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Rule following in functional equivalence classes


EUROPEAN JOURNAL OF BEHAVIOR ANALYSIS

2002, 1 , 21 - 29

NUMBER 1 (SUMMER 2002) 21

Rule following in functional equivalence classes
Sean McGuigan & Mickey Keenan
School of Psychology, University of Ulster at Coleraine

In Experiments 1 and 2 a match-to-sample procedure was used to establish the prerequisite conditional discriminations for two 3-member equivalence classes (A1, B1, C1 & A2, B2, C2) where stimuli A1 and A2 were written instructions. In Experiment 1 tests for transitivity confirmed the emergence of derived relations. Following this, an off-the-baseline test was given to verify the existence of functional equivalence classes. During off-the-baseline testing stimuli B and C from both classes controlled responding appropriate to the instructions contained in A1 and A2 respectively. In Experiment 2, the omission of tests for transitivity and the reversal of instructions contained in A1 and A2 did not impede the emergence of functional equivalence classes. In Experiment 3, classes A1, B1, C1 and E1, F1, G1 were linked via D1 to produce one class (A1, B1, C1, D1, E1, F1, G1); another two classes (A2, B2, C2 & E2, F2, G2) were linked with D2 to produce A2, B2, C2, D2, E2, F2, G2. The A and G stimuli in each class contained competing sets of instructions. When transformation of function was examined in the first class, the functions at C1 and E1 were controlled by the rules at A1 and G1 respectively; D1 controlled responding in accordance with the instructions at A1. Results from all experiments are discussed in the context of procedures designed to investigate transfer/transformation of function. Key words: equivalence class, functional equivalence class, transfer of function, transformation of function, rule-governed behaviour, adults.

Recent developments in the area of stimulus equivalence have provided new impetus for the study of complex behaviour in humans that includes symbolic behaviour, language, and the ability to behave appropriately in novel situations without direct training (Hayes, 1989, 1991; Hayes & Hayes, 1989; Sidman, 1986, 1990; Spradlin & Saunders, 1984). Typically, match-to-sample (MTS) training is used to establish baseline conditional discriminations AB and BC where AB indicates selection of comparisons B1 and B2 conditionally upon samples A1 and A2 respectively while BC indicates selection of comparisons C1 and C2 conditionally upon samples B1 and B2 respectively. Subsequent testing reveals that conditional discriminations BA, CB, AC, and CA emerge without further training (Sidman, 1992). This emergent behaviour is regarded as evidence
This research was conducted as part of the doctoral dissertation of the first author under the supervision of Mickey Keenan. Reprints may be had from Mickey Keenan, School of Psychology, University of Ulster, at Coleraine, Cromore Road, Coleraine, County Derry, Ireland BT52 1SA.

of stimulus classes, members of which are regarded as being equivalent. Within an equivalence class the various emergent relations are classified thus: AA, BB, and CC relations are classified as examples of ‘reflexivity’; BA and CB relations are classified as examples of ‘symmetry’; AC relations are classified as examples of ‘transitivity’; and CA relations are classified as examples of ‘equivalence’ (also called ‘combined symmetry and transitivity’). One aspect of equivalence research that is gaining increasing attention is the phenomenon of ‘transformation of function.’ Transformation of function refers to the finding that a psychological function applied to one member of an equivalence class generally ‘transfers’ to the other members of the equivalence class in the absence of direct training. If this process is demonstrated the equivalence class may then be defined as a functional equivalence class (Dougher & Markham, 1994). The behaviours shown to transfer through equivalence relations are complex and
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varied and the equivalence class is reclassified as a functional equivalence class. Indeed Dougher and Markham (1994) argue: Transfer of function is the test for functional equivalence. It refers to the acquisition of a stimulus function, by a member of a functional stimulus class, resulting from a variable applied to a different member of that class. (p. 73) Examples of functions shown to transfer through an equivalence class include rate of responding (Barnes & Keenan, 1993), discriminative stimulus control (Lazar & Kotlarchyk, 1986), conditional discriminative control (Wulfert & Hayes, 1989), contextual control (Kohlenberg, Hayes, & Hayes, 1991), and eliciting functions (Dougher, Auguston, Markham, Greenaway, & Wulfert, 1994). The aim of the current paper was to add to this list of functions by examining instructional control in an equivalence class. More specifically, the experiments described here explored the relation between rules and functional equivalence by incorporating a rule directly within a class of functionally equivalent stimuli. The general methodology employed in studies of transfer of function is in line with the definition of functional equivalence offered by Dougher and Markham (1994) above. That is, a

