JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

COMPOUND STIMULI IN EMERGENT STIMULUS RELATIONS:EXTENDING THE SCOPE OF STIMULUS EQUIVALENCE

MICHAEL R. MARKHAM AND MICHAEL J. DOUGHER

UNIVERSITY OF NEW MEXICO

Three experiments were conducted to investigate stimulus relations that might emerge when collegestudents are taught relations between compound sample stimuli and unitary comparison stimuli usingmatch-to-sample procedures. In Experiment 1, subjects were taught nine AB-C stimulus relations,then tested for the emergence of 18 AC-B and BC-A relations. All subjects showed the emergence ofall tested relations. Twelve subjects participated in Experiment 2. Six subjects were taught nine AB-Crelations and were then tested for symmetrical (C-AB) relations. Six subjects were taught nine AB-Cand three C-D relations and were then tested for nine AB-D (transitive) relations. Five of 6 subjectsdemonstrated the emergence of symmetrical relations, and 6 subjects showed the emergence of tran-sitivity. In Experiment 3, 5 college students were taught nine AB-C and three C-D relations andwere then tested for nine equivalence (D-AB) relations and 18 AD-B and BD-A relations. Threesubjects demonstrated all tested relations. One subject demonstrated the AD-B and BD-A relationsbut not the D-AB relations. One subject did not respond systematically during testing. The results ofthese experiments extend stimulus equivalence research to more complex cases.Key words: stimulus equivalence, compound stimuli, hierarchical stimulus control, stimulus sets,

stimulus interchangeability, key press, humans

Stimulus equivalence is defined as the emer-gence of a specific set of untrained stimulusrelations (reflexivity, symmetry, and transitiv-ity) when humans are taught a number ofinterrelated conditional discriminations (Sid-man & Tailby, 1982). This area of researchhas attracted much attention lately becausestimulus equivalence provides a frameworkfrom which one can begin to understand someaspects of complex human behavior. In par-ticular, the formation of stimulus equivalenceclasses may be important for accounts of sym-bolic behavior (e.g., Hayes, 1990), language(e.g., Devany, Hayes, & Nelson, 1986; Green,Sigurdardottir, & Saunders, 1991; Sidman,1986), and humans' ability to respond appro-priately in new situations (e.g., Sidman &Tailby, 1982; Spradlin & Saunders, 1984).Further, research has demonstrated that stim-uli can acquire a number of functions simply

Portions of this paper were presented at the annualconvention of the Association for Behavior Analysis, At-lanta, May, 1991, and the 15th Symposium on Quanti-tative Analyses of Behavior: Stimulus Relations, Cam-bridge, Massachusetts, June, 1992. Special thanks to RobertStromer and Richard Saunders for their many helpfulcomments on earlier versions of this paper. During thisstudy, Michael Markham was supported by a Ford Foun-dation predoctoral fellowship. Reprint requests should besent to Michael R. Markham, Department of Psychology,Logan Hall, University of New Mexico, Albuquerque,New Mexico 87131.

by virtue of their membership in equivalenceclasses (Gatch & Osborne, 1989; Green et al.,1991; Hayes, Kohlenberg, & Hayes, 1991;Kohlenberg, Hayes, & Hayes, 1991; Lazar,1977; Lazar & Kotlarchyk, 1986; Wulfert &Hayes, 1988).To date, research on stimulus equivalence

has been largely restricted to an analysis ofdyadic relations among unitary stimuli. Twoexceptions are studies by Stromer and Stromer(1990a, 1990b), who used complex samplestimuli in arbitrary match-to-sample trainingprocedures. In the first study, they taught re-lations of the form AB-D and AC-E, thentested for emergent relations among all pos-sible pairs of single stimuli (e.g., A-B, D-B,B-C, B-E, and D-E). These emergent rela-tions were demonstrated in 14 of 18 subjects.In the second study, they trained the relationsA-C, B-D, and AB-E, then tested for relationsamong all possible pairs of single stimuli (e.g.,A-D, B-C, C-E, and D-E). These relationswere demonstrated in 13 of 14 subjects. Theresults of these studies showed that humansubjects can learn conditional discriminationsusing compound sample stimuli and respondin systematic ways in testing to elements of thecompound samples used in training. However,these studies investigated only the emergenceof symmetrical and transitive relations whensubjects were trained to match unitary com-parisons to compound samples. Given suitable

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1993, 60, 529-542 NUMBER 3 (NOVEMBER)

MICHAEL R. MARKHAM and MICHAEL J. DOUGHER

Fig. 1. Stimuli used in Experiment 1.

training procedures, it should be possible totest for additional emergent relations aftertraining subjects to match unitary comparisonsto compound samples. The present study wasdesigned to test this possibility.

