was predictive of the performance evoked by the same variant in the response transfer tests.

Method

Subjects

Four Queens College/CUNY students were recruited from an introductory psychology class. They received extra credit for their participation in the experiment. Credit was not performance dependent. Each subject participated in five to eight 1-hr sessions.

Apparatus

An MS-DOS compatible microcomputer and custom software controlled stimulus presentation and data collection. Each subject was seated at a table which supported the computer, a monochrome monitor, and the keyboard. Responses were made by pressing specified keys on the keyboard.

Six nonsense syllables and two lines were used as stimuli. The A, B, and C stimuli were nonsense syllables: A1=LEQ, B1=HUK, C1=POV, A2=MEV, B2=GUQ, C2=ZOJ. The D stimuli were horizontal lines composed of contiguous strings of ASCII character 176 ??. Each character was 3mm wide and 5mm high on the computer monitor. In Class 1, the D stimulus was one character long and was designated D1(1). In Class 2, the D stimulus was 25 characters long and was designated D2(25). The numbers in the parentheses indicate the length of each stimulus in characters. The lines used for generalization and response transfer tests ranged from 2 to 24 characters in length and were designated D(2) through D(24).

Procedure

Equivalence Class Formation

Equivalence class training. Training was conducted in blocks containing 8-20 trials; testing was conducted in blocks containing 32-76 trials. The mastery criterion for a block of trials was 100% class-consistent responding. A block was repeated until the subject demonstrated the mastery criterion. The trials in a block were presented in a randomized order without replacement; once a trial in a block was presented, it was not repeated.
Table 1

Symbolic Representation of Trials Used in Conditional
Discrimination
Training and Emergent Relations Testing

Sa Co+ Co- Presented

Train AB
A1 B1 B2 8(*)

BA Symmetry Test
A1 B1 B2 8
B1 A1 A2 8

Train BC
A1 B1 B2 4+
B1 C1 C2 4+

CB Symmetry Test
A1 B1 B2 4
B1 C1 C2 4
C1 B1 B2 8

BA & CB Symmetry Tests
A1 B1 B2 4
B1 C1 C2 4
B1 A1 A2 4
C1 B1 B2 4

AC Transitivity Test
A1 B1 B2 4
B1 C1 C2 4
A1 C1 C2 8

CA Equivalence Test
A1 B1 B2 4
B1 C1 C2 4
C1 A1 A2 8

Symmetry, Transitivity, and Equivalence Tests
A1 B1 B2 4
B1 C1 C2 4
B1 A1 A2 2
C1 B1 B2 2
A1 C1 C2 2
C1 A1 A2 2

Train CD
A1 B1 B2 2
B1 C1 C2 2
C1 D1 (1) D2 (25) 6+

Symmetry, Transitivity, and Equivalence Tests
B1 A1 A2 2
C1 B1 B2 2
A1 C1 C2 2
C1 A1 A2 2
D1 (1) C1 C2 4
B1 D1 (1) D2 (25) 4
A1 D1 (1) D2 (25) 4
D1 (1) B1 B2 4
D1 (1) A1 A2 4

Note. In each trial block, each Co+ appeared equally often on the
left and right (* When less than 100% feedback was scheduled, each
triad appeared four times. + When less than 100% feedback was
scheduled, each triad appeared twice.) Triads are listed for Class
1
only. In each stage, comparable triads were also presented for
Class
2.


After the presentation of the instructions on the computer monitor (see Appendix 1A) and the completion of preliminary keyboard training, two 3-member equivalence classes were formed using the nonsense syllables as stimuli. All the training and testing was conducted with the conditional discrimination trials presented using the simple-to-complex protocol (Adams, Fields, & Verhave, 1993b; Fields et al., 1991). AB training was followed by the BA symmetry test. After the criterion was met on BA symmetry tests, BC was trained, after which CB symmetry was tested. After subjects passed the CB symmetry test, BA and CB symmetry were then reviewed in a single test block. Next, the AC transitivity test was presented until criterion was reached; this was followed by the presentation of the CA equivalence test. Once the CA test was passed, all emergent relations were presented in a review block. Passing the tests in the review confirmed the formation of the 3-member classes.