number of equivalence classes are first established (by both training and/or testing) and then a psychological function is added to one member of one class. A subsequent test is conducted to see whether or not other members of that class (and only that class) also control that function. The methodology used in the current studies represents a significant departure from this tradition. These studies examined the effect of making stimulus A1 a normative rule (i.e., an instruction) in the context of a match-to-sample procedure used to establish the conditional relations AB and BC. Such a procedure would allow us to examine whether the instruction contained in A1 would transform the functional control by stimulus C1. If successful, such a procedure would provide a basis also for examining interactions between competing sets of instructions within emergent stimulus classes? EXPERIMENT 1 Method
Participants

Subjects were 4 undergraduate students enrolled at the University of Ulster, Coleraine, Ireland.

Figure 1. A schematic diagram of the testing board used in off-the-baseline tests for transformation of function.

Rules and equivalence Apparatus and Materials

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Experimental sessions were conducted in an experimental room attached to the School of Psychology, at the University of Ulster, Coleraine, Ireland. Subjects were seated at a table facing an Apple Macintosh microcomputer. A second table was located two metres from the first and was used for off-the-baseline testing. On top of this table was placed a black coloured testing board (see Figure 1). The testing board was 65 cm long and 25 cm wide and consisted of eight countersunk, circular indentations and eight squareshaped indentations. The circular and square indentations were 9 mm in depth and were situated in parallel formation along the length of the testing board. On the table, between the seated subject and the testing board, eight sets of 2 coins (i.e., a 5-pence coin and a 2-pence coin) were placed in side-by-side formation, parallel to the square and circular indentations on the testing board. Between the experimenter and the testing board, were placed a stack of sixteen ‘stimulus cards’. These cards were placed face down on the testing table and contained, in random order, printed versions of stimuli presented on the computer.
General Procedure

All instructions given to subjects appeared on the computer monitor screen. At the beginning of the experiment the following text appeared on the screen: Thank you for taking part in this study, your instructions are quite simple. The first part is conducted on the computer (instructions below), while the second part is conducted on the table beside the door. In a moment you will be presented with a square at the top of the screen containing some text. Your task is to select one of the two squares below this. You make your selection by clicking once on the square of your choice. You will be told if your selection is correct or incorrect.
Training Phases

and A2, and nonsense syllables for B1, B2, C1, and C2. Each sample stimulus appeared at the centre of the computer monitor in a 4-cm square box. The comparison stimuli appeared at the bottom left and right hand corners of the computer monitor, and were identical in dimension to the box that contained the sample stimulus. Subjects selected comparison stimuli using the computer mouse, which was placed to the side of the computer. The sequencing of samples and the positioning of the comparisons varied in a semi-random manner throughout training. When a subject made a correct selection of a comparison stimulus, the word “Correct” appeared on the top right-hand corner of the computer monitor for 3 s and was accompanied by a high pitched tone. When a subject made an incorrect selection, the word “Incorrect” appeared at the top right-hand corner of the computer monitor for 3 s and was accompanied by a low-pitched tone. A-B and B-C relations were first trained using continuous reinforcement for 4 presentations of each sample stimulus. Subsequently, intermittent reinforcement (Random Ratio 2) was used for a mixture of A-B and B-C training, again using 4 presentations of each sample stimulus; i.e., selection of the correct comparison stimulus was reinforced on 50% of occasions. The following instructions appeared at the centre of the computer monitor when intermittent reinforcement was used: In the next part of the experiment you will not always be told if your selection is correct or incorrect. The stimulus combinations were presented in a semi-random order during this condition. A 100% correct criterion was used for responding at each stage of training. If a subject did not meet this criterion after three attempts, the computer was programmed to terminate the experiment.
Off-the-baseline testing