In the present experiments, we trained sub-jects to match unitary comparisons to com-

pound sample stimuli. Specifically, nine re-

lations of the form AB-C were trained. Thispermits the emergence of nine AC-B relationsand nine BC-A relations. If subjects were todemonstrate these emergent relations, it wouldextend the range of stimulus relations shownto emerge in stimulus equivalence research. Inaddition, it would raise interesting questionsabout the nature of the stimulus control op-erating in these experimental arrangements.

EXPERIMENT 1METHOD

SubjectsSubjects were 11 undergraduates (6 females

and 5 males, aged 18 to 24 years) enrolled inintroductory psychology courses at the Uni-versity of New Mexico. They were recruitedthrough in-class and bulletin board announce-ments. They received course credit for theirparticipation. At the beginning of the exper-iment, the general procedures were explainedto the subjects, and they read and signed a

statement of informed consent. After complet-ing the experiment, subjects were fully de-briefed. All procedures were approved by theHuman Research Review Committee of theUniversity of New Mexico.

Apparatus and StimuliAn IBMs personal computer with a 19-cm

monochrome (green on black) display was usedto present stimuli and record data during theexperiment. Each subject was seated before thepersonal computer in a small experiment roomwith a two-way mirror for observation of thesubject.The stimuli were nine abstract forms des-

ignated randomly for each subject as Al, B1,Cl, A2, B2, C2, A3, B3, and C3 (see Figure1). The alphanumeric designations are forpurposes of description only and were nevershown to the subjects. Each stimulus occupieda 4-cm by 5-cm space on the display.

ProcedureNine conditional discriminations involving

compound samples and unitary comparisonswere trained, and 18 emergent relations weretested. Both training and testing used arbitrarymatch-to-sample procedures. The compoundsample appeared at the top center of the screen,followed 2 s later by the three comparisons atthe bottom right, bottom left, and bottom cen-ter of the screen. Compound samples were pairsof stimuli presented side by side on the screen.The elements comprising the sample com-pounds were randomly assigned to the left andright positions for each trial. For each trial,the comparisons were randomly assigned to theleft, middle, or right position at the bottom ofthe screen. The subject selected one of the com-parisons by pressing the "1," "2," or "3" keyon the computer keyboard to select the left,middle, or right comparison, respectively. Af-ter a key was pressed, the screen cleared and,during training, responses to the correct com-parison produced the word "correct" on themonitor, and other choices produced the word"wrong." The screen cleared again after a 5-sdelay. After a 2-s intertrial interval, a newtrial began. Once the subject met the trainingcriterion, feedback was gradually faded over20 trials (e.g., Correc., Corr............. . . . . . ) to reduce the discriminability be-tween training and testing. During testing, nofeedback appeared.

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TRAINED RELATIONS

Al Bi AIB2 Al B3

C1 C3 C

A2 BI A2 B2 A2 B3

3 2 Ci

A3 Bl A3 B2 A3 B3

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EMERGENT RELATIONS

Fig. 2. Relations trained in Experiment 1 (left) and two examples of possibly emergent relations that exemplifythe type tested in the experiment (in box on right).

Subjects were given the following instruc-tions to read:When the experiment begins, you will see setsof symbols appear on the screen. They willappear at the top of the screen, and at thebottom of the screen on the left, middle, andright. Your task is to choose the correct symbolat the bottom of the screen by pressing the "1,""2," or "3" key on the keyboard to select theleft, middle, or right symbol. Early in the ex-periment you will get feedback on every choice.Later in the experiment you will not get feed-back every time. However, there is always acorrect answer. During the first part of theexperiment the task will be easy, and it is tempt-ing not to pay attention. However, the exper-iment will increase in difficulty, and choosingthe correct symbols in the latter parts of theexperiment will depend on the knowledge yougain during the early parts of the experiment.To prevent impulsive responding, the computerwill not accept choices for one second after thesymbols appear. Do you have any questions?