Class size was then expanded to four members by training CD. After CD was learned, tests for DC symmetry, BD and AD transitivity, and DB and DA equivalence were presented in a mixed block. The block was repeated until the subject made no more than one error in a single block. Meeting criterion on these emergent relations tests demonstrated the formation of two 4-member equivalence classes. Symbolic representations of the stimuli used in each stage of training and testing are listed in Table 1.

Feedback for responding. When AB, BC, and CD were being established, informative feedback was presented on a trial-by-trial basis. The selection of the class-consistent comparison occasioned the presentation of the word RIGHT on the computer screen; the selection of the comparison that was not from the same set as the sample occasioned the presentation of the word WRONG on the computer screen. Pressing the R key in the presence of the word RIGHT or the W key in the presence of the word WRONG cleared the screen and initiated the next trial. Once the mastery performance was achieved, the percentage of trials that occasioned informative feedback decreased from 100% to 75% to 25% and then to 0% in successive blocks. This occurred as long as the mastery criterion was maintained. If mastery was not maintained in a block, however, the feedback percentage increased to the next higher percentage level. When no informative feedback was scheduled, the selection of either comparison resulted in the presentation of the letter E on the computer screen. Pressing the E key cleared the screen and initiated the next trial. The letter E was used to indicate the end of a trial and was noninformative with regard to the comparison that was selected; it merely confirmed the selection of a comparison. The letter E was used for this purpose because it is between the letters R and W on a computer keyboard with a QWERTY layout. Noninformative feedback was provided on all emergent relations test trials. For more details, see Adams et al. (1993b) or Fields et al. (1991).

Generalization tests for emergent relations. After the 4-member equivalence classes were formed, the relatedness of the intermediate length lines to all of the class members was evaluated with generalization tests of emergent relations. Each line variant was used as a sample. Comparison stimuli in the primary generalization test were D1(1) and D2(25). In the generalization tests of symmetry, the comparisons were C1 and C2, and in the generalization tests of DB and DA equivalence, the comparisons were B1 and B2 and A1 and A2, respectively.

Twenty generalization test blocks were presented regardless of subject performance. In a given block, the 23 line variants [D(2) through D(24)], and D1(1) and D2(25) each appeared twice with a given pair of comparisons. Thus, each block contained 50 trials. Each line appeared as a sample in 10 trials with each of the four comparison sets. Each comparison appeared equally often on the right and the left. No informative feedback was presented for choices on any of the 1,000 generalization test trials.

Discrimination Training and Response Transfer Testing

At the completion of generalization testing, two new discriminative repertoires were established, after which response-transfer was assessed. Finally, transfer of responding to all line variants was evaluated.

Contingencies in discrimination training and transfer testing. On each discrimination training and each response transfer testing trial, one stimulus was presented alone in the center of the computer screen until a response was made, or for a maximum of 60 s. The stimuli in all blocks were presented in a randomized order with the restriction that no stimulus could be presented more than twice in succession.

Discrimination training. After the presentation of instructions on the computer monitor (listed in Appendix 1B), each subject was taught to press the "J" key five times and then press the <ENTER> key in the presence of the nonsense word LEQ (A1). They were also taught to press the "J" key seven times and then press the <ENTER> key in the presence of the nonsense word MEV (A2). Each stimulus was presented three times in a six-trial block. Training continued until the subject responded with 100% accuracy in a block that provided informative feedback on each trial. As long as 100% response accuracy was maintained, the percentage of trials in a block that produced informative feedback was reduced to 66%, to 33%, and then 0% in successive blocks. If responding did not meet the mastery criterion, the percentage of informative feedback remained at that level for three repetitions of the block. If after three repetitions the criterion was still not met, the block was presented again, but with the previous level of feedback.