Stimuli used during conditional discrimination training consisted of written instructions for A1

During off-the-baseline testing subjects were seated facing the experimenter and given the following oral instruction: In just a few seconds I am going to show you some cards and I would like

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you to respond appropriately using the objects in front of you. Without looking at the contents of the cards the experimenter presented them one at a time, in line with the pair of holes constituting that particular trial. On each trial, subjects responded by placing a coin in either the circular or square indentation of the testing board. The experimenter then placed the card face up beside the pair of holes for that trial. The next trial began immediately after the subject made a response. After the first 8 trials, in which 8 coins had been placed on the board, the coins were removed along with the cards used for those trials and the next 8 trials began. In all experiments no programmed consequences were provided for responses during off-the-baseline testing.
Phase 1:Training

The experimenter presented, individually, 16 printed versions of the B and C stimuli. On each occasion, the subjects responded by placing either a 5-p or a 2-p coin in either the circular or square indentation of the testing board. Results For all subjects responding in tests for transitivity averaged 80-90% correct (Table 1). For three subjects (S1, S2, & S4) testing off-thebaseline indicated that the instructions contained in A1 and A2 determined performance on the testing board in the presence of the B and C stimuli (Table 2). S3’s responding off-the-baseline did not indicate consistent control by the instructions in A1 and A2. Discussion

The prerequisite conditional discriminations for two, 3-member equivalence classes were trained. Stimuli used were as follows:

Phase 2:- Testing for derived relations

Transitive relations were tested; there were no programmed consequences for responding. If subjects reached an 80% correct criterion for responding overall, they progressed to Phase 3.

Phase 3: Off-the-baseline testing

Dougher and Markham (1994) have argued that transfer of function is the test for functional equivalence. Here, when subjects were tested offthe-baseline 3 out of 4 responded in accordance with the outcome expected from two sets of functional equivalence classes (i.e., A1, B1, C1, & A2, B2, C2). That is, in the presence of B and C stimuli the placement of coins on the testing board corresponded with the instructions appropriate to class membership. Instructions contained in A1 controlled responding in the presence of B1 and C1 while instructions contained in A2 controlled responding in the presence of B2 and C2. These findings extend the range of behaviours explored under the umbrella of transfer of function. Of particular interest is the fact that there was no response measure of the instructions contained in A1 and A2. This procedural variation represents a significant departure from previous

Rules and equivalence

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Method
Participants

Subjects were 4 undergraduate students enrolled at the University of Ulster, Coleraine, Ireland.
Apparatus and Materials

The apparatus and materials used in Experiment 1 were used here.
General Procedure

studies where the function controlled by these stimuli would have been tested in part fulfilment of the empirical verification of the existence of transfer of function. The general logic behind the design of procedures to date has been to ensure firstly that a behavioural function was demonstrated at either A1 and/or A2. Following this there is normally a demonstration of how the participation of these stimuli in an equivalence class changes the function of other members of that class. Technically it could be argued that in the absence of a demonstrable function at A1/A2 it makes little sense Table 2. Scores out of 16 for "Put subject coin A1 - "Put theto use the term ‘transfer of function’ to describe 2-p coin A2 - each the 5-p n the test forthe findings here.the square hole" nto the roundtransformation ofSidman (1994) addressed some hole" into function. B1 - ZID general issues about the use of this term and sugB2 - YIM C1 -Subject gested instead that ‘transformation of function’ DIB C2 - PUG Transformation Score would be more appropriate (see also Kerr & S1 Keenan, 1997). The findings here tend to sup16/16 S2 port his suggestion and accordingly the term 16/16 of function’ will be used throughS3 ‘transformation4/16 out the remainder of this paper. S4 16/16

The general training and testing procedures used in Experiment 1 were used here.
Phase 1:Training

Conditional relations were trained between the following stimuli:
A1 - "Put the 5-p coin into the square hole" B1 - ZID C1 - DIB
Phase 2: Off-the-baseline testing

A2 - "Put the 2-p coin into the round hole" B2 - YIM C2 - PUG

The experimenter presented, individually, 16 printed versions of the B and C stimuli. On each occasion, the subjects responded by placing either a 5-p or a 2-p coin in either the circular or square indentation of the testing board.
Phase 3: Retraining

The instructions previously used for A1 and A2 respectively were reversed. Conditional relations were trained between the following stimuli:

EXPERIMENT 2 The primary purpose of Experiment 2 was to see if transformation of function could be demonstrated off the baseline without any intervening tests. As an additional measure of the robustness of these procedures for establishing functional equivalence this study examined also the effects of reversing the instructions at A1 and A2.