After reading the instructions, the subject wasasked to explain the instructions to the exper-imenter. If unable to do so, he or she wasrequired to read the instructions again untilhe or she was able to explain the instructions.After mastering the instructions, the subjectbegan the experiment.The nine AB-C relations shown in Figure

2 were trained until the subject reached atraining criterion of 98 correct out of 100 con-

secutive trials. On all training trials, the com-parison stimuli were Cl, C2, and C3. Thenine baseline AB-C relations were such thatno stimulus was associated exclusively withany other stimulus. Thus, this design pre-vented subjects from responding correctly basedupon only one element of the compound sam-ples. For example, if a subject were to respondcorrectly to the training relation Al Bl-Clbased upon only the presence of B1, then hisor her response to the trial A2B1-C3 wouldnecessarily be incorrect, because control by B1would in this case require a response to C1.The baseline relations were presented in

blocks of nine trial types, each consisting ofone compound sample and its appropriatecomparison array. Within each block of train-ing trials, trial types were presented in a ran-dom order. Once these baseline relations wereestablished, we tested subjects for nine AC-Band nine BC-A relations. The trial types forthese tests are shown in Table 1.

During testing, 20 blocks of these 18 trialtypes were presented. Within each block, trialtypes were presented in a random order. Aswas the case in training, responding only toelements of the stimulus compounds wouldnecessarily lead to a majority of incorrect re-sponses. For example, if a subject's choice ofBi in the presence of AlCl were controlledby Cl alone, then the subject would also selectBI in the presence of A2C1, which is an in-

Al C2 B3C2

B3 AlAC-B & BC-A Relations: 18 total

(2 from each trained relation)

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MICHAEL R. MARKHAM and MICHAEL J. DOUGHER

Table 1

Trial types presented during testing in Experiment 1.

Comparisons

Sample Correct Incorrect Incorrect

AlCl B1 B2 B3BlCl Al A2 A3A1C3 B2 Bl B3B2C3 Al A2 A3A1C2 B3 B1 B2B3C2 Al A2 A3A2C3 BR B2 B3B1C3 A2 Al A3A2C2 B2 BR B3B2C2 A2 Al A3A2C1 B3 BR B2B3C1 A2 Al A3A3C2 Bl B2 B3BIC2 A3 Al A2A3CI B2 BR B3B2C1 A3 Al A2A3C3 B3 BR B2B3C3 A3 Al A2

correct selection (see Table 1). Thus, correctresponding during testing must be controlledby both elements of the sample in conjunctionwith the correct comparison.The experiment ended when subjects com-

pleted the testing phase of the experiment. Allsessions were limited to 4 hr in duration.

RESULTS AND DISCUSSIONExcept for Subjects LF, LC, and BB, who

required two sessions, all of the subjects com-

pleted the experiment in one session. Numberof training trials required to reach criterionand time required to reach criterion are shownin Table 2. Test data for all subjects, graphedas percentage of trials correct over 18-trialblocks, are shown in Figures 3 and 4. All sub-jects maintained a high level of accuracy

throughout testing. Subject BB terminated theexperiment after completing seven blocks oftesting trials (126 trials), but performed atnear-perfect accuracy during the completed testtrials. These results show that all 11 subjectsclearly showed the emergence of AC-B andBC-A relations.

Although these results suggest the emer-

gence of previously unreported relations amongstimuli, at least two questions arise. The firstis whether equivalence relations also emergedfrom these experimental arrangements. The

Table 2

Number of trials and time (in hours and minutes) requiredto reach training criterion in Experiment 1.

