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CONDITIONAL DISCRIMINATIONS AND DERIVED RELATIONS

PINPOINTING THE MOMENT OF EMERGENCE

THESIS

Presented to the Graduate Council of the

University of North Texas in Partial

Fulfillment of the Requirements

For the Degree of

MASTER OF SCIENCE

By

Manish Vaidya, B.A.A.S

Denton, Texas

August, 1994

<1

Vaidya, Manish, Conditional Discriminations and Derived

Relations: Pinpointing the Moment of Emergence. Master of

Science (Behavior Analysis), August, 1994, 108 pp., 32

illustrations, bibliography, 19 titles.

Four subjects were exposed to the four trial types that

define stimulus equivalence from the beginning of the

experiment. Procedures were designed to identify

acquisition dynamics and relate these observations to

responding indicative of equivalence class formation. The

data show that, for all subjects, the acquisition of

training conditional discriminations was correlated with

systematic changes in the subjects' selection responses.

The results also indicate that the traditional percent

correct measures obscure some important information about

the subjects' behavior. The data are discussed in the

context of the following statements. 1) Subjects'

performances on derived trials are not indicative of

relations among stimuli at some other level of analysis but

are instances of "equivalencing". 2) "Equivalencing" itself

can be characterized as changes in the conditional and

conditionally discriminative functions of stimuli involved

in the experiment. The potential benefits of this

preparation are discussed.

TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONS iv

Chapter

I. INTRODUCTION 1

II. METHOD 13

Subjects Apparatus

Procedure

III. RESULTS 19

IV. DISCUSSION 98

REFERENCES 106

LIST OF ILLUSTRATIONS

Page

Figure 1. Schematic representation of the stimuli and trial types involved in a 3-choice match-to-sample task 3

Figure 2. Arrangement of sample and comparison stimuli on the monitor 16

Figure 3. List of all trial types in a 3-choice conditional discrimination task 17

Figure 4. Percent of correct trials per session for all configurations of stimuli for four subjects . 23

Figure 5. Trial by trial data for all trial types involving stimuli Al, B1 and CI for SI . . . 25

Figure 6. Trial by trial data for all trial types involving stimuli A2, B2 and C2 for SI . . . 27

Figure 7. Trial by trial data for all trial types involving stimuli A3, B3 and C3 for SI . . . 29

Figure 8. Cumulative frequencies of selection for all A-B (trained) and all B-A (symmetry) configurations for SI 32

Figure 9. Cumulative frequencies of selection for all B-C (trained) and all C-B (symmetry) configurations for SI 34

Figure 10. Cumulative frequencies of selection for all A-C (transitive) and C-A (symmetrically transitive) configurations for SI 36

Figure 11. Trial by trial data for all trial types involving stimuli Al, B1 and CI for S2 . . . 40

Figure 12. Trial by trial data for all trial types involving stimuli A2, B2 and C2 for S2 . . . 42


Figure 14. Cumulative frequencies of selection for all A-B (trained) and all B-A (symmetry) configurations forS2 47

Figure 15. Cumulative frequencies of selection for all B-C (trained) and all C-B (symmetry) configurations for S2 49

Figure 16. Cumulative frequencies of selection for all A-C (transitive) and C-A (symmetrically transitive) configurations for S2 51




Figure 20. Cumulative frequencies of selection for all A-B (trained) and all B-A (symmetry) configurations for S3 65






Figure 26. Cumulative frequencies of selection for all A-B (trained) and all B-A (symmetry) configurations for S3 80


VI


Figure 29. Cumulative frequencies of selection of the experimenter designated "correct" stimulus given novel configurations for SI 89

Figure 30. Cumulative frequencies of selection of the experimenter designated "correct" stimulus given novel configurations forS2 91

Figure 31. Cumulative frequencies of selection of the experimenter designated "correct" stimulus given novel configurations for S3 93

Figure 32. Cumulative frequencies of selection of the experimenter designated "correct" stimulus given novel configurations for S4 95

CHAPTER 1

INTRODUCTION TO THE STUDY

Stimulus equivalence is demonstrated when, after

training a series of conditional discriminations among sets

of arbitrary stimuli (given A pick B, given B pick C),

untrained conditional discriminations are observed with

subjects in the same experimental setting. If, for example,

in the presence of the spoken word "cat" (A) human subjects

who have no English language history are trained to select

the written word CAT (B) and in the presence of the written

word CAT (B) subjects are trained to select a picture of a

cat (C), they will, without further training, respond

relationally in several other ways. In the presence of the

written word CAT (B) they will select the spoken word "cat"

(A) and in the presence of a picture of a cat (C) they will

select the written word CAT (B). Additionally, in the

presence of the spoken word "cat" (A) subjects will pick the

picture of a cat (C) and in the presence of a picture of a

cat subjects will pick the spoken word "cat" (A). The

subjects' untrained conditional discriminations are said to

exemplify reflexive, symmetric and transitive relations

among stimuli involved in the originally trained conditional

discriminations (Sidman, 1990; Sidman & Tailbv, 1982) .

Reflexive relations among stimuli are said to exist

when subjects select comparison stimuli that are physically

identical to the sample stimuli (Fig. 1). Symmetrical

relations are said to exist when subjects respond in

predictable ways to sanqple and comparison stimuli when their

roles are reversed relative to the originally trained

conditional discriminations (i.e., subject picks Al given B1

when explicitly trained to pick B1 given Al during original

conditional discrimination training). Transitive relations

among the originally trained stimuli are said to exist when

the selection of comparisons from one of the originally

trained conditional discriminations occurs reliably under

control of sample stimuli from other originally trained

conditional discriminations (i.e., trained to pick B1 given

Al and to pick CI given Bl, the subject picks CI given Al).

Symmetrically transitive relations are said to exist when

selections are under combined control of symmetric and

transitive relations among stimuli involved in the original

conditional discrimination training (Sidman, 1986, 1992;

Sidman & Tailby, 1982; cf. Saunders & Green, 1992 for an

alternative discussion of these definitions).

The formation of equivalence classes has traditionally

been investigated using a train-and-test preparation. The

typical stimulus equivalence experiment involves training

the original relations to some degree of accuracy (defined

arbitrarily by the experimenter) and testing for the

6 S to

6 6 w

A1 A2 A3 (

1 ' t 1

B1 B2 B3

> f y t > >

CI C2

< C3

P 3 w

W VJ 3 - 3 "S P> 3 w

Fig. 1: Schemat ic represen ta t ion of the condit ional discr iminat ions involved in a 3 choice m a t c h - t o - s a m p l e task. The double lines indicate t ra ined condit ional discr iminat ions and the single lines indicate novel, un t ra ined conditional discriminations. For all re la t ions indicated, t he arrows point to the comparison stimuli. The st imuli in the horizontal rows were always p resen ted toge ther in the comparison array.

emergence of relations that indicate the existence of

equivalence classes. Notice, however, that the terms used

to describe subjects' behavior in equivalence tasks imply-

more than what is directly observable. That is, in terms of

specifiable behavior-environment interactions, the training

and testing can be said to consist of nothing more than

conditional discriminations. From this perspective,

original relations training can be said to be complete when

particular sample stimuli exert reliable conditional control

over the discriminative functions of particular cotrqparison

stimuli. In a similar sense, equivalence relations can be

said to have formed when we see that the conditional and

discriminative functions of the stimuli involved in the

training have become interchangeable. The identification of

stimulus function interchangeability as the dependent

variable of interest allows us to talk about stimulus

equivalence in purely procedural terms. Terms that imply

the formation of relations among stimuli are then reserved

until we have some evidence to invoke them.

From this perspective, there are some issues that have

not been completely resolved. What, for example, are the

conditions under which stimulus function interchangeability

will reliably occur? Under what conditions will it not

occur? How is the acquisition of conditional and

discriminative functions by stimuli during training related

to the "emergent" interchangeability of those functions

during test trials? How do the training and testing trial

configurations affect conditional and discriminative

function interchangeability?

There has been some interest in these issues.

Researchers at the City University of New York (CUNY), for

example, have investigated at least one such necessary

condition by examining nodes (Fields & Verhave, 1987;

Fields, Verhave & Fath, 1984). A node is any stimulus which

serves either as a sample or comparison or both in two or

more originally trained conditional discriminations.

According to Fields and Verhave (1987), "N stimuli can

become a class if (N-l) two-term relations are established

by training and if each of the stimuli in the class is used

in at least one of the two-term training relations" (p.

317). Similarly, Sidman and his colleagues have commented

at length (e.g., Carrigan & Sidman, 1992; Johnson & Sidman,

1993; Sidman, 1980; 1987; 1992; Stikeleather & Sidman, 1990)

on the different kinds of stimulus control relations that

can emerge during an experiment. They have also identified

some procedures to allow better specification of the nature

of the stimulus control relation that obtains between

stimuli within the context of the experiment (Johnson &

Sidman, 1993; Sidman, 1987; 1992). Sidman (1987), for

example, points out that the use of only two choices in the

comparison array does not allow a precise specification of

the kind of stimulus control (S+/S-) responsible for the

selection response. For example, we may train a subject to

select Bl and not B2 in the presence of Al. The source of

control for the selection of B2 and not Bl in the presence

of A2, however, might be the conditionally discriminative

function of B2 in the presence of A2 or simply the rejection

of Bl given A2. The use of at least three stimuli in a

comparison array obviates this problem. These kinds of

suggestions have allowed a greater specification of the

procedural requirements for occasioning and measuring the

interchangeability of stimulus functions.

