JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

CONTEXTUAL CONTROL OF EMERGENTEQUIVALENCE RELATIONS

KAREN M. BUSH, MURRAY SIDMAN, AND TANIA DE ROSE

WASHINGTON AND JEFFERSON COLLEGE, THE NEW ENGLAND CENTER FOR AUTISM,AND SAO CARLOS, BRAZIL

Three college students in Experiment 1 and 1 student in Experiment 2 learned visual conditionaldiscriminations under contextual control by tones; the visual comparison stimulus that was correctwith a given sample stimulus depended on whether a high tone or a low tone was present. Two ofthe subjects in Experiment 1 then demonstrated the emergence of two sets of contextually controlledthree-member classes of equivalent stimuli, and the subject in Experiment 2 showed the emergenceof contextually controlled four-member classes; the class membership of each stimulus varied as afunction of the tones. Class membership was demonstrated by the subjects' performance of newconditional discriminations that they had never been taught directly. In Experiment 2, the procedureswere intended to ensure that the tones exerted second-order conditional control and did not simplyform compounds with each of the visual stimuli, but the subject's verbal description of the taskssuggested that this intention might not have been successful. It could not be ascertained, therefore,whether the tones exerted contextual control as independent second-order conditional stimuli or simplyas common elements of auditory-visual stimulus compounds.Key words: stimulus equivalence, stimulus classes, second-order conditional discrimination, condi-

tional discrimination, touch screen, key press, college students

With human subjects, equivalence classescontaining words, pictures, objects, designs, andother stimuli readily emerge from conditionaldiscriminations that share samples or com-parisons (e.g., Devany, Hayes, & Nelson, 1986;Lazar, 1977; Lazar, Davis-Lang, & Sanchez,1984; McDonagh, McIlvane, & Stoddard,1984; Sidman, Kirk, & Willson-Morris, 1985;Sidman & Tailby, 1982; Stromer & Osborne,1982; Wetherby, Karlan, & Spradlin, 1983).For example, the upper part of Figure 1 sum-marizes a procedure for establishing threeclasses of equivalent stimuli, each class con-taining the names of three historical figures.The classes to be established are:

Class 1: Al, Bi, Cl (Renoir, Constable,Pollock)

Class 2: A2, B2, C2 (Twain, Voltaire,Byron)

This research was conducted at Northeastern Universityand was supported in part by Grant HD20688 from theNICHHD of the National Institutes of Health to Wash-ington and Jefferson College. The authors are grateful toF. Garth Fletcher for assistance with apparatus and withcomputer programming. Reprints may be obtained fromKaren M. Bush, Department of Psychology, Washingtonand Jefferson College, Washington, Pennsylvania 15301,or Murray Sidman, The New England Center for Autism,33 Turnpike Road, Southborough, Massachusetts 01772.

Class 3: A3, B3, C3 (Churchill, Kennedy,De Gaulle).

These classes can be expected to emerge af-ter a subject is taught the AB and BC condi-tional discriminations indicated by the solidarrows that point from sample to comparison.First, a sample is presented with the compar-ison stimuli Constable (Bl), Voltaire (B2), andKennedy (B3), and the subject learns: If thesample is Renoir (Al), then pick Constable(B 1); if the sample is Twain (A2), then chooseVoltaire (B2); and if Churchill (A3), thenKennedy (B3). (Throughout these experi-ments, the subjects were exposed to the rein-forcement contingencies in standard condi-tional-discrimination procedures. Although thecontingencies may well generate verbal rules-e.g., "match people by occupation"-the sub-jects were not explicitly given any rules.) Next,with a former comparison, BI, B2, or B3, asthe sample, and with Cl, C2, and C3 as com-parisons, the subject learns: If Constable (B1),then Pollock (C 1); if Voltaire (B2), then Byron(C2); and if Kennedy (B3), then De Gaulle(C3).The CA conditional discriminations indi-

cated by dashed arrows in Figure 1 (a C stim-ulus as sample and the A stimuli as compar-isons) can then provide a test for equivalence

29

1989, 51, 29-45 NUMBER 1 (JANUARY)

KAREN M. BUSH et al.

DI SC I PL I NECONSTABLE

81 <......