Response transfer to class members. The transfer test began with the presentation of instructions on the computer monitor (see Appendix 1C). Transfer of responding to the other class members was tested. Each of the eight stimuli was presented five times in a 40-trial block. The block was repeated until each stimulus occasioned at least 90% class-consistent responding. These computations were based on the data collected in two consecutive blocks because each stimulus was presented only five times per block.

Response transfer to line variants. Once the criterion for response transfer to class members was met, response transfer to the line variants was tested. Each line variant as well as D1(1) and D2(25) was presented twice in a block of 50 trials. Testing was terminated after the presentation of five blocks or 250 trials, regardless of subject performance.

Results

Equivalence class formation. Table 2 lists the number of blocks needed for each subject to learn each conditional relation and to pass each emergent relations test. All subjects learned each of the baseline [TABULAR DATA FOR TABLE 2 OMITTED] conditional relations in four to six blocks. A minimum of four blocks was required to meet the criterion for acquisition of each baseline relation. Therefore, all subjects rapidly learned the three baseline conditional relations in each class.

All subjects met criterion on each emergent relations test in the first block, with the exception of the CB symmetry test for Subject 279. Thus, the simple-to-complex protocol resulted in the rapid formation of two 4-member equivalence classes with little intersubject variation. These results replicate the findings reported by Adams et al. (1993b).

[TABULAR DATA FOR TABLE 3 OMITTED]

Discrimination training and response transfer to class members. Subjects 277, 278, 279, and 281 learned the A1/A2 discrimination in 4, 5, 6, and 13 blocks respectively. Table 3 lists the number of blocks required by each subject to complete the test of response transfer from the A stimuli to the other class members (B, C, and D). It also lists the specific errors occasioned by each stimulus in each block. All subjects completed the response-transfer test, albeit at different rates. Two subjects (279 and 277) responded at high levels of accuracy from the start of testing and completed the transfer test in the minimum number of blocks. For Subject 278, the relatively high error rate in the first test block consisted of responses trained to the stimulus from the opposite class. Performance shifted suddenly to class-related responding in the second test block, and transfer was completed by the third block. Thus, class-consistent responding emerged with the repeated presentation of stimuli in the absence of feedback (Fields, Adams, Verhave, & Newman, 1993; Wulfert & Hayes, 1988). For Subject 281, a high rate of cross-class errors was maintained during the first three test blocks. This suggested a breakdown of the equivalence classes; therefore, the baseline conditional relations were retrained. After retraining, the subject responded with complete accuracy on all transfer tests.

Of the 44 incorrect responses made by all subjects, five were errors in response topography. In each case, the typed sequence included one more key press than that which had occasioned reinforcement in the presence of the corresponding class-related A stimulus. Because these responses were not correlated with particular stimuli, they were considered to be errors in production. For the remaining 39 errors, the stimuli in one class occasioned the response trained to the A stimulus from the other class; these were failures of stimulus control.

Generalization tests of emergent relations. Table 4 illustrates the performances occasioned by each variant and each line length that was [TABULAR DATA FOR TABLE 4 OMITTED] a class member for each type of emergent relation test for each subject. When a given variant was presented as a sample, the D2, C2, B2, and A2 comparisons were chosen with similar frequencies. In addition, these values did not differ as a function of test type. These findings were observed for all subjects.