The role of reinforcement in the acquisition of the

original conditional discriminations has also been evaluated

(e.g., Harrison & Green, 1990/ Saunders, Saunders, Kirby &

Spradlin, 1988). Saunders et al. (1988) presented subjects

with conditional discrimination trials in which the samples

were selected from one pre-existing equivalence class and

the comparisons from another equivalence class. No

differential consequences were programmed for any responses.

The researchers reported that the subjects reliably picked a

particular comparison in the presence of a particular

sample. They further reported that "[s]ubsequent tests

showed the emergence of equivalence relations between

stimuli from classes linked by the unreinforced conditional

selections" (Saunders et al., 1988, p.145).

Harrison and Green (1990), in a similar vein, were able

to establish original conditional discriminations without

reinforcement. The original conditional discriminations

were trained by presenting the desired sample-comparison

pairs together while varying the other comparison stimulus

in a two-choice match-to-sample preparation. No

differential consequences were programmed for any responses.

In Experiment 1, the researchers trained original

conditional discriminations with three adult subjects using

the method just described. Subsequent tests for

transitivity, according to the authors, were equivocal. In

a second experiment, the researchers trained original

conditional discriminations with four children in a similar

manner. Subsequent tests, according to the authors,

demonstrated the emergence of equivalence classes with one

subject and the emergence of symmetry without equivalence

for another. Of the two remaining subjects, one failed to

acquire the original conditional discriminations at all, and

another failed to demonstrate the emergence of derived

relations after acquiring the original conditional

discriminations (Harrison & Green, 1990).

It is important to note that in terms of specifiable

behavior-environment interactions the failure to demonstrate

the emergence of equivalence relations is not equivalent to

the absence of responding. Rather, it is the non-occurrence

of predicted conditional discriminations. Any conditional

discriminations that may be occurring are obscured by the

use of percent correct as the dependent measure. The

8

combined use of train-and-test methods and percent correct

as the dependent measure have given equivalence a somewhat

static characteristic. Equivalence classes seem to lose the

dynamic feature typical of behavior-environment

interactions.

A common finding reported in the equivalence literature

is the emergence of derived relations during repeated

exposure to testing trials. This has given rise to

questions involving the role of testing conditions in the

formation of equivalence classes and, relatedly, the

existence of such classes prior to testing (Saunders,

Spradlin & Saunders, 1989). Saunders et al. (1989), for

example, trained conditional discriminations and reported

the emergence of responding indicative of four 3-member

equivalence classes (A1-B1-C1, A2-B2-C2, E1-F1-G1 and E2-F2-

G2) during phase 1. The first two classes of stimuli (A#-

B#-C#) were functionally distinct from the last two classes

(E#-F#-G#). In phase 2, they arranged for unreinforced

conditional discriminations in which the samples were drawn

from the first two classes and the comparisons from the last

two classes. Previous research on the expansion of

equivalence classes suggested that the conditional

discriminations occurring during phase 2 would have resulted

in a merger of previously independent equivalence classes.

Rather than presenting the tests at this point, however, the

experimenters reversed the conditional discriminations that

were observed during phase 2 via differential reinforcement

(phase 3). The presentation of probe trials, following the

reversal, occasioned responding that was indicative of

equivalence relations consistent with the conditional

discriminations observed during phase 2. The authors

concluded that equivalence classes had formed following the

conditional discrimination history of phase 2 even though

they were not tested for until the end of phase 3. In other

words, the authors concluded that equivalence class

formation had occurred prior to testing for the emergence of

the equivalence classes.

Mcllvane and Dube (1990) suggest that "questions such

as 'do stimulus classes exist before they are tested' are

not good ones to ask" (p. 7). Indeed, whether or not

stimulus classes exist before they are tested is not an

answerable question in that the tests are required to

document the existence of equivalence classes. These kinds

of questions "create conceptual problems that behavior

analysis usually helps us to avoid" (Mcllvane & Dube, 1990,

p. 13). This is not to say that the question, per se, is

not worth asking. Rather, the form of the question and the

inadequacy of the standard experimental preparation to

provide an unequivocal answer are problematic.

The present study sought an alternative approach to

addressing these problems. Specifically of interest were

the changes in behavior that occurred during training of the

10

original conditional discriminations, and related changes

indicative of untrained relational responding. There were

two important requirements that had to be met in order to

pursue such an approach. First, I had to be able to measure

more precisely the acquisition of the original conditional

discriminations. Second, I had to be able to observe the

"path" by which stimulus functions became interchangeable.

The first of these requirements was met with a slight

modification of Touchette's (1971) procedure for measuring

the moment of transfer of a discriminative stimulus

function. The second requirement was met by replacing the

traditional train-and-test preparation with an alternative

procedure.

Touchette (1971) trained simple form discriminations

using a delayed prompting procedure. The subjects' pressing

responses were brought under discriminative control of a red

key (Sd) as opposed to a simultaneously present white key.

A black figure (target stimulus) was then superimposed on

the red key. Any response to the compound stimulus (black

figure - red key) resulted in a change in presentation

conditions of the following trial: the onset of the red

background was delayed by 500 milliseconds. Pressing

responses occurring under control of the black figures prior

to the onset of the red background in any trial were said to

be indicative of the transfer (or extension) of the

discriminative function of the red background to the

11

previously neutral black figures. Measurement of the point,

during the experiment, at which the black figures were

consistently selected before onset of the red background

allowed a specification of the "moment of stimulus control

transfer" (Touchette, 1971). In the present study, the

moment of acquisition of the original conditional

discrimination was pinpointed in the same way with a slight

modification of Touchette's (1971) procedure.

The second requirement was to ascertain when stimulus

functions become interchangeable. There is evidence that

conditional discriminations indicative of derived relations

emerge during the post-training probe trials (e.g.,

Saunders, Spradlin & Saunders, 1989; Stikeleather & Sidman,

1990). This suggests that the configuration of stimuli

during probe trials plays an important role in the

occurrence of the novel conditional discriminations during

probe trials. Tracking the emergence of novel conditional

responding has not been possible, however, because of the

train-and-test preparation and the use of percent correct as

the dependent measure during the probe trials. An

alternative was to pinpoint the emergence of novel

conditional discriminations relative to the acquisition of

the original conditional discriminations by presenting all

configurations (training and testing) from the beginning of

the experiment. The purpose of such an approach was to

specify more precisely the relationship between the

12

acquisition of the original conditional discriminations and

the "emergent" stimulus function interchangeability.

To restate, the questions of interest in this

experiment were: 1) How is the acquisition of conditional

and discriminative functions by stimuli during training

related to the "emergent" interchangeability of those

functions during test trials? 2) What is the role of the

training and testing trial configurations on conditional and

discriminative function interchangeability? This experiment

attempted to shed some light on these questions.

CHAPTER II

METHOD

Subjects

Four students at the University of North Texas served

as subjects during the experiment. The subjects were

recruited through an advertisement placed in the classified

section of the city newspaper. The criteria for inclusion

included no exposure to behavior analysis or psychology

classes. Subjects were not allowed to take any materials

(including watches, purses, etc.) into the lab.

getting

All sessions were conducted in one of the human

behavior laboratories at the Center for Behavior Analysis.

Apparatus

Throughout the experiment subjects interacted with an

IBM-compatible 80386 PC and a 640 x 480 resolution VGA

monitor. All selection responses (defined below) were made

using a Logitech mouse. The custom-written software

presented randomized trials, collected latency and selection

data and delivered points according to the experimenter's

specifications.

14

Stimuli

Nine 2-dimensional figures were used as stimuli during

the entire experiment. Each figure was enclosed in a 120 x

120 pixel frame. The geometric dimensions of the figures

were arbitrary to preclude the possibility that the stimulus

dimensions might have a pre-existing function in the

subjects' repertoires.

The selection response

The "selection response", in the context of this

experiment, was defined as the placement of a cursor within

the 120 X 120 pixel frame containing a figure followed by a

press of the left-most button on the mouse.

iiiswctj-gns

Subjects were given an instruction sheet immediately

prior to the first session. The experimenter read aloud

from the instruction sheet while the subject read along on

his/her copy. The subjects were told only that 1) the mouse

and its left-most button would be used exclusively during

the entire experiment and that 2) their task was to try to

earn as much money as possible. Any other interactions were

kept to a minimum and no further instructions were given for

the remainder of the experiment.