Phase 4: Off-the-baseline testing

The experimenter presented, individually, 16 printed versions of the B and C stimuli. On each occasion, the subjects responded by placing either a 5-p or a 2-p coin in either the circular or square indentation of the testing board.

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Sean McGuigan and Mickey Keenan

Results Results for all subjects in both the first and second tests for transformation of function are shown in Table 3. The results are very clear and similar for all subjects. In each test, the functions controlled by A1 and A2 were evident for B1, C1 and B2, C2 stimuli respectively for all subjects. Discussion In this experiment, probe-tests for transitivity were omitted. However, the stimulus pool used for A-B-C training was identical to Experiment 1. In the first off-the-baseline test, subject responding indicated emergent rule-following. After the reversal of stimuli A1 and A2 in the second A-B-C training phase, subsequent off-thebaseline measures also indicated reversal of emergent rule following with subject scores of 60% to 100% correct. An interesting note from the available literature suggests that variations in equivalence training and/or testing procedures may have some bearing on the transformation of a behavioural function (Hayes, Kohlenberg, & Hayes, 1991). Indeed in Experiment 2, three out of four subjects increased their off-the-baseline scores from the first to the second test. More importantly, though, the data obtained in Experiment 2 demonstrate that when tests for transitive relations are omitted after conditional discrimination training functional equivalence classes are still evident (see also Dougher & Markham, 1994; Hayes, Kohlenberg, & Hayes, 1991).

EXPERIMENT 3 Experiments 1 and 2 provide the first empirical demonstration that functional equivalence classes develop when conditional discrimination training includes a set of instructions as a class member. With these procedures new empirical questions become possible. For example, it is now possible to examine the effects of competing instructions in a functional equivalence class. This was the primary focus of Experiment 3. The general procedure was similar to the procedures described above. The prerequisite conditional discriminations for two 3-member equivalence classes (A1, B1, C1 & A2, B2, C2) were first trained with instructions at A1. This procedure was repeated for two other sets of stimuli (E1, F1, G1 & E2, F2, G2) using a different set of instructions at G1. Later another set of conditional discriminations were established between C1, D1, E1 and C2, D2, E2 with a view to forming two larger classes (A1, B1, C1, D1, E1, F1, G1 & . A2, B2, C2, D2, E2, F2, G2) (Sidman, 1994). Method
Participants

Subjects were 3 undergraduate students enrolled at the University of Ulster, Coleraine, Ireland.
Apparatus and materials

In this experiment 10-pence, 2-pence, 5-pence and 1-pence coins were used in off-the-baseline testing in Phase 5. Apart from this, the apparatus and conditional discrimination training procedures were the same as those described above.

Rules and equivalence Phase 1:Training A-B-C

27

Conditional relations were trained between the following stimuli:

Phase 5: Off-the-baseline testing

Phase 2: Training E-F-G

Conditional relations were trained between the following stimuli:

The experimenter presented, individually, 16 printed versions of the B1, C1, D1, E1 and F1 stimuli. On each occasion, the subjects responded by placing either a 5-p, a 2-p, a 1-p, or a 10-p coin in either the circular or square indentations of the testing board. Results In Phase 3, results indicated that responding at C1 and E1 were in line with the instructions contained in A1 and G1 respectively; subjects responded 100% correctly in the off-the-baseline test (Table 4).