RBVOLTAIRE

\ BC

82

KENNEDY

/> /e B3 <. \

RENOIR TWAIN CHURCHILL DE GAULLE BYRON POLLOCKAl A2 A3 C3 C2 Cl

_ _ __._.....| A|.....A...Aj A

L - -- II

CRNAT I ONAL I TY

CONSTABLE

RB BCVOLTAIRE

/ 1: B2 n .\

KENNEDY8 .....

RENOIR TWAIN CHURCHILL DE GAULLE BYRON POLLOCKAl A2 A3 C3 C2 Cl

~A .... ..Al Al 6l

* A...... ...... .. A | ............. ... ..

CRFig. 1. Contextually controlled classes of equivalent

stimuli. The context of "discipline" or "nationality" de-termines class membership for particular stimuli.

relations. If the conditional relation betweensample Al and comparison B1 is also an equiv-alence relation, and if sample Bi and com-

parison C1 enter into the same equivalencerelation as B1 and Al, then, without additionalexplicit teaching, the subject will select com-

parison Al when Cl is the sample. For ex-

ample, having learned to choose Constable (B1)when Renoir (Al) was the sample, and Pollock(Cl) when Constable (BI) was the sample,the subject will then select Renoir (Al) whenPollock (Cl) is the sample. Similarly, withByron (C2) as the sample, the subject willselect Twain (A2); and with De Gaulle (C3),Churchill (A3).From a CA test performance consistent with

the dashed arrows in Figure 1, one can inferthat the AB and BC conditional relations metthe requirements of symmetry and transitivitythat equivalence demands (Sidman et al., 1982;Sidman & Tailby, 1982). A thorough evalu-ation of equivalence, however, would also testthe symmetric and transitive relations as de-picted by the dotted arrows in Figure 1. Test-ing for BA (a B stimulus as sample and the Astimuli as comparisons) and CB (a C stimulus

as sample and the B stimuli as comparisons)would indicate whether the AB and BC re-lations were symmetric. An AC test (an Astimulus as sample and the C stimuli as com-parisons) would indicate whether the relationswere transitive.

Stimuli need not confine their membershipto a single equivalence class. The bottom halfof Figure 1, for example, shows the same A,B, and C stimuli, with the solid arrows againindicating the conditional discriminations thatare to be taught explicitly. But the AB and BCrelations are different. Now, the sample, Re-noir (Al), goes with the comparison Voltaire(B2), and Voltaire (B2) with De Gaulle (C3).Similarly, the other conditional discrimina-tions relate each sample to a new comparison.If the new conditional discriminations alsogenerate equivalence relations, new equiva-lence classes should emerge:

Class 1: Al, B2, C3 (Renoir, Voltaire,De Gaulle)

Class 2: A2, B3, Cl (Twain, Kennedy,Pollock)

Class 3: A3, BI, C2 (Churchill, Constable,Byron).

The CA test (dashed arrows) now showsthe subject selecting Twain (A2) with Pollock(C1) as the sample, Churchill (A3) with Byron(C2), and Renoir (Al) with De Gaulle (C3).The symmetry tests (BA and CB) and the tran-sitivity test (AC) illustrated by dotted arrowsshould also reflect the new AB and BC con-ditional discriminations.

For the A, B, and C stimuli to belong si-multaneously to both sets of equivalence classesdiagrammed in Figure 1 would require somekind of contextual control. For example, with-out such control, the top diagram would haveRenoir (Al) equivalent to Constable (B1), butthe bottom diagram would have Renoir (Al)equivalent to Voltaire (B2). Sharing the samesample, Renoir (Al), would place Constable(Bl) and Voltaire (B2) in the same class. WithVoltaire (B2) and Twain (A2) also sharingclass membership in the upper diagram, andwith Twain (A2) and Kennedy (B3) in thesame class in the lower diagram, Twain (A2),Kennedy (B3), Voltaire (B2), Constable (Bi),and Renoir (Al) would merge into one class.Ultimately, all the stimuli would becomeequivalent to each other. The six stimulusclasses (three in the upper diagram and threein the lower) would collapse into one, and thesubject's behavior when confronted with any

30

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

of the conditional discriminations would be-come unpredictable.