Procedure

Structural specifications of the trials: When a

subject entered the lab he/she saw the words "Press spacebar

to begin" on the monitor. A press on the spacebar initiated

15

the session and presented a figure (sample stimulus) in the

center of the top third of the screen. A selection response

(defined above) to the sample stimulus produced a 3-

comparison array in a "V" shaped arrangement in the center

of the bottom two-thirds of the screen (see Fig. 2). In

order to preclude the occurrence of a "forced" conditional

discrimination, a 100 X 50 pixel frame with the words "Can't

Answer" was presented in the center of the diamond shaped

sample-comparison arrangement on each trial (cf. Duarte,

Rosales, Eikeseth & Baer, 1991). A selection response to

one of the comparison stimuli was followed either by a point

delivery screen or by a blank screen depending on the trial

type and the selection response. In either case, there was

a l-s inter-trial interval from the offset of the comparison

array following a response to the presentation of the next

sample stimulus.

Original conditional discrimination training

In a 3-choice conditional discrimination, there are 18

possible trial types (excluding identity matching trials).

Figure 3 delineates each of the trial types and the stimuli

involved in each. Each session consisted of 5 trials of

each of the 18 trial types for a total of 90 trials per

session. Each training and testing trial type was presented

within a block of 18 randomly ordered trials before

proceeding to the next block of 18. The original

conditional discriminations were trained using Touchette's

16

Sample

Stimulus

Comparison

Stimulus

(Pos. 1)

Can't Answer

Option

Comparison

Stimulus

(Pos. 3)

Comparison

Stimulus

(Pos. 2)

Fig. 2: A r e p r e s e n t a t i o n of t h e a r r a n g e m e n t of s amp le and c o m p a r i s o n s t imul i on t h e m o n i t o r fo r all t r i a l types . The c o m p a r i s o n a r r a y cons i s ted of t h e b o t t o m two—thirds of t h e s c r een and was p r o d u c e d by clicking on t h e s amp le s t imulus .

17

Sample Comparison Array

01 A1 [Bl] B2 B3 02 A2 B1 [B2] B3 03 A3 Bl B2 [B3]

04 B1 [CI] C2 C3 05 B2 CI [C2] C3 06 B3 CI C2 [C3]

07 B1 [Al] A2 A3 08 B2 A1 [A2] A3 09 B3 Al A2 [A3]

10 CI [Bl] B2 B3 11 C2 Bl [B2] B3 12 C3 Bl B2 [B3]

13 A1 [CI] C2 C3 14 A2 CI [C2] C3 15 A3 CI C2 [C3]

16 CI [Al] A2 A3 17 C2 Al [A2] A3 18 C3 Al A2 [A3]

Original Relations

Symmetrical Relations

Transitive Relations

Symmetrically Transitive Relations

Fig. 3: A list of all possible trial types (excluding identity matching trials) in a 3 - c h o i c e m a t c h -to—sample task. Brackets around the st imulus names indicate the experimenter designated "correct" stimulus.

18

(1971) delayed prompting procedure in the following manner.

An observing response to a sample stimulus (e.g., Al)

produced a 3-comparison array (Bl, B2, B3). Five hundred

milliseconds (.5 second) after the presentation of the

comparison array, the S+ (in this case, Bl) turned blue.

The blue color and geometric dimensions of the comparison

stimulus, then, were a compound stimulus analogous to

Touchette's black figure-red key compound stimulus.

Selection of the compound stimulus designated correct

delayed the change in color by 500 milliseconds (.5 second)

following each successful trial. The consistent selection

of Bl in the presence of Al prior to the change in color

indicated the acquisition of a conditionally discriminative

function by Bl in the presence of Al.

Tests for stimulus function interchanqeabilitv

Testing trials (bottom 3 panels in Fig. 3) were

presented randomly among the training trials in each block

of 18 trials. The delayed prompting procedure was specific

to the training trials and was not used with testing trials.

Stimulus-function interchangeability was defined in terms of

the conditional discriminations described in Chapter 1

(Introduction to the Study).

CHAPTER III

RESULTS

The program recorded the following aspects of the

subjects' conditional discriminations: the comparison

stimulus selected, the latency from comparison array onset

to selection response, the programmed delay to the change in

color (prompt) for original conditional discriminations, and

the position of the comparison stimulus in the array at the

time of selection.

A brief overview of graphed data is provided below to

familiarize the reader with graphs. Following the overview,

detailed analyses of the data are provided. Figure 4 shows

the percent of trials correct per session for all trial

types (see Fig. 3) for each of four subjects (S1-S4). The

percent correct measure is obtained by dividing the number

of times a particular stimulus was selected (per session) by

the number of times that same stimulus was designated

correct by the experimenter (per session) and multiplying

that value by 100.

Figures 5-7, 11-13, 17-19, and 23-25 show which

stimulus was selected and the latency to that selection

response for every trial in the experiment for all subjects.

The top two graphs on each figure show selection latencies

20

(represented by dots) and delay to prompt onset (represented

by solid line) for all trained conditional discriminations.

The middle two graphs on each page present data for trials

where the configuration of stimuli is exactly reversed with

respect to the trained conditional discriminations (i.e.,

symmetry trials). The bottom left set of graphs on each

page present data for trials where the current sample

stimulus has been a sample stimulus in one of two

consequated conditional discriminations and the current

"correct" comparison has been a "correct" comparison in the

other consequated conditional discrimination (i.e.,

transitivity trials). The bottom right set of graphs

present data for trials where current samples have been

"correct" comparisons in one of two consequated conditional

discriminations and the current comparisons have been

samples in the other consequated conditional discriminations

(i.e., symmetrical transitivity or equivalence trials). On

the bottom four graphs in each of these figures, the top

panels always present data with respect to the experimenter-

designated correct stimulus. The bottom panels always

present data with respect to the "Can't Answer" (CA) option.

On all graphs, bars that touch the top of the graphs

indicate that the selection latency was greater than the

maximum range of the axis.

Figures 8-10, 14-16, 20-22, and 26-28 present

cumulative frequencies of selection for all stimuli for all

21

trial types. On each graph, the solid line represents the

cumulative frequency of selection of the experimenter

designated "correct" stimulus, the dotted line represents

the cumulative frequency of selection of the CA option and

the other two lines represent cumulative frequencies of

selection for the other stimuli in the comparison array.

The top right graph in Fig. 8, for example, shows the

cumulative frequencies of selection of Al, A2, A3 and CA in

the presence of B1 as sample stimulus. The slope of the

lines indicate the rate at which a particular comparison

stimulus was being selected across trials. A horizontal

line, then, indicates that a stimulus was not selected at

all. Figures 8, 9, 14, 15, 20, 21, 26, and 27 present

cumulative frequencies of selection for the trained

conditional discriminations (left columns) and related

symmetry trials (right columns). Figures 10, 16, 22, and 28

present cumulative frequencies of selection for transitivity

(left columns) and equivalence trials (right columns).

Figures 29, 30, 31, and 32 present cumulative

frequencies of selection of the experimenter designated

correct stimulus on testing trials for each of three

experimenter designated classes. The top graph on Fig. 29,

for example, presents cumulative frequencies of selection of

Al given B1 (symmetry), B1 given CI (symmetry), CI given Al

(transitivity), and Al given CI (equivalence) for SI.

22

Returning to Figure 4 for more details, the top graph

shows percent of correct trials for all trial types across

all sessions of the experiment for SI. Notice that accurate

responses on original relation trials (reinforced

conditional discriminations) occurred at or near 100% for

the duration of the experiment. Selection of the

experimenter designated "correct" stimuli on derived trials

was approximately 20% initially, increased to a somewhat

higher percent and then decreased to between 0-10% correct.

While this pattern was observed for accurate responses on

all derived trial types, it was most pronounced on symmetry

configurations in the presence of which the "correct"

stimulus was selected around 60% of all symmetry trails for

4 sessions before it decreased to 0% correct.

Figures 5-7, which track subject l's responding trial

by trial, show that the decrease in accuracy on derived

trial types seen in Figure 4 was a function of the exclusive

selection of the CA option on 10 of the 12 derived trial

types presented. Figures 6 & 7 further show that, for the

two remaining derived trial types (A3-C3 (transitivity) and

C2-A2 (equivalence)), the drop in accuracy was a function of

the selection of C2 given A3 as the sample (A3-C2, bottom

left set of graphs, Fig. 7) and the selection of A3 given C2

as the sample (C2-A3, bottom right set of graphs, Fig. 6),

respectively. Figures 5-7 also show that the beginning of

the almost exclusive selection of CA on all derived trial

23

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80

60

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20

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randomized.

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removed

C Additional

instruct ions

given (S2)

o Original

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A Equivalence

1 0 0

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Consecutive Sessions

24

Fig. 4: Percent of correct trials per session for 4 trial

types (original, symmetry, transitivity and symmetrical

transitivity) for 4 subjects in the experiment. The phase

changes (indicated by the vertical dotted lines on SI and

S2's graphs) are explained in the text.