Phase 3: Off-the-baseline testing

The experimenter presented, individually, 16 printed versions of the C1 and E1 stimuli. On each occasion, the subjects responded by placing either a 5-p, a 2-p, a 1-p, or a 10-p coin in either the circular or square indentations of the testing TableDIB Table 5. The breakdown16 responding in the in2-p coin 4. of subject the C1 "PutScores outcoinof for each"Put thetest for transformation of function in Phase 5. The numbers above A1 and E1 -- VEKtheboard. of times eachYIPC2 - PUG C1, D1, E1, and F1 were presented. The numbers beneath A1 E2 -- of the A1 indicate the number 5-p A2 G1 forJAX est YUK transformation in Phase-3.hole" D1- -the square hole"of function DAQ stimuli B1, D2 F1 F2 - the roundRAL nto into

E1-VEK 1-p 4: TrainingB2 "Put - 10-p E2 G1 -- ZID thePhasecoin G2 - YIM the YIP coin B1 "Put C-D-E Subject nto the square Conditional -the roundScore intorelations hole" C1 -Subject hole" Transformationwere trained between the DIB C2 PUG B1 C1 D1
S1 S1 16/16 following stimuli: 3 3 S2 A1 G116/16 A1 G1 3 0 16/16 3 0 S3
A1 3 A1 3 3 G1 0 G1 0 A1 3 A1 3 3 G1 0 G1 1 A1 4 A1 4 A1 4 4

nd G1 indicate the number of times the functions associated with these stimuli appeared at B1, C1, D1, E1, or F1. E1 3 F1 3

A1 A1 G1 G1 In Phase G1when two classes (A1, B1, C1 and 5, 0 3 0 3 0 E1, F1, G1) were joined via D1, results indicated G1 0 G1 0 A1 0 A1 2 3 G1 3 G1 1 A1 0 A1 1 3 G1 3 G1 2

S2

4

S3

3

3

4

3

3

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Sean McGuigan and Mickey Keenan

that responding at C1 and E1 was still in line with the instructions contained in A1 and G1 respectively (Table 5). Similarly, responding at B1 and F1 were in accordance with instructions contained in A1 and G1 respectively. For all subjects, responding at D1 was controlled by instructions at A1. Discussion Experiment 3 examined what would happen when two separate functional equivalence classes containing competing instructions were brought together to form one larger class. It was found that generally the initial functional class performance was retained and that the stimulus used to ‘join’ the classes together acquired the function attached to A1. Interestingly, although there were opportunities for combinations of behaviours to occur (e.g., two coins could have been placed into one hole) this did not happen. This latter finding is similar to findings from a related study by Bones et al (2001). In Experiment 1 of their study a 3-member functional equivalence was established using clapping as the response with adult subjects. Later a topographically distinct response (stamping) was trained to one of the class members and the effects examined at other class members. During testing there was an opportunity for both clapping and stamping to occur but this did not happen. In subsequent experiments combinations of clapping and stamping occurred when 6-year-old children participated. GENERAL DISCUSSION In the experiments described here the prerequisites for equivalence responding were established using a match-to-sample procedure. The primary goal was to investigate the effects of making one of the stimuli in a 3-member class a normative rule. Across all three studies the results were consistent. Normative rules in the form of written instructions that comprised one member of a class (e.g., A1) determined the responding controlled by other members of that class

(e.g., B1 & C1). Previous studies traditionally have used discrete stimuli to which observable functions were added in a further training phase over and above conditional discrimination training. In so far as the results reported here correspond to findings from these traditional procedures they extend the range of functions that have been shown to participate in an equivalence class. The inclusion of normative rules within match-to-sample training can be said to have resulted in emergent rule following at B and C stimuli. It is unclear, though, whether the transformation of function shown here arose directly from the existence of equivalence classes or whether both equivalence classes and functional equivalence classes contributed to this effect. What confuses matters is that the match-to-sample procedure requires a selection response which itself constitutes a function shared by both stimulus classes. It would be interesting to see whether a respondent-type procedure designed to produce a stimulus equivalence class inevitably results in rule following when instructions are used at A1. Such a finding would support Dougher and Markham’s (1994) suggestion that “it may be more useful to speak of transfer of function as a particular type of functional equivalence that results from the procedures, and operations, that also produce stimulus equivalence” (p. 74-75). To conclude, the procedures described here pave the way for future research aimed at investigating more complex networks of functional classes or functional equivalence classes using a greater variety of behaviours than has hitherto been the case. Much of the functional equivalence research to date has been limited to investigating the basic transfer/transformation effect using discrete behaviours in a single class. With the procedures developed here and in Bones et al (2001) it will now be possible to examine, for example, the laws governing how rules and contingency-shaped behaviours interact in functional equivalence classes, or how compatible and incompatible behaviours interact in functional equivalence classes.