But, of course, that need not happen. Any-one familiar with these names knows that thediagrams can coexist. The labels Discipline(upper diagram) and Nationality (lower dia-gram) indicate topical contexts. If we are dis-cussing disciplines, Renoir, Constable, andPollock go together as artists; Twain, Voltaire,and Byron as writers; and Churchill, Kennedy,and De Gaulle as heads of state. If we arediscussing nationality, Renoir, Voltaire, andDe Gaulle go together as French; Twain, Ken-nedy, and Pollock as American; and Churchill,Constable, and Byron as British.The contextual labels place the original first-

order conditional discriminations under sec-ond-order conditional control. With disciplineas the topic, for example, the relations, "ifRenoir, then Constable," "if Constable, thenPollock," and so on, hold true. With nation-ality as the topic, however, the relations, "ifRenoir, then Voltaire," "if Constable then By-ron," and so forth, hold true.A few studies of second-order conditional

discriminations have been reported (Fucini,1982; Lazar & Kotlarchyk, 1986; Nevin &Liebold, 1966; Santi, 1978; Weigl, 1941). Itremains to be shown, however, that emergentequivalence classes also can be under second-order control. Will contextually dependentclasses of equivalent stimuli emerge from con-textually controlled conditional discrimina-tions? With AB and BC conditional discrim-inations brought explicitly under contextualcontrol, will the new conditional discrimina-tions (CA, BA, CB, and AC) that emerge with-out explicit teaching also prove to be undercontextual control?

In each of the two experiments reportedhere, we attempted to teach subjects first-orderconditional discriminations that were them-selves under second-order control. With anyparticular sample, one comparison was thecorrect choice in the presence of a high tone,and a different comparison was correct in thepresence of a low tone. Tests then determinedwhether the emergent conditional discrimi-nations that defined equivalence relations hadalso come under control by the tones.

EXPERIMENT 1In Experiment 1, we sought to determine

whether teaching subjects conditional discrim-

HIGH TONE

RB ....B1 t S<......* B.C

rB BB2 C.

/ /v g B3 g X .nIA A2Q R3- CM3 C22 Clr

I....................... ..............................................CR

LOW TONE

Bl1wB2 -

pi a

BC

/--/p-----DJ If*A-*X

RIA R2A A3E U31 C2EA clrI. I A:.A.. .....A IA

........... j- ..............

CRFig. 2. Procedure for Experiment 1. The solid arrows

indicate the conditional discriminations taught directly (ABand BC). The dashed arrows indicate conditional discrim-inations (CA), the emergence of which would demonstratethat the AB and BC conditional discriminations had alsogenerated equivalence relations. The dotted arrows indi-cate emergent conditional discriminations that would dem-onstrate symmetry (BA and CB) and transitivity (AC) ofthe AB and BC relations. Conditional relations betweenvisual stimuli differ in the presence of the high and lowtone.

inations under second-order control wouldproduce classes of equivalent stimuli that werealso under second-order control. The proce-dures depicted in Figure 2 are like those inFigure 1 except that experimental stimuli havebeen substituted for the names. Tones providedthe context, a high tone for the relations in thetop diagram and a low tone for the relationsin the bottom diagram. All other stimuli werevisual forms that resembled Greek letters.The subjects learned 12 conditional discrim-

inations: three AB and three BC relations inthe high tone and three AB and three BCrelations in the low tone. For example, witha high tone and Al as the sample, the correctcomparison was B1, but with a low tone, thecorrect comparison was B2. If the stimuli inthe conditional discriminations had becomemembers of equivalence classes, the explicitly

31

KAREN M. BUSH et al.

taught relations would be reflexive, symmetric,and transitive (Sidman et al., 1982; Sidman &Tailby, 1982). Reflexivity, testable by gener-alized identity matching (in which the subjectmatches each stimulus to itself) can be assumedfor the normal adult subjects in this study.Symmetry can be tested by reversing the rolesof samples and comparisons (dotted arrows,BA and CB in Figure 2). For example, havinglearned the AB relations (an A stimulus assample and the B stimuli as comparisons), willsubjects show the expected BA relations (a Bstimulus now serving as sample, and the Astimuli as comparisons)? Also, will they showthe CB relations that demonstrate BC sym-metry? Finally, after the subjects have learnedAB and BC, will the AC relations (also in-dicated by dotted lines in Figure 2) show theexpected transitivity?CA is called a test for equivalence because

it tests simultaneously, although indirectly, forsymmetry and transitivity of the AB and BCrelations. If the explicitly taught relations didnot possess these properties of equivalence re-lations, we would have no basis for predictingthe subject's performance on the CA test. Toverify this theoretical assumption, however, wemust also test the relations directly for sym-metry and transitivity.