Training TrainingSubject time trials

BB 2:14 7931:28 566

DW 0:49 324GM 0:32 213JD 1:08 448LC 3:11 1,009

0:27 174LF 2:38 1,031

0:21 150LP 1:11 518RG 1:30 620SK 1:17 378TC 1:09 422TT 1:55 653

second is whether these results could be ex-plained by simple (rather than conditional)stimulus control. It is possible that the subjectswere responding to nine different ABC stim-ulus compounds as individual discriminativestimuli rather than the AB compound samplesexerting conditional control over the discrim-inative functions of the C comparisons. Thus,the results of Experiment 1 may have resultedfrom simple discriminative control by the nineABC compounds that were simply spatiallyrearranged. This interpretation of the resultsis analogous to that suggested by Bush, Sid-man, and DeRose (1989) and Lynch and Green(1991) in response to the issue of whether Bushet al. had demonstrated contextual (higher or-der) control of equivalence classes. These in-vestigators have argued that the test for con-ditional or higher order stimulus control is thedemonstration of the independent functions ofthe putative conditional and discriminativestimuli. Experiment 2 was designed to addressboth issues.We reasoned that if symmetry and transi-

tivity emerge from the baseline conditional dis-criminations established using the proceduresof Experiment 1, it could be argued that stim-ulus equivalence does result from these pro-cedures. Moreover, the emergence of transitiverelations would demonstrate that conditionalstimulus control can result from these proce-dures.

EMERGENT STIMULUS RELATIONS

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EXPERIMENT 2Two groups of subjects participated in Ex-

periment 2. One group was taught the nineAB-C relations described in Experiment 1 andwas tested for nine symmetrical (C-AB) re-lations. The other group received the same

training, with the addition of three C-D re-

lations, and was then tested for the emergenceof nine transitive (AB-D) relations.

METHODSubjects and Apparatus

Twelve undergraduates, recruited and com-

pensated as described in Experiment 1, par-

ticipated in the experiment. Six of these sub-jects (4 females and 2 males, 20 to 23 yearsold) were assigned to the symmetry group, and6 (3 females and 3 males, 19 to 27 years old)were assigned to the transitivity group. Theapparatus and setting were the same as inExperiment 1 with the addition of three stim-uli designated as D1, D2, and D3 (see Figure5).

ProcedureThe general procedures were the same as

in Experiment 1. Subjects in the symmetrygroup were taught the nine AB-C relations

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shown in Figure 6. Subjects in the transitivitygroup were taught the same nine AB-C re-lations and three CD relations (Cl Dl, C2D2,and C3D3; see Figure 6). For CD trainingtrials, the sample (Cl, C2, or C3) appearedat the top center of the screen and the com-parisons were always Dl, D2, and D3. Train-

Fig. 5. Additional stimuli used for Experiment 2.

18-TRIAL BLOCKS18 over 18-trial blocks for 5 subjects during the testing phase of Experi-

ing for all subjects continued until they reacheda criterion of 70 of 72 consecutive trials correct.

Subjects in the symmetry group were thentested for nine symmetrical C-AB relations.These nine trial types are shown in Table 3.Subjects in the transitivity group were testedfor nine transitive AB-D relations. The trialtypes used for transitivity tests are also shownin Table 3. All subjects received 30 blocks ofnine trials each during testing, for a total of270 trials.

RESULTS AND DISCUSSIONNumber of training trials to criterion is

shown for subjects in both groups in Table 4.Test data for subjects in the symmetry group,graphed as percentage of trials correct over

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EMERGENT STIMULUS RELATIONS 535

TRAINED RELATIONS

AIBi A1 B2 AI B3

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A3 B1 A3 B2 A3B3 A1 B3 D24 ~~~~~~~~~~~~Symmetrical Transitive

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Fig. 6. Relations trained in Experiment 2 (left) and examples of tests for symmetry and transitivity (box at right)that occurred following training.

nine trial blocks, are shown in Figure 7. Fivesubjects (RV, MH, LP, ME, and MB) main-tained near-perfect performance throughouttesting. Subject GP responded at chance ac-

curacy for 219 trials, then terminated the ex-

periment. Thus, 5 of 6 subjects clearly dem-onstrated the emergence of symmetrical C-ABrelations.

Test data for subjects in the transitivitygroup, graphed as percentage of trials correctover nine trial blocks, are shown in Figure 8.With the exception of Subject DY, all subjectsmaintained near-perfect accuracy during mostof testing. Subject DY performed at 44.4%(four of nine) and 88.8% (eight of nine) ac-

curacy for Trial Blocks 1 and 2, respectively,then maintained near-perfect performanceduring the rest of the experiment. Subject DFmaintained high levels of accuracy during test-ing, but terminated the experiment after com-pleting 26 blocks of testing trials. These resultsclearly show the emergence of transitive AB-Drelations in all subjects.The results of this experiment indicate that

symmetry and transitivity emerged from con-ditional discrimination training using com-pound samples and unitary comparisons. These

Table 3

Trial types presented during testing in Experiment 2.