25

0) T5 C o o <D

00

>N o c <D

0) "O C O a <D

00

10 n

8

6

4

2

0

10

A1-B1

5 -

10

5 -

10

>> ^ o

o5 10

0

10

IU

Jj

(I)

X> c o u 0) c/)

5 -|

10

5 H

10

>, 5 o S 10

5 -I

0

i 1 1

kL

1 I ilitliiliiiii|iiiiiiniiiiiiiiliiiililii

B1-C1

7 B1-A1

B1-A2

B1-A3

B1-CA

HllllllliliH|nliiiiiiiniiiiiliJHlll

A1-C1

A1-C2

A1-C3

A1-CA

] r i 1 1

mi i i .1

iitiniii

C1-B1

C1-B2

C1-B3

C1-CA

i lliltil tiiiln.

C1-A1

C1-A2

C1-A3

C1-CA

j 111. ilIn1111 i j

0 15 30 45 60 75 90 105 0 15 30 45 60 75 90 105

Consecutive Trials Consecutive Trials

26

Fig. 5: Trial by trial data for SI on A1-B1-C1 set of

stimuli. The top two graphs represent all original relation

trials presented throughout the experiment. The solid

diagonal line represents the delay to prompt onset; the dots

represent the latency to selection. The remaining graphs

present trial by trial data for all related derived

relations. The graphs indicate the specific stimulus

selected, the vertical lines represent latencies to

selection.

27

CO

~o c o o <U

00

o c <D

A 2 - B 2 B 2 - C 2

CO

"O C

O O 0

C O

o c CD

o

(0 X5 c o o CD

C O

>N o c CD

0

10

5

10

5

10

5

10

5

0

10

5

10

5

10

5

10

5

0

t i r

ILLJ

||j I lllihjllnl.iiiiniljlinJlllllllij

B 2 - A 2

B 2 - A 1

B 2 - A 3

B 2 - C A

- ,

1 1 lilllllll

II h

1 hliii ii|iiiiiiiii,i|iiiiih.i...,i|....jiiiiiiiii

A 2 - C 2

A 2 - C 1

H in II1IH1II.HI

A 2 - C 3

A 2 - C A

11 111 tlillniliiiiiiiiJlilllill

C 2 - B 2

C 2 - B 1

C 2 - B 3

C 2 - C A

C 2 - A 2

C 2 - A 1

C 2 - A 3

C 2 - C A

0 15 30 45 60 75 90 105 0 15 30 45 60 75 90 105


28









selection.

29

in ~o c o o CD

00

>N o c 0)

if) ~o c o o <D

00

o c 0) o

if) ~u c o o <D

00

o c 0

-f—' o

10

8

6

4

2

0

10

5

10

5

10

5

10

5

0

10

5

10

5

10

5

10

5

0

A 3 - B 3

V •

i r 1 1 1 1

B 3 - C 3

ll 1 I iililii liiiJ

-

i

1 ll ill ,li|iiiittt]jiiiii|liiiliiittiiii|iitlJlitIlliiii

Mil

IIIIIHIIIIIHIIH iHlmllliiH

B 3 - A 3

B 3 - A 1

B 3 - A 2

B 3 - C A

A 3 - C 3

A 3 - C 1

A 3 - C 2

A 3 - C A

} 1 1 1 1 1

llllinllllilfllllllll

I lni l i l i i i i i i . i l . . t l l l l l l l l l l

C 3 - B 3

C 3 - B 1

C 3 - B 2

C 3 - C A

C 3 - A 3

C 3 - A 1

C 3 - A 2

C 3 - C A

0 15 30 45 60 75 90 105 0 15 30 45 60 75 90 105


30









selection.

31

types coincided closely with the acquisition of the original

conditional discriminations (the point at which SI stopped

waiting for prompt onset to make a selection response).

Notice that prior to the "discovery" of the CA option, SI

selected all of the other stimuli in the array to some

extent or another. This pattern is discussed in more detail

next.

Figures 8-10 present cumulative selection frequencies

for SI for all stimuli in the experiment in terms of the

configuration in which they appeared. Figures 8 & 9 show

that, prior to exclusive selection of the CA option (dotted

lines on all graphs), SI selected the experimenter

designated "correct" stimulus (solid lines on all graphs)

more often than any other stimulus on 5 of the 6 symmetry

configurations (right columns, Figures 8 & 9). Figure 10

(left column) shows that the same was not true for

transitivity configurations. In fact, given transitivity

configurations with A1 and A2 as samples (top two graphs in

left column, Fig. 10), SI selected the experimenter

designated "correct" stimulus about as often as the other

stimuli in the comparison array before switching to the CA

option. Notice that for transitivity configurations with A3

as the sample, however, (bottom graph in left column, Fig.

10) SI selected C2 more often than any other stimulus and

about as often as the CA option until session 10. Figure 10

(right column) shows that given equivalence configurations,

32

c o

-+->

o Q) CD 00

O >N o c 0) D G~ CD L—

Li_

0 >

-4—'

_o

D

D O

105

90

75

60

45

30

15

0

A 1 - B 1 B 1 - A 1 / A 2 / A 3 / C A

A 2 - B 2

i — T

A3—B3

1 I I I T

0 3 6 9 12 15 18 21

i i i \ r

B 2 - A 2 / A 1 / A 3 / C A

i i — i — T

B 3 — A 3 / A 1 / A 2 / C A

A1 B1 B1 A1

A1 B2

B1 A2

A1 B3

B1 A3

A1 CA

B1 CA

I I

"1 1 1

I I I I ^ ^ I

0 3 6 9 12 15 18 21

Consecutive Sessions Consecutive Sessions

33

Fig. 8: SI - Cumulative selections are plotted for each

comparison stimulus in the array (including the Can't Answer

option) given a particular sample stimulus. From the top,

the graphs in the left column present cumulative selections

of all B stimuli given Al, A2 and A3 as samples,

respectively. The graphs in the right column present

cumulative selections of all A stimuli given Bl, B2 and B3

as samples, respectively. In the legend, identifiers

flushed left apply to the graphs in the left column,

identifiers flushed right apply to graphs in the right

column. Phase changes (indicated by vertical dotted lines)

are explained in the text.

34

B1-C1

c o o Q) (D

00

(J c CD D O"

0 LL_

0 > H—'

_G

D

£ D o

B 2 - C 2

B 3 - C 3

C1-B1/B2/B3/CA

n — ^ ^ — i — T

C2—B2/B1/B3/CA

I ^ 1 1 1 1 1

C3-B3/B1/B2/CA

n — ^ — i — r

0 3 6 9 12 15 18 21

B1 C1

C 1 B1

B1 C2

C1 B2

B1 € 3

C1 B3

B1 CA

C1 CA

B3 C3

C3 B3

B3 C1

C3 B1

B3 C2

C3 B2

B3 CA

C3 CA

n I I I I I 1 0 3 6 9 12 15 18 21


35





of all C stimuli given Bl, B2 and B3 as samples,


cumulative selections of all B stimuli given CI, C2 and C3






36

c .2 -4—'

o _CD

<D 00

o c CD

D CT CD

CD >

'-+-J _o 3

£ 3 o

105

90

75

60

45

30

15

0

105

90

75

60

45

30

15

0

105

90

75

60

45

30

15

0

A 1 - C 1 C 1 - A 1 / A 2 / A 3 / C A

— i — i — i — r A 2 - C 2

— r — i — i — i — i — i — i A 3 - C 3

1 I I I I I I 0 3 6 9 12 15 18 21

i i i r C 2 - A 2 / A 1 / A 3 / C A

1 I

— i — i — i — r C 3 - A 3 / A 1 / A 2 / C A

"l 1

1 1 1 1 1 1 1 0 3 6 9 12 15 18 21

A1 C1

C1 A1

A1 C2

C1 A2

A1 C3

C1 A3

A1 CA

C1 CA


37





of all C stimuli given Al, A2 and A3 as samples,


cumulative selections of all A stimuli given CI, C2 and C3






38

Si selected the experimenter designated "correct" stimulus

(A3) most often when C3 was the sample (bottom graph in

right column, Fig. 10). Notice, however, that SI also

selected A3 more often than any other stimulus given CI and

C2 (before switching to the CA option). Thus the apparent

conditionally discriminative function of C3 given A3 was an

artifact produced by a bias with respect to the selection of

C3 given transitivity configurations.

Finally, Figures 5-7 show that, by session 12, the

latencies to selection of CA option for SI had dropped

considerably for all derived trial types. The short

latencies to selection and the fact that CA was selected

only on novel configurations (un-consequated) suggested that

the selection of CA represented maximization. That is, SI

was able to earn all possible points while at the same time

minimizing overall session time by selecting CA. Selecting

CA was the most efficient choice because the customized

software program always presented the cursor on the CA

option when the comparison array was presented. To check

for the possibility that SI was maximizing, the mouse cursor

position was altered to occur randomly on one of the 3

comparison stimuli (and not on the CA option). Fig. 5-7

show that aside from slight increases in the latencies

(presumably the time required to reposition the mouse

cursor), SI continued selecting CA. For the last 3 sessions

of the experiment, the CA option was removed from the

39

comparison array. Figures 5-7 show that SI immediately

began to select the experimenter designated "correct"

stimuli on all trial types.