Performances consistent with the CA rela-tions shown in the upper and lower diagramsof Figure 2 suggest the emergence of condi-tionally controlled stimulus classes-classesdependent on a context. For example, with ahigh tone and C2 as the sample, the correctcomparison would be A2, but if the tone werelow, the correct comparison would be A3. (Weuse the term correct merely to refer to the com-parison whose selection by the subject in thepresence of a given sample would indicate theformation of equivalence classes.)

Labels corresponding to "French, British,and American," or "Painter, Writer, andStatesman," are, of course, not available forthe stimuli in Figure 2. Whether such labels,which define functional stimulus classes (Gol-diamond, 1966), are required to mediate theemergence of equivalence relations is an im-portant question that has not yet been an-swered satisfactorily (see, e.g., Devany et al.,1986; Lazar et al., 1984; McIntire, Cleary, &Thompson, 1987; Sidman, Cresson, & Will-son-Morris, 1974; Sidman, Willson-Morris,

& Kirk, 1986).1 The present study, like otherinvestigations of emergent equivalence rela-tions, may highlight this question but was notdesigned to provide an answer.

METHODSubjectsThe subjects, all between 18 and 25 years

old, were 3 Northeastern University under-graduates, recruited by a notice on a bulletinboard. Subject AXP, a male premedical stu-dent, participated in 8 teaching and 19 testingsessions. Subject JLR, a female nursing stu-dent, had eight teaching and nine testing ses-sions. Subject JXT, a female student in thecriminal justice program, had seven teachingand seven testing sessions. The duration ofeach session ranged from 0.5 to 1.5 hours.

ApparatusA Digital Equipment Corporation LSI 11/

030 computer presented stimuli, managedcontingencies, and recorded and analyzed data.Visual stimuli, displayed on the 11-in. (28-cm) monitor of a Heathkit H 19 ® computerterminal, were constructed from elements ofthat terminal's graphics character set. Whitelines 1 mm wide defined five rectangular "keys"arranged in a matrix shaped like a cross; thekey in the center of the monitor had a keyabove, below, to the left, and to the right of it.The key outlines, 3.3 cm wide and 3.8 cm highand spaced 0.6 cm apart horizontally and 1.0cm apart vertically, remained displayedthroughout an experimental session. Visualsamples always appeared in the center key,and comparisons appeared in three of the foursurrounding keys. One of the comparison keyswas always blank (no stimulus within the out-line), with the position of the blank key varyingfrom trial to trial.A transparent touch screen (TSD Display

Products, Inc., Model TF-12H) was mountedinside the casing and over the face of the mon-itor. When subjects touched the visually dis-played stimuli, the computer program re-corded the location of each touch on the screen

I See also Lowe, C. F. (1986, May). The role of verbalbehavior in the emergence of equivalence relations. Paperpresented at the meeting of the Association for BehaviorAnalysis, Milwaukee, WI.

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

as being within a particular key or in the areaoutside the keys.

Auditory stimuli were two easily discrimi-nable tones, one high and one low, presentedby a voice synthesizer (AstroTronics Model 001 -0007). The tonal qualities were generated byadjusting several of the parameters availableon the synthesizer. Tones were discontinuous,lasting 1 s and repeated at 0.5-s intervalsthroughout a trial.

Throughout the experimental session, thenumber of points a subject had earned wasdisplayed as a three-digit number on a whitebackground 2.3 cm wide and 6 mm high inthe lower left corner of the monitor. At theend of each session, points were exchanged formoney at the rate of 2 cents per point. Subjectsearned amounts ranging from $5 to $15 persession.