Comparisons

Sample Correct Incorrect Incorrect

Symmetry testsC1 AlBl A2B2 A3B3C3 A1B2 A2B3 A3B1C2 AMB3 A2B1 A3B2C3 A2B1 AMB3 A3B2C2 A2B2 AlBl A3B3C1 A2B3 A1B2 A3B1C2 A3B1 A1B2 A2B3C1 A3B2 AMB3 A2B1C3 A3B3 AlBl A2B2

Transitivity testsAlBl Dl D2 D3A1B2 D3 Dl D2AMB3 D2 Dl D3A2B1 D3 Dl D2A2B2 D2 Dl D3A2B3 Dl D2 D3A3B1 D2 Dl D3A3B2 Dl D2 D3A3B3 D3 Dl D2

MICHAEL R. MARKHAM and MICHAEL J. DOUGHER

Table 4Number of trials required to reach training criterion inExperiment 2.

TrainingSubject trials

Symmetry groupGP 219PB 245MB 390ME 221MH 238RV 273

Transitivity groupDF 592DY 648ES 182SL 252RC 766PM 213

findings show that the conditional discrimi-nation training used in Experiment 1 can leadto the emergence of stimulus equivalence aswell as those relations obtained in Experiment1. Thus, the relations that can emerge fromconditional discrimination arrangements do notappear to be restricted to reflexivity, symme-try, and transitivity. Moreover, the results ofthe transitivity tests in this experiment supportthe conclusion that the baseline relationstrained in Experiment 1 met the conditions ofconditional stimulus control as outlined by Sid-man (1986). That is, subjects' responses onthese test trials showed that the AB compoundsdid, in fact, control choices of the appropriateD stimuli. Because the D stimuli had neverbefore been associated directly with the ABcompounds, there was no opportunity for thestimuli to act as unitary ABD compounds that

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9-TRIAL BLOCKSFig. 8. Percentage of choices consistent with transitive stimulus control during nine-trial test blocks for the other

6 subjects in Experiment 2.

could then exert simple discriminative controlover the subjects' behavior.

Figure 9 presents additional stimulus re-lations that may be derived from conditionaldiscrimination training with compound sam-ples and unitary comparisons. In Experiment3, we tested for these equivalence (D-AB) re-lations, as well as AD-B and BD-A relations.We chose these relations for two reasons. First,they would extend the range of demonstratedderived relations that are possible with thesetraining procedures. Second, they would pro-vide more convincing evidence that the emer-

gent relations are not the result of simple dis-criminative control. The logic here is thatbecause the D stimuli have never before beenassociated with the AB compounds before test-ing, and the D stimuli now function as samplestimuli or elements of sample compounds, itis not possible to explain the emergence ofthese relations in terms of simple discrimina-tive control. This is the same logic that applies

to tests for stimulus equivalence using unitarystimuli (e.g., Lynch & Green, 1991). Althoughthis cannot demonstrate conclusively that therelations obtained in Experiment 1 were a re-sult of conditional stimulus control, it lendssome support to this possibility.

EXPERIMENT 3Experiment 3 tested for the emergence of

equivalence (D-AB) as well as AD-B andBD-A relations after subjects were taught nineAB-C and three C-D relations.

METHODSubjects and Apparatus

Five subjects (1 female and 4 males, 20 to22 years old), recruited and compensated as

described in Experiments 1 and 2, participatedin the experiment. The apparatus and settingwere identical to those in Experiment 2.

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MICHAEL R. MARKHAM and MICHAEL J. DOUGHER

TRAINED RELATIONSAl Bi A1 B2 A1 B3

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A2 Bl A2 B2 A2 B3

24

A3 B1 A3 B2 A3 B3

C1 C2 03

D1 D2 D3

EMERGENT RELATIONS

Fig. 9. Relations trained in Experiment 3 (left) and examples of the types of potentially emergent relations testedfor (box at right).