Subject 2's performance resembled Si's in several

respects. Like SI, S2 selected the correct stimulus on

greater than 90% of the training trials for the duration of

the experiment (see Fig. 4). Additionally, S2's selection

of the "correct" stimulus on symmetry trials, like SI,

started out at 20% correct, increased to approximately 80%

correct and decreased to 0% correct by session 11. S2's

accuracy on transitivity and equivalence trials fluctuated

around chance levels until session 11 before dropping to 0%

correct.

Detailed inspection of S2's performance shows that

accurate responses on training configurations occurred at or

near 100% for all sessions except sessions 6-8,

where they occurred around 80% correct. Figures 11-13 show

that the "inaccurate" responses were occurring for only 3 of

the 6 trained conditional discriminations (Al-Bl, B2-C2 and

B3-C3 trials). An analysis of the individual selection

responses (see Figs. 14-16) on each of these trials revealed

that the drops in accuracy were a function of the selection

of B2 on the Al-Bl trials (Fig. 14) and CI on the B3-C3

trials (Fig. 15). There was no discernible pattern of

errors for the B2-C2 trials.

40

A 1 - B 1 V)

~o C O o <D

CO

o c (D -+->

D

CO "O c o o 0

00

o c 0

cn ~u c o o 0 00

o c 0

-4—̂ o

I lilt Nil

I 111 ii hi iilliill

B 1 - C 1

B 1 - A 1

B 1 - A 2

B 1 - A 3

B 1 - C A

A 1 - C 1

A 1 - C 2

A 1 - C 3

A 1 - C A

lb ll IB nil i ll III 1 lll!ifllll!l

I ll 1 1 1 Ml! 1 ill

lllk 1 li [in H 111

llU-

C 1 - B 1

C 1 - B 2

C 1 - B 3

C 1 - C A

- I I ii , . i».hiiiHj

- 1 i l rt 1 ill 1 II i it

M i 1 till i h. II ii ..11 \

1

C 1 - A 1

C 1 - A 2

C 1 - A 3

C 1 - C A

0 25 50 75 1 0 0 1 2 5 1 5 0 1 7 5 0 25 50 75 1 0 0 1 2 5 1 5 0 1 7 5

Consecut ive Trials Consecut ive Trials

41

Fig. li: Trial by trial data for S2 on A1-B1-C1 set of







selected, the vertical lines represent the latency to

selection.

42

CO ~o c o o CD

i f )

>s o c CD

2 5 1

2 0 -

15

10

5

CO ~o c o o CD

i f )

>x o c CD

CO

~o c o o CD

i f )

o c CD

-4—1

D

0

10

5

10

5

10

5

10

5

0

10

5

10

5

10

5

10

5

0

A 2 - B 2 B 2 - C 2

t 1 n — i f r — i

l U i i tii, ii

. i 8 mi l l i til

" n i II i il 11 111 1 ill b

l i l ^ L L p J i l u i a j

B 2 - A 2

B 2 - A 1

B 2 - A 3

B 2 - C A

_1 I I llllllhll Jii

_ L l l l n i ' l i i

11

i_y_

A 2 - C 2

A 2 - C 1

A 2 - C 3

A 2 - C A

. i i

u faihli • lit

Li i in il ii mi

C 2 - B 2

C 2 - B 1

C 2 - B 3

C 2 - C A

C 2 - A 2

C 2 - A 1

C 2 - A 3

C 2 - C A

0 25 50 75 100125150175

Consecutive Trials

0 25 50 75 1 0 0 1 2 5 1 5 0 1 7 5

Consecutive Trials

43

Fig. 12: Trial by trial data for S2 on A2-B2-C2 set of








selection.

44

A 3 - B 3

CO TD C o o 0) (/)

o c 0

(0 ~G c o o d) </)

u c CD

CO ~O c o o <D

00

o c <L>

ill 1 ill Hi llml

B 3 - C 3

tn #v«. •

B 3 - A 3

B 3 - A 1

B 3 - A 2

A 3 - C 3

A 3 - C 1

A 3 - C 2

A 3 - C A

I I i

Hm In li .inn isIrihtm

j Hili ifa»

B 3 - C A Y ^

_ J i IUII tat

C 3 - B 3

C 3 - B 1

C 3 - B 2

C 3 - C A

li lllli ii

L u In I I I I INH.I I n

C 3 - A 3

C 3 - A 1

C 3 - A 2

C 3 - C A

0 35 70 105 140 175 0 35 70 105 140 175


45









selection.

46

Selection of the experimenter designated "correct"

stimulus on derived trial types started out low and

increased, with symmetrical responding hovering around 75%

during sessions 2-7 (see Fig. 4). "Correct" responding on

all derived trial types dropped to 0% correct by session 11.

Figures 11-13 show that the drop in accuracy on derived

trials seen in Figure 4 was a function of the almost

exclusive selection of CA option, given novel

configurations, beginning around session 10 (trials 45-50).

Notice also that this exclusive shift to CA coincided with

acquisition of the original conditional discriminations as

it did in the case of SI. By the end of session 9, S2 had

stopped waiting for prompt onset for all original relations

trials. S2's responses on derived trials during session 9

were particularly interesting. On the five presentations of

each derived trial type, S2 selected each of the comparison

stimuli once and the CA option twice. As stated earlier,

beginning with session 10, S2 began to select the CA option

exclusively on all derived trials.

Figures 14 and 15 show that prior to the exclusive

selection of CA, S2 selected, for all 6 of the symmetry

trial types, the experimenter-designated "correct" stimuli

more often than any others. Figure 16 shows that, as with

SI, the same was not true for S2's selections given

transitivity and equivalence configurations. Two

particularly interesting patterns can be seen in Figure 16.

47

A 1 - B 1

C o H—' u _CL) 0

i f ) M— o >> o c CD D cr CD L_

L l_

CD >

_ D

D

D CJ

B 1 — A 1 / A 2 / A 3 / C A

A 2 - B 2

175 -i

150 -

125

100 -

75 -

50 -

25 -

0 r A 3 - B 3

t — r ~ T

150 -

\ i I r B 2 - A 2 / A 1 / A 3 / C A

i i ^—T B 3 - A 3 / A 1 / A 2 / C A

0 1 1

5 10 15 20 25 30 35

"l—i


i \ i ^ i ^ i 0 5 10 15 20 25 30 35


A 1 B 1

B 1 A 1

A 1 B 2

B 1 A 2

A 1 B 3

B 1 A 3

A 1 C A

B 1 C A

48

Fig. 14: S2 - Cumulative selections are plotted for each












49

c o u Q) CD

( / )

>N o c CD D O" CD

CD >

-4—'

_o D

E Z5

o

175

150 -

125 -

100 -

75 -

50 -

25 -

0 -

B1-C1 C 1 - B 1 / B 2 / B 3 / C A

B 2 - C 2

150 -

B 3 - C 3

1 0 0 -

0 5 10 15 20 25 30 35


— i — r C2—B2/B1 / B 3 / C A

1 1

i — i — i — T C3—B3/B1/B2/CA

"1 I

1 1 1 1 1 1 0 5 10 15 20 25 30 35


B2 C2

C2 B2

B2 C1

C2 B1

B2 C3

C2 B3

B2 CA

C2 CA

B3 C3

C3 B3

B3 C1

C3 B1

B3 C2

C3 B2

B3 CA

C3 CA

50













51

c o o _0) CD 00

o c CD D cr (D L_

Ll-

CD >

'-4-J

JO

D E D o

175

150 -

125 -

100

75

50

25

0

A 1 - C 1 C 1 - A 1 / A 2 / A 3 / C A

A 2 - C 2

175

150 -

125 -

100 -

75 -

50 -

25 -

0 -

1 — i — i — i

r — r A 3 - C 3

" i — r

175

150 -

125 -

100 -

75 -

50 -

25 -

0 -

. . .Z

^ i i i i i i

0 5 10 15 20 25 30 35

i—i—i—i C 2 — A 2 / A 1 / A 3 / C A

— i — i — i — i — i — i C 3 — A 3 / A 1 / A 2 / C A

A1 C1

C1 A1

A1 C2

C1 A2

A1 C3

C1 A3

A1 CA

C1 CA

• n " — i — i — i — i — i — i

0 5 10 15 20 25 30 35


52













53

Notice that when A3 was the sample, S2 selected CI slightly

more often than the experimenter designated "correct"

stimulus (bottom graph in left column, Fig. 16). At the

same time, given CI as sample (top graph in right column,

Fig. 16), S2 selected A3 more often than the "correct"

stimulus. Similarly, notice that when A1 was the sample, S2

selected C3 more often than any other stimulus (top graph in

left column, Fig. 16) and when C3 was the sample, S2

selected A1 more often than any other stimulus (bottom graph

in right column, Fig. 16) before switching to the CA option.

These patterns, in traditional tems, would be said to be

indicative of relations among the stimuli involved in the

conditional discriminations. Notice also, however, that the

typical percent correct measures would be unable to detect

these kinds of patterns.