ProcedureInstructions to subjects. When first seated be-

fore the screen, which showed all keys but witha stimulus on only one of the outer (compar-ison) keys, the subject received no verbal in-struction except, "Touch it." Nothing hap-pened unless the subject pressed the key thatcontained the stimulus. Sometimes the instruc-tion had to be repeated-as when the subjectpressed a blank key and then stopped-buteventually the subject touched the key that con-tained a stimulus, producing the beep, the firstpoint on the counter, and another stimulus onanother key. The counter was then brought tothe subject's attention, and he or she was toldthat sometimes a point would be added to thecounter, that each point was worth 2 cents,and that the amount of money indicated by thecounter would be paid at the end of each ses-sion. The subject was then told again, "Touchit."When the subject was reliably pressing only

the key with a stimulus, the nature of the trialschanged. Each trial now began with a stimuluson the center (sample) key; touching the sam-ple key brought a single stimulus onto one ofthe comparison keys. As before, touching thecomparison key that displayed a stimulus pro-duced the beep, a point, and the next trial.When the subject was reliably touching thesample and comparison in sequence, he or shewas ready for conditional-discrimination trialsthat presented stimuli on the sample key and

on more than one comparison key at a time.This preliminary phase was accomplishedwithout any additional verbal instructions. Thestimuli differed from those to be used later inthe experiment.

All questions, at the start or later, aboutwhat to do next were answered with gener-alities like, "Keep going," "Give it a try," "Seefor yourself," or "Do your best," and questionsabout the purpose of the experiment were an-swered with a promise to explain everythingat the end. During the first few sessions, thesubject was occasionally asked, "How manypoints do you have?"

Preteaching and teaching contingencies. Trialsbegan with a visual sample displayed in thecenter key. In second-order conditional dis-criminations either the high or the low toneaccompanied the visual sample. By touchingthe sample, the subject produced three com-parisons in the surrounding keys. The re-maining key stayed blank. Visual samples re-mained present, and auditory stimuli continuedto be repeated throughout the trial. When thesubject touched a comparison key, the trialended: All stimuli disappeared, a 0.68-s in-tertrial interval occurred, and the next trialbegan. If the subject touched a correct com-parison on a trial in which reinforcement wasscheduled, the computer beeped and added apoint to the reinforcement counter before theintertrial interval began. When reinforcementwas not scheduled, neither beeps nor pointswere given.

Errors were recorded if the subject touchedan incorrect comparison or touched both thecorrect and an incorrect comparison within 0.1s. Touching the blank comparison key or thearea outside the keys had no programmed ef-fect (except during the delayed-cue proceduredescribed below). Responses during the inter-trial interval reset the interval, delaying theonset of the next trial.

Trial sequences. The computer program thatmanaged the procedures presented trial se-quences that were subject to the following re-strictions: With each combination of sampleand comparison stimuli defined as a trial type(the number of trial types in a session de-pended on the current phase of the experi-ment), each trial block included one occurrenceof every trial type; no trial type occurred onconsecutive trials; no key was correct on con-

33

KAREN M. BUSH et al.

secutive trials; and every block of trials con-tained a different sequence of trial types andof correct keys.

Delayed-cue procedure. Conditional discrim-inations were taught by a variation of the de-layed-cue technique (Touchette, 1971). Eachtrial began with the presentation of a sample,and when the subject touched the sample key,the comparisons appeared. On the first severaltrials, however, the incorrect comparisons dis-appeared immediately (0.1 s), leaving onlyblank keys with the sample and the correctcomparison. Pressing a blank key that had con-tained an incorrect comparison was treated asan error, but this rarely happened; the dis-appearance of the incorrect comparisons madethe correct choice obvious. Each time the sub-ject completed a block of trials without error,the interval between presentation of the com-parisons and removal of the incorrect com-parisons increased, the amount of the increasegrowing larger as the subject progressed. Theinterval could have become as long as 20 s, butbefore waiting that long, subjects always beganselecting the correct comparison while the in-correct comparisons were still on the screen.When a subject responded correctly prior tothe removal of the incorrect comparisons for16 consecutive trials, the delayed cue wasdropped from that particular teaching phase.Once subjects had become familiar with thedelayed-cue procedure, they often learned sub-sequent conditional discriminations almosterrorlessly.

Standard learning criteria. Subjects com-pleted any teaching phase by meeting the fol-lowing criteria: an overall accuracy of at least95% during six consecutive trial blocks and nomore than one error in any trial type duringthose six blocks.