Figure 1 shows how the selection of the Class-2 comparisons in the presence of each variant was related to the lengths of the line variants. Because a variant produced overlapping performances in all emergent relations tests, as seen in Table 4, the data for a given variant were averaged across emergent relations tests. For Subject 281, test lines from 24 to 14 units in length occasioned the selection of the Class-2 comparisons on at least 90% of the test trials. Selection of the Class-2 comparisons declined rapidly and systematically for the next three shorter line variants. For the remaining line variants, the Class-2 comparisons were selected on no more than 5% of the test trials. For Subject 279, test lines from 24 to 8 units in length occasioned the selection of the Class-2 comparisons on at least 98% of the test trials. Selection of the Class-2 comparisons declined rapidly and systematically for the next three shorter lines. For the remaining line variants, selection of the Class-2 comparisons occurred on no more than 5% of the test trials. For Subject 278, lines from 24 to 7 units in length occasioned the selection of the Class-2 comparisons on at least 95% of the test trials. Selection of the Class-2 comparisons declined systematically for the next three shorter lines. For the remainder of the lines, selection of the Class-2 comparisons occurred on no more than 8% of the trials. Finally, for Subject 277, lines from 24 to 2 units in length occasioned the selection of the Class-2 comparisons on at least 95% of the test trials. Selection of the Class-2 comparisons did not occur for the 1-unit line. The gradients based on the selection of the Class-1 comparisons are not shown because they are simply mirror images of the Class-2 gradients.

Response transfer to line variants. Figure 1 also illustrates the relative frequency with which the Class-2 response (7J) was evoked by all intermediate length lines and the lines that were class members. The 7J response was almost always occasioned by the Class-2 line and was rarely occasioned by the Class-1 line. For Subject 281, test lines from 24 to 13 units in length evoked the 7J response on more than 90% of the test trials. Evocation of the 7J response declined rapidly and systematically for the next two shorter line variants. The remaining line variants evoked the 7J response on no more than 5% of the trials. For Subject 279, test lines from 24 to 8 units in length evoked the 7J response on at least 98% of the test trials. Evocation of the 7J response declined rapidly and systematically for the next four shorter line variants. The remaining line variants never evoked the 7J response. For Subject 278, test lines from 24 to 7 units in length evoked the 7J response on more than 90% of the test trials. Evocation of the 7J response declined rapidly and systematically for the next two shorter line variants. The remaining line variants never evoked the 7J response. For Subject 277, test lines from 24 to 2 units in length evoked the 7J response on at least 90% of the test trials. The remaining line variant never evoked the 7J response.

Comparison of response transfer and generalization test performances. Figure 1 also shows the extent to which the generalization test performances were predictive of the response transfer performances. The variants that occasioned the selection of Class-2 comparisons with very high relative frequencies (at least 90%) also occasioned the 7J response with correspondingly high relative frequencies. This was the case for the 24- to 15-unit line variants for Subject 281, the 24- to 8-unit line variants for Subject 279, the 24- to 7-unit line variants for Subject 278, and the 24- to 2-unit line variants for Subject 277.

The variants that occasioned the selection of Class-2 comparisons with very low relative frequencies (no more than 5%) occasioned the 7J response with correspondingly low relative frequencies (no more than 10%). This was the case for the 11- to 2-unit line variants for Subject 281, the 4- to 2-unit line variants for Subject 279, and the 3- and 2-unit line variants for Subject 278.

The remaining variants occasioned intermediate performances on the generalization tests of emergent relations (less than 90% but greater than 10%). For these stimuli, relatively large disparities were observed in the performances occasioned by each type of test for Subjects 281 and 279, small disparities were observed for Subjects 278 and 277. Thus, the emergent relations test performances did not predict the response transfer performances with the same precision as the variants that produced extreme test score values.
Table 5

Errors Occasioned by Each Test Line in All Transfer Tests to
Variants for Each Subject

Subject Stimulus # Response Sequence

277 D2 1 JJJJJJJJ
 D3 1 JJJJJJJJJJJJJJJ
 D4 1 JJJJJJJJ
 D11 1 JJJJJJKJ
 D12 2 JJJJJJJJ
 D14 1 JJJJJJJJ
 D15 1 JJJJJJJJ
 D17 1 JJJJJJJJ
 D18 1 JJJJJ9JJ
 D18 1 JJJJJJJJ
 D25 1 JJJJJJJJ

278 D17 1 JJJJJJJJ
 D21 1 JJJJJJJJ

279 D2 1 JJJJJJ
 D3 1 JJJJJJ
 D7 1 JJJJJJJJ
 D10 1 JJJJJJJJ
 D13 1 UJJJJJJJ
 D15 1 JJJJJJJJ
 D19 1 JJJJJJJJ
 D21 1 JJJJJJJJ
 D25 1 JJJJJJJJ

Note. The numeral in the # column indicates the number of times the
adjacent response sequence occurred.