Figures 11-13 show that by the end of session 12

(trials 55-60), the latencies to CA selection on derived

trials had dropped considerably. As with SI, the pattern of

responding raised the possibility that the selection of CA

represented maximization for S2. To check for this

possibility, the position of the mouse cursor was changed as

described for SI starting with session 18 (phase A, Fig. 4).

Figures 11-13 show that S2 stopped selecting the CA option

for two sessions, returned to exclusive CA selection for 2

sessions, stopped selecting CA for 1 session and then

reverted to exclusive CA selection. Figures 11-13 further

54

show that during the sessions when the CA option was not

selected, other stimuli were selected approximately equally

as often as each other. A closer look at the raw data

revealed that this approximately equal selection of all

stimuli given derived configurations was a function of S2's

selection of the stimulus upon which the cursor appeared on

derived trials. This pattern further suggests that the

exclusive CA selection (and the subsequent selection of any

stimulus upon which the cursor appeared) was a part of

maximization for S2. S2's selection of the "correct"

stimuli on trained conditional discriminations was

unaffected.

S2's eventual return to exclusive CA selection

(beginning with session 23) led to experimental removal of

the CA option as with SI (phase B, Fig. 4). The mouse

cursor was reprogrammed to appear in the center of the

sample - comparison configuration. Figures 11-13 show that

unlike SI, S2 began selecting all of the stimuli about

equally as often as each other. Analyses of the position of

the stimuli selected on each trial revealed that the

apparently equal selection of all stimuli was an artifact

produced by the exclusive selection of Position 1. Again

this pattern of responding was the most efficient as it

required no observing responses with respect to the

positions in which particular stimuli appeared. S2 simply

selected the stimulus that appeared in position 1 on all

55

derived trial types. After 6 sessions with no change in

S2's performance, the subject was given the following

instruction: "If you get all trials correct, you will

receive a total of $2.50 for the session" (cf. Sidman et

al., 1992). This amount was greater than twice the amount

usually earned. Figures 11-13 show that there was no change

in S2's responses for the first session following

instruction delivery. The instruction was repeated in

exactly the same way for every session for the remainder of

the experiment. Figures 4 and 11-13 show that starting with

the second instructed session, S2 began to select the

"correct" stimulus on all original and derived trial types.

S3's performance differed from SI and S2 in a number of

ways. Figure 4 shows that, unlike SI and S2, S3's accuracy

on training trials fluctuated until session 23, at which

point S3 began to select the correct stimulus on greater

than 90% of all training trials for the remainder of the

experiment. More specifically, Figures 20 and 21 show that

the initial drop in accuracy was a function of S3's

responses on 3 of the 6 training trial types - the selection

of B3 given A2 as the sample (middle graph in left column,

Fig. 20), C3 given B2 as the sample (middle graph in left

column, Fig. 21) and CI given B3 as the sample (bottom graph

in left column, Fig. 21).

Returning to Figure 4, notice that, during sessions 5-

9, the "correct" stimulus was selected on 90-100% of all

56

training trials presented before dropping to 65% for session

10. Once again, Figs. 20 & 21 show that this decrease was a

function of S3's selections on only 3 of the 6 training

trial types - the exclusive selection of B2 given A3 (bottom

graph in left column, Fig. 20), C3 given B2 (middle graph in

left column, Fig. 21) and CI and C2 given B3 (bottom graph

in left column, Fig. 21) during sessions 10-15. Following

that, Figure 4 shows that the percent of "correct" training

trials increased steadily until session 19. Figures 20 & 21

show that the slight decreases in percent of correct

training trials seen during sessions 20 and 21 (Fig. 4) was

almost exclusively a function of the selection of B3 given

A2 as sample (middle graph in left column, Fig. 20).

Finally, Figure 4 shows that the percent of correct training

trials increased to and remained at 100% for the remainder

of the experiment.

With respect to the derived trial types, S3's

performance differed from SI and S2 in that S3 rarely

selected the CA option and never demonstrated equivalence.

Figure 4 shows that on transitivity and equivalence probe

trials, S3 selected the "correct" stimulus on 25 - 60% of

trials presented per session throughout the experiment.

With respect to transitivity, Figure 22 shows that the

experimenter designated "correct" stimulus was selected more

often than any other stimulus on only one of the three

transitivity configurations presented (A3-C3, bottom graph

57

in left column, Fig. 22). Interestingly, the stimulus

selected most often, given A1 & A2 as samples in

transitivity configurations, was also C3. It is possible

that the increasing "accuracy" observed on A3-C3 trials was

partly a function of a bias toward the selection of C3 on

transitivity probes.

With respect to equivalence trials, Fig. 22 (right

column) shows that the "correct" stimulus was selected more

often than any other stimulus on only one of the three

equivalence configurations presented (C3-A3, bottom graph in

right column, Fig. 22). Given CI and C2 as samples in

equivalence probes, A3 was selected more often than any

other stimulus in the comparison array.

Figures 17-19 show that, in general, latencies to

selection given transitivity and equivalence configurations

had decreased considerably by the end of session 11. A

close analysis of the bottom two sets of graphs on these

figures reveals that the decreases in latencies for all

three of the equivalence configurations were approximately

correlated with original conditional discrimination

acquisition. The same kinds of correlations are apparent

with two of the three transitivity configurations (A2-C2,

A3-C3).

S3's responses on symmetry trials were particularly

interesting. Figure 4 shows that given symmetry

configurations, the "correct" stimulus was selected on 25-

58

A 1 - B 1

CO I 5

B 1 - C 1

10

-o 1 0 c O f -

o b 0

00 10 c >> 5 o « 10

-4—'

o ^ 5

0

JUL

JliL

B 1 - A 1

B 1 - A 2

B 1 - A 3

B 1 - C A

i Ml » i

I I I I 111 i

lillll 11 ll l l l l l l l l l l lUl^l iitihi

Jh

A 1 - C 1

A 1 - C 2

A 1 - C 3

A 1 - C A

II u Id i

llllih il ill ilill

C 1 - B 1

C 1 - B 2

C 1 - B 3

C 1 - C A

C 1 - A 1

C 1 - A 2

C 1 - A 3

C 1 - C A

0 45 90 135 180 0 45 90 135 180


59









selection.

60

in ~o c o G <D

(J)

O c CD

A 2 - B 2

CO ~o C O O CD

00

O c CD

00 ~o c o o CD

( / )

>N o c 0

0

10

5

10

5

10

5

10

5

0

10

5

10

5

10

5

10

5

0

m *%3ki

h

\k

B 2 - A 2

B 2 - A 1

B 2 - A 3

B 2 - C A

i , i ili il lil

< HI 11 iJ 11» iti

T

A 2 - C 2

A 2 - C 1

A 2 - C 3

A 2 - C A

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0 45 90 135 180 0 45 90 135 180


61









selection.

62

A 3 - B 3 CO

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l i i ! 111

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0 45 90 135 180 0 45 90 135 180

C o n s e c u t i v e T r i a l s C o n s e c u t i v e T r i a l s

63









selection.

64

60% of all trials presented for the first 12 sessions. The

percent of "correct" symmetry trials increased

systematically over sessions 13-25 and remained stable at

over 90% through session 30. Correct responding on symmetry

trials then declined and became more variable, hovering

around 80% across sessions 31-38.

Figures 20 and 21 show that the low accuracy scores

seen in Figure 4 during the first 12 sessions were a

function of S3's responses on 4 of the 6 symmetry trial

types. Figure 20 shows that given B3-A3 trials (bottom

graph in right column, Fig. 20), S3 selected all of the

comparison stimuli (excluding the CA option) in the

comparison array about equally as often for the first 12

sessions. Figure 21 shows that given CI or C2 as samples,

S3 selected B3 more often than any other stimulus in the

comparison array during the first 12 sessions. Finally, the

bottom graph in Figure 21 shows that given C3 as the sample,

S3 selected B2 more often than any other stimulus.

Nevertheless, Figures 20 & 21 show that, by session 20, the

experimenter designated "correct" stimulus was selected more

often than any other stimulus in the comparison array for 5

of the 6 symmetry configurations presented in the

experiment. Figures 17-19 show that decreases in latencies

to selection on symmetry trials followed closely behind

acquisition of the original conditional discrimination for

all 6 training trial configurations. These figures further

65

A 1 - B 1 B 1 - A 1 / A 2 / A 3 / C A

C

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66













67

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80 60 40 20

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180 160 140 120 100 H

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68













69

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C G

(J _cd a) (/) M— o >> o c CD D CT CD

CD >

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180 160 140 120 100

80 60 40 20

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180 160 140 120 100

80 60 40 20

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i i i i r

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70













71

show that acquisition of the original conditional

discriminations was also approximately correlated with an

increase in the frequency with which the "correct" stimulus

was selected for 5 of the 6 symmetry configurations. The

exception was interesting. Given training trial

configurations and B2 as the sample, Figure 21 shows that S3

selected C3 to the exclusion of the experimenter designated

"correct" stimulus between sessions 10 - 17. Notice that,

given symmetry configurations with C3 as the sample, S3

selected B2 to the exclusion of the "correct" stimulus

during the same time period. As mentioned earlier with

respect to S2's data, identification of orderly relations

such as these is not possible with simple percent correct

measures.