ProcedureThe general procedure was the same as the

procedures used in Experiments 1 and 2. Sub-jects were taught the nine AB-C relationsshown in Figure 9 and three C-D relations(ClDl, C2D2, and C3D3). These relationswere presented in randomized blocks of 12trials each until subjects met a criterion of 70of 72 consecutive trials correct. Testing wasconducted in two phases. Subjects were firsttested for the emergence of nine D-AB rela-tions. The trial types used to test for theserelations are shown in Table 5. Ten blocks ofthese nine trial types were presented. Subjectswere then tested for the emergence of nineAD-B and nine DB-A relations. The trial typesused for these tests are also shown in Table 5.Subjects completed 10 blocks of these 18 trialtypes. Thus, subjects experienced a total of 270test trials.

RESULTS AND DISCUSSIONNumber of training trials required to reach

criterion is shown for all subjects in Table 6.Test data for all subjects, graphed as percent-age of trials correct over 9- or 18-trial blocks,are shown in Figure 10. Three subjects (JC,

ET, and JF) clearly demonstrated the emer-gence of both equivalence (D-AB) and AD-Band BD-A relations. One subject (WR) didnot demonstrate equivalence, but showed in-dications of the emergence ofAD-B and BD-Arelations. Finally, 1 subject (AS) responded atabout chance accuracy throughout tests forequivalence and AD-B and BD-A relations.

These results demonstrate the emergence ofextraordinarily complex relations from com-pound-sample conditional discrimination pro-cedures. Moreover, the results suggest thatthese emergent relations, as well as those fromExperiments 1 and 2, cannot be explained bysimple discriminative control by unitary com-pound stimuli. During test trials, subjectsdemonstrated AD-B and BD-A relations, al-though training trials were never conductedwith AB and D stimuli present on the sametrial. It appears, then, that the samples exertedconditional control over the subjects' behavior,at least as defined by Sidman (1986).

GENERAL DISCUSSIONThe experiments described here examined

emergent stimulus relations involving com-

EMERGENT STIMULUS RELATIONS

Table 5

Trial types presented during testing in Experiment 3.

Comparisons

Sample Correct Incorrect Incorrect

Equivalence testsDl AlBl A2B2 A3B3D3 A1B2 A2B3 A3B1D2 AlB3 A2B1 A3B2D3 A2B1 A1B3 A3B2D2 A2B2 AlBl A3B3Dl A2B3 A1B2 A3B1D2 A3B1 AlB2 A2B3Dl A3B2 A1B3 A2B1D3 A3B3 AlBl A2B2

AD-B and BD-A testsAlDl B1 B2 B3BlDl Al A2 A3A1D3 B2 Bi B3B2D3 Al A2 A3AID2 B3 Bi B2B3D2 Al A2 A3A2D3 BI B2 B3B1D3 A2 Al A3A2D2 B2 B1 B3B2D2 A2 Al A3A2D1 B3 Bl B2B3D1 A2 Al A3

A3D2 B1 B2 B3B1D2 A3 Al A2A3D1 B2 Bi B3B2D1 A3 Al A2A3D3 B3 Bi B2B3D3 A3 Al A2

pound stimuli. In Experiment 1, subjects weretaught nine AB-C relations and were thentested for nine AC-B relations and nine BC-Arelations. Although the pattern of results across

all subjects was consistent and clearly sug-gested the emergence of previously unreportedrelations, stimulus equivalence was not ex-

amined, and the possibility remained that thebaseline relations were under simple discrim-inative rather than conditional control. Ex-periment 2 was designed to address these is-sues.

Two groups of subjects participated in Ex-periment 2. Subjects in the symmetry groupwere taught nine AB-C relations and werethen tested for nine symmetrical (C-AB) re-

lations. Subjects in the transitivity group were

taught nine AB-C relations and three C-Drelations and were then tested for nine tran-sitive (AB-D) relations. Five of the 6 subjectsin the symmetry group clearly showed theemergence of symmetrical stimulus control. All

Table 6Number of trials required to reach training criterion inExperiment 3.

TrainingSubject trials

AS 430ET 798JC 349JF 593WR 288

6 subjects in the transitivity group showed theemergence of transitive stimulus control. Theseresults provide support for the assertion thatthe subjects' behavior was under conditional(rather than simple) discriminative control.Nevertheless, because Experiments 1 and 2used different training and testing procedures,claims about subjects' performances in Ex-periment 1 based on the results of Experiment2 were inconclusive. Moreover, a number ofrelations other than those tested in Experi-ments 1 and 2 could emerge from the trainedbaseline relations. Therefore, a third experi-ment was conducted to address these two is-sues.