Errors during the transfer tests with variants. Of the 1000 responses recorded in the transfer test for variants (250 responses for each of four subjects), only 23 were neither 5J nor 7J sequences. Each of these responses is illustrated in Table 5. Two were 6-letter sequences, one was a 15-letter sequence, and 20 were 8-letter sequences. With the exception of three key strokes, all responses consisted of sequences of Js. In addition, these responses were not correlated with line length. Thus, these incorrect responses were typographical production errors.

The 6-letter sequences could have been overestimates for the 5J response or underestimates for the 7J response. These incorrect sequences were not interpretable typographical errors. The 15J sequence was also not interpretable. In contrast, the 8J sequences were more clearly interpretable as being typographical errors for the 7J response. If the criterion for Class-2 responses is relaxed to include the 8J sequences, most of the variants that produced 80% and 90% Class-2 responding would now produce 100% Class-2 responding. Thus, the disparity between the generalization and transfer performances would be reduced to a minimum, and the predictability of transfer performances from the emergent relations performances would increase to an even higher level than that seen in Figure 1.

In summary, variants that produced Class-2 performances in the generalization tests of emergent relations precisely predicted Class-2 performances in the response transfer tests for the same variants. Variants that produced Class-1 performances in the generalization tests of emergent relations precisely predicted Class-1 performances in the response transfer tests for the same variants. These correlations prevailed regardless of the range of variants that produced extreme performances for a specific subject.

Discussion

Generalized equivalence classes. When the generalization tests of emergent relations were conducted, many variants of one class member all produced the same test performances as did other stimuli that were members of one of the basal equivalence classes. This finding replicates those reported by Fields et al. (1991) and Fields, Adams, Brown, and Verhave (1993). All of these variants functioned in the same manner as the members of the basal equivalence classes even though they were not used in the establishment of the basal equivalence classes. Because the variants were arrayed along a continuous dimension, the number of variants that functioned as class members was not determinate. The variants and the class members, therefore, constituted a generalized equivalence class (Adams et al., 1993a) which is analogous to other traditional categories in the sense that they also contain an indeterminate number of exemplars (Herrnstein, Loveland, & Cable, 1976; Hrycenko & Harwood, 1980; Hull, 1920; Keller & Schoenfeld, 1950; Lea, 1984; Lubow, 1974; Malott & Siddal, 1972; Medin & Smith, 1984; Seigel & Honig, 1970; Smoke, 1932; Wasserman, Kiedinger, & Bhatt, 1988; Wright, Cook, Rivera, Sands, & Delius, 1988).

Generalized functional classes. When the response transfer tests were conducted, the response trained to the A stimulus in each basal equivalence class was evoked by the B, C, and D stimuli in the same class. Because these stimuli evoked a particular J response with the same likelihood, all were members of the same functional class (Goldiamond, 1966; Mackay & Sidman, 1984; Sidman, Wynne, Maguire, & Barnes, 1989; Vaughan, 1988; Wasserman & deVolder, 1993; Wulfert & Hayes, 1988) or disjunctive class (Millenson & Leslie, 1979). The response trained to the A stimulus in a class was also evoked by many line variants. These variants also acted as members of the same functional class as that defined by the A, B, C, and D stimuli. Because all of these variants were acting in the same manner as the members of a functional class, the set of stimuli as a whole constituted a functional class that was extended by generalization, or a generalized functional class.