S4's performance differed from the other subjects in a

number of ways. Unlike the other subjects, S4 sometimes

selected the CA option on the (prompted) training trials

even though this reduced the total amount of money earned

per session. Additionally, S4's latencies to selection, on

all trial types, frequently exceeded 30 seconds resulting in

sessions that lasted for an hour or more. The combination

of smaller total amounts and longer sessions reduced S4's

overall rate of earning far below that of the other subjects

who almost always earned the total amount possible and spent

approximately 15 minutes (on the average) in the sessions.

Figure 4 shows that the percent of training trials on which

72

S4 selected the "correct" stimulus was variable until the

last 6 sessions of the experiment. Figures 26 and 27 show

that there was no clear pattern of selection of the other

stimuli in the comparison array.

With respect to the derived trial types, Figure 4 shows

that S4 selected the "correct" stimulus on 10 - 40% of all

trials until session 17. Figures 23-25 show that on probe

trials, there was approximately even selection of all

stimuli in the comparison array excepting for the CA option.

Until session 17, the CA option was selected more often than

any other stimulus in the comparison arrays (see Fig. 26-

28). Figures 23-25 also show that the acquisition of

original conditional discriminations was very closely

followed by a general drop in selection latencies for some

trial types. Notice also that the selection of the CA

option ceased immediately although it continued to be

available for the duration of the experiment.

With respect to symmetry configurations, specifically,

Figures 23-25 show that acquisition of

related conditional discriminations closely coincided with

general decreases in selection latencies for all symmetry

trial types. Notice that for 3 of the 6 symmetry

configurations (Bl-Al, Cl-Bl, and C2-B2), acquisition of

related conditional discriminations was also closely

followed by an increase in the frequency with which the

"correct"stimulus was selected. Figures 26 & 27 show that

73

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74









selection.

75

B 2 - C 2 A 2 - B 2

O 10

B 2 - A 2

I hi ih B 2 - A 1

B 2 - A 3

B 2 - C A

A 2 - C 2

I nil

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76









selection.

77

CO ~o c o o <D

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i i r n i 1 r 0 40 80 120 160 0 40 80 120 160


78









selection.

79

S4 began selecting the "correct" stimulus to the exclusion

of all other stimuli given symmetry configurations with B1

(top right graph, Fig. 26), CI (top right graph, Fig. 27)

and C2 (middle right graph, Fig. 27) as samples. Figures 26

& 27 also show that, given the other three symmetry

configurations (with B2, B3, and C3 as samples), S4

continued to select the "correct" stimulus about as often as

other stimuli in the comparison array. The CA option,

however, was no longer selected.

With respect to transitivity and equivalence

configurations, Figures 23-25 (bottom set of graphs) show

that there were general decreases in selection latencies

loosely correlated with acquisition of related conditional

discriminations for all of the transitivity and equivalence

trial types. Notice, however, that there were almost no

changes with respect to the specific stimuli selected.

There were two exceptions - 1) S4 abruptly stopped selecting

the CA option on all derived trial types and 2) she began

selecting C2 when A2 was the sample to the exclusion of all

other stimuli (including the CA option) in the comparison

array (see middle left graph in Fig. 28).

One particularly interesting difference between S4 and

the other subjects' performance was the abrupt appearance of

the original conditional discriminations and the abrupt

cessation of CA selection for all trial types during one

80

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B 3 - A 3 / A 1 / A 2 / C A

0 6 12 18 24 30


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A1 B3

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81













82

B1-C1 C1 —B1/B2 /B3 /CA

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180 160 140 120 100

80 60 40 20

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B 2 - C 2

B 3 - C 3

i \ r C2—B2/B1/B3/CA

i i i i r C 3 - B 3 / B 1 / B 2 / C A


i i i i r

0 6 12 18 24 30


B1 C1

C1 B1

B1 C2

C1 B2

B1 €3

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B2- -C2

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B3 C3

C3 B3

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C3 CA

83













84

A 1 - C 1 C1 — A 1 / A 2 / A 3 / C A

C o V-' u

_CD

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150 -

120 -

90 -

6 0 -

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150 -|

120

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60

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6 12 18 24 30

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1 I T 0 6 12 18 24 30

A1 C1

C1 A1

A1 C2

C1 A2

A1 C3

C1 -A3

A1 CA

C1 CA


85













86

session (session 17). Prior to the beginning of session 17,

S4 informed the experimenter that she no longer had access

to personal transportation and that she would be relying on

her family members to bring her to the sessions. She also

asked if her "ride" could wait in the lobby while she

participated in the experiment. It is quite likely that

this situation exerted some control over the latencies to

selection with respect to all trial types. Particularly, it

appears to have resulted in S4's not waiting for the prompt

before selecting a conparison stimulus on the training

trials and not selecting the CA option on the derived

trials.

The preceding section described each subject's

performance in some detail. The following section will

compare subjects' performances and identify some patterns.

First, only 2 of the 4 subjects' (SI & S2) performance could

be said to be indicative of equivalence class formation.

Performances of SI & S2 were comparable in several respects.

Notice that, for both subjects, accuracy of responses on the

derived trial types started out low, soon increased to above

60% correct, and then gradually decreased to between 0 - 10%

correct by the 10th session. Also notice that for both

subjects, this decrease in accuracy was a function of the

exclusive selection of the CA option given derived trial-

type configurations of stimuli. Note additionally, the

increase and then decrease in "correct" responding on probe

87

trial types was most pronounced for symmetry trials for both

subjects. It is apparent, however, with respect to the

accuracy of responses on all derived relations for SI. It

is also apparent for 2 of the 3 derived relations for S2.

Another interesting similarity between SI and S2 was

the transition to exclusive CA selection following original

conditional discrimination acquisition. Notice that, for

both subjects, derived trial configurations reliably

occasioned the selection of the CA option. Notice

additionally that for both subjects, responding indicative

of equivalence class formation began occurring abruptly.

For SI, the abrupt change in the stimuli selected beginning

with the first session in which the CA option was no longer

available. For S2, the abrupt change was observed during

the second instructed session (the CA option was not

available).

S3 & S4's performances were also similar to each

others'. Notice that these two subjects' selections of the

"correct" stimulus on the training trials were considerably

more variable than SI or S2. Notice also that both

subjects' performances on derived trial types fluctuated

around chance levels of accuracy for the first 5 - 6

sessions. S3's accuracy on transitive and equivalence trial

types increased slightly over the next 5-6 sessions and

began fluctuating around 40 - 50% correct. S4's accuracy on

transitive and equivalence trials remained at around chance

88

levels until session 15. For both subjects, percent of

"correct" trials was highest on symmetry trial types (see

Fig. 4, bottom two graphs).

For all subjects, selection of the experimenter

designated "correct" stimulus occurred most often on

symmetry trial types. Figures 29, 30, 31, and 32 show that

of the 12 derived configurations of stimuli presented (2

symmetry, 1 transitivity and 1 equivalence per class for 3

classes (A1-B1-C1, A2-B2-C2, A3-B3-C3)), the cumulative

frequency of "correct" selections was highest for 5 of the 6

symmetry trials for SI, 6 out of 6 for S2, 5 out of 6 for S3

and 3 out of 6 for S4. In most cases, the cumulative

frequencies of "correct" stimulus selection were highest for

symmetry configurations followed by transitivity and

equivalence configurations in that order.

Finally, notice that for all subjects, acquisition of

the original conditional discriminations coincided with

changes in the features of the selection responses on

derived trial types for all subjects. There was, for

example, a general decrease in selection latencies on almost

all derived trial types for all subjects following

acquisition of the original conditional

discriminations. More importantly, there were also some

systematic changes with respect to the selection of

particular stimuli and the conditions under which they were

selected. S3, for example, began to select the "correct"

45

30

89

15

c _o o

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ID M— o >N u c 0 Z5 cr 0

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9 12 15 18 21

12 15 18 21

Symmetrical choices

Transitive choices

• 'Equivalence' choices

15 -

0 I i I i i i i

0 3 6 9 12 15 18 21

Consecut ive Sessions

90

Fig. 29: SI - Cumulative frequencies of selection of the

designated "correct" stimuli for each of the three

arbitrarily arranged classes: A1-B1-C1 (top graph), A2-B2-C2

(middle graph) and A3-B3-C3 (bottom graph) are presented.

The phase change lines are explained in the text.

91

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92

Fig. 30: S2 - Cumulative frequencies of selection of the





93

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94






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96






97

stimulus more often than any other stimulus in the

comparison array following original conditional

discrimination acquisition (see Figs. 17-19) on 5 of the 6

symmetry trial types (Bl-Al, Cl-Bl, B2-A2, C2-B2 and B3-A3).