Rules and equivalence

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REFERENCES Barnes, D., & Keenan, M. (1993). A transfer of function through derived arbitrary and non arbitrary stimulus relations. Journal of the Experimental Analysis of Behavior, 59, 61-81. Bones, R., Keenan, M., Askin, D., Adams, L., Taylor, D., & Nicholas, O. (2001). The effects of response topography on functional equivalence class formation. The Psychological Record, 51, 89-110. Dougher, M. J., & Markham, M. R. (1994). Stimulus equivalence, functional equivalence, and the transfer of function. In S. C. Hayes, L. J. Hayes, M. Sato, & K. Ono (Eds.), Behavior analysis of language and cognition (pp.71-91). Reno, NV: Context Press. Dougher, M. J., Augustson, E., Markham, M. R., Greenaway, D. E., & Wulfert, E. (1994). The transfer of respondent eliciting and extinction functions through equivalence classes. Journal of the Experimental Analysis of Behavior, 62, 331351. Hayes, S. C. (1989). Nonhumans have not yet shown equivalence. Journal of the Experimental Analysis of Behavior, 51, 385-392. Hayes, S. C. (1991). A relational control theory of stimulus equivalence. In L. J. Hayes & P. N. Chase (Eds.), Dialogues on verbal behavior (pp.19-40). Reno, NV: Context Press. Hayes, S. C., Kohlenberg, B. S., & Hayes, L. J. (1991). The transfer of specific and general consequential functions through simple and conditional equivalence relations. Journal of the Experimental Analysis of Behavior, 56, 119-137. Hayes, S. C., & Hayes, L. J. (1989). The verbal action of the listener as a basis for rule-governance. In S. C. Hayes (Ed.), Rule-governed behavior: Cognition, contingencies, and instructional control. (pp.191-220) New York: Plenum.

Kerr, K. P. J., & Keenan, M. (1997). Rules and rule-governance: New directions in the theoretical and experimental analysis of human behaviour. In K. Dillenburger, M. F. O’Reilly, & M. Keenan (Eds.), Advances in Behaviour Analysis. University College Press. Kohlenberg, B. S., Hayes, S. C., & Hayes, L. J. (1991). The transfer of contextual control over equivalence classes through equivalence classes: A possible model of social stereotyping. Journal of the Experimental Analysis of Behavior, 56, 505-518. Lazar, R. M. & Kotlarchyk, B. J. (1986). Second order control of sequence-class equivalences in children. Behavioral Processes, 13, 205-215. Sidman, M. (1986). Functional analysis of emergent verbal classes. In T. Thompson and M. D. Zeiller (Eds.), Analysis and integration of behavioral units. Hillsdale, N.J : Earlbaum. Sidman, M. (1990). Equivalence relations: Where do they come from? In H. Lejeune & D. Blackman (Eds.), Behavior analysis in theory and practice: Contributions and controversies (pp. 93114). Hillsdale, N.J : Earlbaum. Sidman, M. (1992). Equivalence relations: Some basic considerations. In S. C. Hayes & L. J. Hayes, (Eds.), Understanding verbal relations (pp. 15-27). Reno, NV: Context Press. Sidman, M. (1994). Equivalence relations and behavior: A research story. Boston: Authors Cooperative. Spradlin , J., & Saunders, R. R. (1984). Behaving appropriately in new situations: A stimulus class analysis. American Journal of Mental Deficiency, 88, 574-579. Wulfert, E., & Hayes, S. C. (1989). Transfer of conditioned ordering response through conditional equivalence classes. Journal of the Experimental Analysis of Behavior, 56, 489-504.


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