In Experiment 3, subjects were taught nineAB-C relations and three C-D relations andwere then tested for the emergence of equiv-alence (D-AB) as well as AD-B and BD-Arelations. Three of 5 subjects showed the emer-gence of all tested relations. One subject didnot demonstrate equivalence but did demon-strate AD-B and BD-A relations. The re-maining subject demonstrated neither.

There are two obvious limitations of thepresent study. Most notably, due to restrictedduration of experimental sessions, each subjectdid not encounter all stimulus relations tested.Thus, one could argue that a single subjectmight not show the emergence of all relationstested in Experiments 1, 2, and 3. Furtherresearch is needed to address this issue.

Second, only 3 of the 5 subjects in Experi-ment 3 demonstrated both types of tested stim-ulus relations. Although the results of this ex-periment demonstrated the emergence ofequivalence as well as AD-B and BD-A re-lations in some subjects, the sources of inter-subject variability were not investigated. Onepossible cause is insufficient baseline training.Further research should investigate the vari-ables responsible for this variability. Despitethese limitations, the present experiments

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BLOCKS of 9 or 18 TRIALSFig. 10. Percentage of choices out of nine consistent with equivalence (leftmost five points in each graph) and

percentage of choices out of 18 consistent with predicted emergent relations of the AD-B and BD-A types (remainingpoints) for the 5 subjects of Experiment 3.

demonstrate the emergence of previously unre-ported derived stimulus relations.

Apart from extending the range of relationsthat can emerge from conditional discrimina-tion training, the present results raise someinteresting conceptual questions. How, for ex-ample, should we describe the stimulus controlexerted by the compound stimuli? The resultsof Experiments 2 and 3 show that the com-pound samples functioned as independent con-ditional stimuli. However, the results of Ex-periments 1 and 3 suggest that the compoundsdid not function as unitary stimuli. In theseexperiments, the elements of the compounds

were separated and then combined with therelated comparisons to exert independent stim-ulus control. Although the compound samplesappear to be independent functional units, theelements of the compounds can also serve in-dependent functions.

It could be argued that one of the elementsof each compound sample functioned as a con-textual stimulus for the conditional functionof the other element. For example, in the base-line relations Al Bl-Cl, A2B1-C3, and A3Bl -

C2, Al and A2 might have functioned as con-textual stimuli for the conditional function ofBi. Conversely, BI might have functioned as

H0w0

zw0wa-

540

EMERGENT STIMULUS RELATIONS 541

a contextual stimulus for the conditional func-tions of the A stimuli. On what basis can wedetermine which element served a conditionalfunction and which served a contextual func-tion? Thomas and Schmidt (1989) discusseda similar problem in identifying conditionaland discriminative functions in some condi-tional discrimination arrangements.

Moreover, the results of Experiments 1 and3 show that both elements of the AB samplesfunctioned independently as comparisons dur-ing test trials, indicating that they entered theequivalence classes. If these stimuli had, infact, functioned as contextual stimuli duringtraining, these results would contradict Sid-man's (1986) assertion that contextual stimulicannot enter equivalence classes. Additionalresearch is needed to examine the nature ofthe functional relation between the elementsthat comprise compound stimuli.As it stands, we are left with results that

are difficult to interpret within existing ac-counts of stimulus equivalence. One way ofdescribing the compound stimulus control ob-served in the present study is suggested byStromer, McIlvane, and Serna (in press). Theyargue that what are called conditional discrim-inations in match-to-sample arrangements mayactually be an example of simple discrimina-tive control by compound stimuli with sepa-rable and substitutable elements. Subjects'performances during tests for emergent rela-tions could then be explained in terms of dis-criminative control by such separable com-pounds. The present findings lend support tothis account.

In addition, the results of the present ex-periments raise several other questions to beaddressed by future research. For example,there are a number of possible stimulus rela-tions that may emerge when subjects are taughtto match single comparison stimuli to com-pound samples. Only a few were tested in thepresent study; the rest should be explored infuture studies. In addition, more research con-cerning stimulus control by compound stimuliis needed (e.g., Stromer, Mcllvane, Dube, &Mackay, 1993). Finally, future research shouldexamine the relation between transfer of stim-ulus functions (Gatch & Osborne, 1989; Greenet al., 1991; Hayes et al., 1991; Kohlenberg etal., 1991; Lazar, 1977; Lazar & Kotlarchyk,1986; Wulfert & Hayes, 1988) and the rela-

tions that emerge when compound stimuli areused in conditional discrimination procedures.