In this experiment, two equivalence classes were established by training AB, BC, and CD in two sets, after which a separate response was trained to each A stimulus in each class. The transfer of responding to the other class members and to the variants of the D stimuli that functioned as class members, then, could have occurred through transitivity alone rather than through equivalence. Although this is a possibility, we do not view it as likely because the A, B, C, and D stimuli had become equivalent prior to conducting the response transfer tests. Indirect support of this position is provided by the many studies which have shown that responses trained to one member of an equivalence class transfer through equivalence to the other members of same class (Barnes & Keenan, 1993; Catania et al., 1989; Fields, Adams, Verhave, & Newman, 1993; Green et al., 1991; Hayes et al., 1987; Lazar & Kotlarchyk, 1986; Mackay & Sidman, 1984; Sidman, 1971; Wulfert & Hayes, 1988), and the Barnes and Keenan (1993) study which showed the transfer of a response, through equivalence, from one member of an equivalence class to other members of the same class as well as to one variant of another member of the same equivalence class. The matter could be assessed empirically, however, by establishing equivalence classes through training of AB, BC, and CD relations, identifying the variants of A that functioned as members of the class, and then measuring the transfer of a response trained to the D stimulus to the members of the generalized equivalence class.

Overlap of generalized equivalence and functional classes. The variants that produced very high levels of selecting comparisons from one class in the emergent relations tests also produced correspondingly high levels of evoking the response trained to one class member in the response-transfer tests. This correlation of behavioral functions was observed for all four subjects. This correlation prevailed even though the range of variants that produced them differed dramatically for three of the four subjects. Thus, the overlap of behavioral function did not depend on the range of variants that were members of a generalized class. The stimuli that were members of a generalized equivalence class were also members of the same generalized functional class regardless of the range of variants that acted as class members.

Range of stimuli that are members of generalized equivalence classes. Different ranges of line variants acted as class members for three of the four subjects. These between-subject differences would be expected because no explicit contingencies were used in this experiment to specify the range of variants that should become related to the lines that were members of Classes 1 or 2. The observed intersubject variation, then, probably reflected each subject's preexperimental reinforcement history with respect to lines. Those histories could have established different boundary conditions for assigning the labels "long" and "short" to lines of different lengths (Barnes, 1994; Hayes & Hayes, 1992; Steele & Hayes, 1991). Those histories could also have led each subject to scale the lines along different dimensions such as their length, their length/width ratio, or their perceived orientation (Hrycenko & Harwood, 1980; Wright, Cook, & Kendrick, 1989). Additional research would be needed to identify the variables that govern the range of variants that become members of a generalized equivalence or functional class.

General Discussion

Open- and close-ended categories. By definition, equivalence classes (Sidman & Tailby, 1982), functional or dysjunctive classes (Goldiamond, 1966; Millenson & Leslie, 1979), and polymorphous categories (Lea & Harrison, 1978) all contain a finite number of exemplars. Thus, Herrnstein (1990) called them close-ended categories. In contrast, traditionally defined perceptual or fuzzy categories, such as pictures of PEOPLE, MACHINES, MAN-MADE OBJECTS, CATS, or FLOWERS, and relational categories, such as TRIANGLES, BIGGER THAN, SAME AS, all contain an indeterminate number of exemplars (Herrnstein et al., 1976; Hull, 1920; Keller & Schoenfeld, 1950; Lea, 1984; Lubow, 1974; Medin & Smith, 1984; Smoke, 1932; Wasserman et al., 1988; Wright et al., 1988). Herrnstein (1990) called these categories open ended. It would appear that a category would have to be either open or close ended. This position is not supported by the results of the current experiment. An indeterminate number of new stimuli that were dimensional variants of a class member came to act as members of a basal equivalence or functional class. Thus, a close-ended equivalence or functional class became an open-ended class. Indeed, any close-ended category can be converted to an open-ended class by generalization. Although equivalence classes and functional classes may differ in critical ways from other open-ended classes, the determinacy of the number of exemplars in a class is not one of the critical differences.