SI and S2 began to select the CA option exclusively on all

derived trial types after original conditional

discrimination acquisition. Figures 5-7 (SI) and 11-13 (S2)

further show that the latencies to selection of CA on

derived trial types were quite low. Finally, recall that SI

and S2 selected the "correct" stimulus on all training trial

types during the same time period. The combination of

exclusive CA selection on derived trial types, the low

latencies to selection and the consistent selection of the

experimenter designated "correct" stimuli on all training

trial types during the same time period suggests that SI and

S2's selection responses had come under control of the

entire configuration of stimuli on the screen rather than

particular relations (or the lack thereof) between

particular sample and comparison stimuli. In other words,

derived trial types, regardless of the particular trial,

reliably occasioned CA selection while training trial types,

regardless of the particular trial, reliably occasioned the

selection of the "correct" stimuli.

CHAPTER IV

DISCUSSION

This section will address some of the implications of

the data described in the results section. Following that,

some broader issues will be discussed which do not derive

directly from the data but are appropriately discussed in

their context. To restate, the questions of interest in

this experiment were: 1) What is the effect of original

conditional discrimination acquisition on the occurrence of

untrained conditional discriminations? and 2) What is the

role of the training and testing configurations on the

occurrence of these conditional discriminations?

With respect to the first question, the data presented

above show that original conditional discrimination

acquisition, for all subjects, was coincident with changes

in the particular stimuli selected on derived trials and the

latency to the occurrence of those selections. Si and S2,

for example, reliably began selecting the CA option on

derived trial types while selecting the experimenter

designated "correct" stimulus on all training trial types.

S3 began to select the "correct" stimulus more often than

any other on 5 of the 6 symmetry trial types presented. For

all subjects, a general decrease in latency was observed on

99

derived trial types coincident with original conditional

discrimination acquisition.

Notice, however, that original conditional

discrimination acquisition was not coincident with

"equivalence class formation" for any of the four subjects.

Subjects 1 and 2 began to respond in ways consistent with

the predictions made by the experimenter on the basis of the

trained conditional discriminations only after the CA option

was removed (SI) or after additional instructions were given

(S2). The ease with which derived relational responding is

observed with adult human repertoires (see any sample of

existing stimulus equivalence literature) and the fact that

it was not observed with any of the subjects in the current

experiment is interesting. It is possible that the

availability of all trial types from the beginning of the

experiment and/or the availability of the Can't Answer

option played a critical role. Some implications of these

possibilities will be discussed later.

With respect to the second question, recall that SI

and S2 began selecting the CA option exclusively on all

derived trial types while selecting the experimenter

designated "correct" stimulus on all training trial types.

The combination of exclusive CA selection on all derived

configurations, the low latencies to selection, and

selection of the "correct" stimuli on training trials

suggests that SI and S2's selections had come under control

100

of the entire configuration of stimuli rather than the lack

of specific stimulus-stimulus relations. This point is

further supported by the fact that selections indicative of

equivalence relations among stimuli began occurring

immediately after the removal of the CA option for SI. S2's

performance was similarly relevant in this regard in terms

of the abrupt appearance of responding indicative of

equivalence relations. The reader should recall that the

change in S2's performance was not seen following the

removal of CA but after instructions with respect to his

performance in the task were given.

It would appear that the current preparation is not

very effective in terms of arranging conditions which

occasion conditional discriminations that are said to be

indicative of equivalence class formation. As mentioned

earlier, it is quite possible that the availability of the

CA option arranged conditions under which the most efficient

response was to select CA. Presenting all trial types from

the beginning of the experiment might also have exerted some

control over the functions of the stimuli involved in the

trials which accounted for the occurrence of un-predicted

conditional discriminations.

Notice that the above statements describe (as opposed

to explain) the observed patterns of responding. It is

suggested that the determination of 1) whether the

conditions described immediately above were responsible for

101

the non-occurrence of derived conditional discriminations

and if they were, 2) what it was about the presentations

that accounts for the non-occurrence would help our

understanding of the processes involved in stimulus

equivalence. In other words, determining the exact nature

of the (possibly) limiting conditions described above would

enhance our understanding of stimulus equivalence. Notice,

finally, that the above questions are empirical in nature.

There are several important aspects of this preparation

that need to understood in more detail. The CA option, for

example, was observed to be critical with at least 2 of the

4 subjects used in this experiment. For SI and S2, the CA

option appeared to provide an opportunity to maximize

overall rate of reinforcement. This opportunity could be

directly manipulated by changing the response

Although the preceding section has identified some

important weaknesses with the current preparation, there are

some important benefits. These will be discussed next. A

possible implication of these findings is that the current

concerns with identifying S+ or S- control (exerted by the

comparison stimuli) might be slightly misplaced. It is

quite possible that the selection responses of interest are

not under exclusive S+ gr S- control but under multiple (S+

and S-) control. That is, it is possible that the selection

of B1 is not only under control of the discriminative (S+)

function of B1 in the presence of A1 but also under S-

102

control of the other stimuli in the comparison array. This,

it seems, is consistent with the way we identify sources of

control in any complex environment. Notice that whether or

not this suggestion has any merit is, ultimately, an

empirical question. It is suggested, however, that the

preparation employed here may be more useful than

traditional preparations in terms of our abilities to ask

and answer such questions.

One of the reasons for the concern with identifying the

nature of the control as S+ or S- may derive from the use of

percent of correct trials as the dependent measure. Notice

that "percent correct" is a measure of the subject's

performance in terms of the conditional discriminations

predicted by or of interest to the experimenter. Another

way of saying this is that percent correct, as it is

typically defined, is a measure of S+ control only. From

this perspective, orderly patterns in the data are

identified only in terms of the accuracy of the responses as

defined by the experimenter. Any other orderly relations

are obscured. The alternative in this experiment was to

measure every selection response regardless of whether or

not it would be predicted by the experimenter. This

strategy allows the identification of orderly relations in

the data that are obscured by the percent correct measure.

In other words, orderly relations can be measured not only

in terms of accuracy of responses but also in terms of the

103

subject's interactions with all trial types. There are some

important benefits to be gained from this alternative.

Recall, for example, that S3's increasing accuracy on A3-C3

(transitivity) trials was actually found to be a function of

a bias with respect to the selection of C3 given

transitivity configurations. The same pattern is apparent

with respect to S3's performance on C3-A3 (equivalence)

trials (i.e., a bias toward the selection of A3 given

equivalence configurations). Recall that this pattern is

also evident with respect to SI and S2's performance on

equivalence trial types. The percent correct measure does

not allow for the identification of these kinds of orderly

relations.

Another methodological benefit of this preparation

derives from the ability to relate subjects' performances on

derived trial types with their performances on training

trial types. The presentation of derived trial types from

the beginning allows us, in effect, to obtain baseline

measures of the responses of interest. Consideration of the

presentation of all derived trial types from the beginning

as baseline measures can be clarified in the following way.

Suppose that we presented the subjects with a series of

derived trial types before any training was conducted, then

presented training trials (consequated) for 5 sessions, re-

presented the derived trial types for 1 session and so on

until responses indicative of equivalence class formation

104

were observed. We would have no problem, in this context,

characterizing the first presentation (and possibly

subsequent presentations) of derived trial types as measures

of baseline performance. The continuous presentation of

derived trial types, then, is simply one end of a continuum

upon which this sort of strategy lies.

At a more general level, there are some important

problems that need to be addressed with respect to stimulus

equivalence. Pilgrim (1993) observed that "[i]n numerous

demonstration studies, no true independent variable is

manipulated and tests of untrained stimulus relations may

seem to be designed more to reveal underlying processes then

to evaluate functional relations responsible for the

observed structure " (p. 478). It is possible that the

methodological features of current stimulus equivalence

research have led to conceptual problems upon which Pilgrim

(1993) comments. Whether or not that is true, there are

some important problems with the way we have traditionally

talked and continue to talk about stimulus equivalence.

The problem, in general, is the working assumption that

particular combinations of experimental and pre-experimental

histories cause stimuli to become related in a class and

post-hoc tests can then document the existence of such

classes. More consistent with a behavior analytic

perspective is to say that the subjects' performance in

match-to-sample tasks are instantiations of the relations

105

and not indications of the existence of those relations.

This is analogous to the way we talk about operant classes.

The occurrence of a response does not indicate the existence

of an operant class, rather it is an instance of the

operant. It is suggested that, in precisely the same way,

equivalence classes do not exist independently of the

conditional discriminations said to indicate their

existence. Accurate conditional discriminations on probe

trials do not document the (presumably previous) existence

of "stimulus-stimulus relations" - called equivalence

classes -- rather they are instances of "equivalencing".

From this perspective, attempts to identify the

variables that control the occurrence of the "instance" are

the only relevant concerns for a behavioral analysis.

Traditional preparations, especially the use of percent

correct measures, explicitly ignore the local variables that

may effect the occurrence of these instances of

"equivalencing". It is suggested that this preparation

allows a more dynamic approach to the understanding of

what we call stimulus equivalence and is consistent with our

fundamentally unique approach to our subject matter.

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