REFERENCESBush, K. M., Sidman, M., & DeRose, T. (1989). Con-

textual control of emergent equivalence relations. Jour-nal of the Experimental Analysis of Behavior, 51, 29-45.

Devany, J. M., Hayes, S. C., & Nelson, R. 0. (1986).Equivalence class formation in language-able and lan-guage-disabled children. Journal of the ExperimentalAnalysis of Behavior, 46, 243-257.

Gatch, M. B., & Osborne, J. G. (1989). Transfer ofcontextual stimulus function via equivalence class de-velopment. Journal of the Experimental Analysis of Be-havior, 51, 369-378.

Green, G., Sigurdardottir, Z. G., & Saunders, R. R.(1991). The role of instructions in the transfer ofordinal functions through equivalence classes. Journalof the Experimental Analysis of Behavior, 55, 287-304.

Hayes, S. C. (Ed.). (1990). Rule-governed behavior: Cog-nition, contingencies, and instructional control. New York:Plenum.

Hayes, S. C., Kohlenberg, B. S., & Hayes, L. J. (1991).The transfer of specific and general consequential func-tions through simple and conditional equivalence re-lations. Journal of the Experimental Analysis ofBehavior,56, 119-137.

Kohlenberg, B. S., Hayes, S. C., & Hayes, L. J. (1991).The transfer of contextual control over equivalenceclasses through equivalence classes: A possible modelof social stereotyping. Journal ofthe Experimental Anal-ysis of Behavior, 56, 505-518.

Lazar, R. M. (1977). Extending sequence class mem-bership with matching to sample. Journal of the Ex-perimental Analysis of Behavior, 27, 381-392.

Lazar, R. M., & Kotlarchyk, B. J. (1986). Second-ordercontrol of sequence-class equivalence in children. Be-havioural Processes, 13, 205-215.

Lynch, D. C., & Green, G. (1991). Development andcrossmodal transfer of contextual control of emergentstimulus relations. Journal of the Experimental Analysisof Behavior, 56, 139-154.

Sidman, M. (1986). Functional analysis of emergentverbal classes. In T. Thompson & M. D. Zeiler (Eds.),Analysis and integration of behavioral units (pp. 213-245). Hillsdale, NJ: Erlbaum.

Sidman, M., & Tailby, W. 0. (1982). Conditional dis-crimination vs. matching-to-sample: An expansion ofthe testing paradigm. Journal of the Experimental Anal-ysis of Behavior, 37, 5-22.

Spradlin, J., & Saunders, R. (1984). Behaving appro-priately in new situations: A stimulus class analysis.American Journal of Mental Deficiency, 88, 574-579.

Stromer, R, McIlvane, W. J., Dube, W. V., & Mackay,H. A. (1993). Assessing control by elements of com-plex stimuli in delayed matching to sample. Journal ofthe Experimental Analysis of Behavior, 59, 83-102.

Stromer, R., McIlvane, W. J., & Serna, R. W. (in press).Complex stimulus control and equivalence. The Psy-chological Record.

Stromer, R., & Stromer, J. B. (1990a). The formation

542 MICHAEL R. MARKHAM and MICHAEL J. DOUGHER

of arbitrary stimulus classes in matching to complexsamples. The Psychological Record, 40, 51-66.

Stromer, R., & Stromer, J. B. (1990b). Matching tocomplex samples: Further study of arbitrary stimulusclasses. The Psychological Record, 40, 505-516.

Thomas, D. R., & Schmidt, E. K. (1989). Does con-ditional discrimination learning by pigeons necessarilyinvolve hierarchical relationships? Journal of the Ex-perimental Analysis of Behavior, 52, 249-260.

Wulfert, E., & Hayes, S. C. (1988). Transfer of a con-ditional ordering response through conditional equiv-alence classes. Journal of the Experimental Analysis ofBehavior, 50, 125-144.

Received October 20, 1992Final acceptance July 8, 1993