Naturally occurring categories and generalized equivalence classes. Naturally occurring categories, natural kind categories (Gelman, 1988a; 1988b; Gelman & Markman, 1986; 1987) and superordinate fuzzy categories (Rosch & Mervis, 1975; Rosch, Mervis, Gray, Johnson, & Boyes-Bream, 1976; Medin & Smith, 1984) all contain an indeterminate number of stimuli. Some of the stimuli resemble each other and other stimuli are perceptually disparate (Adams et al., 1993a). All of the stimuli in one of these categories are related to each other and also evoke at least one common response. An example would be the written words SEATS, TABLES, and LIGHTING, as well as many pictures of different seats, tables, and lamps, all of which would evoke the word "furniture."

The constellation of stimuli that constitute one of these categories is the same as the stimuli that constitute a generalized equivalence class. The stimulus-stimulus relations and the transfer of response functions shown by the stimuli in the former categories are also the functions acquired by the stimuli in generalized equivalence classes. Thus, naturally occurring, natural kind, fuzzy superordinate categories, and generalized equivalence classes are identical both in terms of stimulus inclusion and emergent behavioral function. It appears, then, that the same psychological phenomenon is denoted by four different names.

There are no operationalized descriptions of the manner in which natural kind categories or fuzzy superordinate categories are established. In contrast, generalized equivalence classes can be established by (a) training a set of conditional discriminations in which some stimuli are members of at least two such relations, (b) testing for emergent relations, and (c) testing for generalization of emergent relations with variants of class members. Transfer of responding to the members of a generalized equivalence class results from (d) discrimination training of a response to one member of an equivalence class and (e) testing for generalization of the response to the other members of the generalized equivalence class. Given the structural and functional similarities of generalized equivalence classes, naturally occurring, natural kind, and superordinate fuzzy categories, perhaps the five procedures that account for the emergence of generalized equivalence classes and the transfer of responding among such class members could also account for the development of these other categories.

A great number of natural kind and fuzzy superordinate categories develop during childhood. A procedurally based account of their development would be supported by a demonstration of the formation of generalized equivalence classes and the transfer of responding among the members of those classes in children. To date, however, the formation of generalized equivalence classes and the transfer of responding among the members of such classes have been studied in college students only. The five procedures mentioned above have not yet been used to establish generalized equivalence classes and induce transfer of responding among the members of a generalized equivalence class in children. Such a demonstration would substantially strengthen a procedurally based account of the development of naturally occurring, natural kind, and superordinate fuzzy categories in children.

References

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Appendix

1A. INSTRUCTIONS USED AT THE START OF THE EXPERIMENT

Thank you for volunteering to be a subject in this experiment. PLEASE DO NOT TOUCH ANY OF THE KEYS ON THE KEYBOARD YET. In this experiment you will be presented with many trials. Each contains three CUES, these will be common words, or three letter nonsense words such as ZEQ or WUV. YOUR TASK IS TO DISCOVER WHICH WORDS GO TOGETHER.

Initially there will also be INSTRUCTIONS that tell you how to respond to the cues, as well as LABELS that will help you to identify the cues on the screen. The labels and the instructions which tell you which KEYS to press will slowly disappear. Your task will be to RESPOND CORRECTLY to the CUES and the INSTRUCTIONS by pressing a key on the computer's keyboard.

The experiment is conducted in phases. When each phase ends, the screen will tell you how you did. If you want to take a break, please call the experimenter.

1B. INSTRUCTIONS USED PRIOR TO DISCRIMINATION TRAINING

In this section of the experiment you will see some nonsense words. They will be presented one at a time.

While each word is on the screen, press the J key a number of times. Then press the <Enter> key.

You will receive feedback after each response. YOUR GOAL IS TO RESPOND CORRECTLY TO EACH WORD.

1C. INSTRUCTIONS PRESENTED PRIOR TO THE RESPONSE TRANSFER TESTS

This section will contain MANY MORE trials than the previous section. The only keyboard responses that you may type are JJJJJ and JJJJJJJ

Please be patient and stick with the task. Thank you for your cooperation!
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Author:Fields, Lanny; Adams, Barbara J.; Buffington, Dawn M.; Yang, Wei; Verhave, Thom
Publication:The Psychological Record
Date:Sep 22, 1996
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