Preteaching. Preteaching familiarized sub-jects with the equipment, trial and reinforce-ment procedures, first- and second-order con-ditional discriminations, and the delayed-cueprocedure. With visual stimuli that differedfrom those to be used later in the experiment,they learned first-order conditional discrimi-nations, first with visual samples and then withauditory samples (the same tones that were tobe used later). Then they learned second-orderconditional discriminations that combined thevisual and auditory samples. At the end ofpreteaching, subjects were matching visualsamples and comparisons, with the correct

comparison on a given trial depending onwhether the high or the low tone was present.They had also learned to use the delayed-cueprocedure efficiently when faced with new trialtypes.

Teaching. With the delayed-cue procedure,subjects first learned the conditional discrim-inations labeled AB in Figure 2. When thetone was high and the visual sample was anuppercase lambda (Al), subjects learned tochoose lowercase gamma (Bl). But with a lowtone sounding with uppercase lambda (Al),subjects learned to choose lowercase xi (B2).Similarly, with A2 and A3 as samples, thecorrect comparison depended on whether thehigh or the low tone sounded during the trial.In this way, the visual-visual AB conditionaldiscriminations came under tonal control.Once subjects met the learning criterion on

the AB conditional discriminations, they con-tinued to review them at the start of each ses-sion while learning the BC tasks, the latteralso under control by the tones. After attainingcriterion on BC, they received a series of mixedAB and BC trials until they again met thelearning criterion. These AB and BC trialsserved as a baseline into which probes wereinserted to assess whether the relations thathad not been explicitly taught had emerged.Variations in the teaching sequence will bedescribed in conjunction with the results.

Extinction pretest. Because all tests weregiven in extinction, it was necessary to makesure the subjects would maintain their highaccuracy on the baseline conditional discrim-inations even in the absence of a beep and apoint for correct responses. Before testing be-gan, subjects were told, "This time you willnot get any beeps or points, but you can makeup the points on some easy ones later." Then,on completing the same number of unrein-forced trials that were to be used in subsequenttests, the subjects were allowed to make uptheir missed points by matching numbers andnumber names. Once subjects had demon-strated the standard accuracy criterion withoutreinforcement, testing of emergent conditionaldiscriminations began. After each test, subjectswere given enough number-matching trials tomake up for their missed reinforcers duringthe unreinforced baseline trials of the test.

Probe tests. Before any test, subjects re-viewed the baseline conditional discrimina-tions that they had been taught explicitly. Dur-

34

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

ing these reviews, subjects received the usualbeeps and points after correct choices. Onlywhen they met a review criterion of at least95% accuracy with no more than one error pertrial type in three consecutive blocks of trialswas a test given.The trials that assessed emergent relations

were usually presented as probes mixed withtrials of the baseline conditional discrimina-tions (exceptions are noted below). On eachtrial, the sample appeared, the subject touchedthe sample, the comparisons appeared, thesubject touched a comparison, and the trialended. After the intertrial interval, the nexttrial began. Without points or differentialfeedback on any trial, subjects received no di-rect instruction about correct choices on probetrials.

In earlier experiments in this laboratory,probe trials had been interspersed among in-termittently reinforced baseline trials. Occa-sionally, however, subjects discriminated thedifferential reinforcement contingencies,maintaining high accuracy on their baselinesbut showing selective extinction on the probes(e.g., Subject EH in Sidman et al., 1985). Thisobservation gave rise to the current extinctionprocedure for both baseline and probe trials.

Subjects received tests for CA (combined testof symmetry and transitivity), AC (test of tran-sitivity), and BA and CB (tests of symmetry).The sequence of tests varied with subjects andwill be described with the results.

Verbal reports. After all tests for emergentrelations were completed, some subjects re-ported verbally on their performance. Probetrials were presented in extinction, and sub-jects were asked to describe what they weregoing to do and why. The conversations wererecorded on tape and later transcribed.

RESULTSExcept where noted below, tests had 18, 36,

or 54 probes interspersed among AB and BCbaseline trials, and the subjects' accuracy onbaseline trials remained above 90%. Figures 3and 4 are cumulative records of the probe trialsfor Subjects JLR and JXT. The curves cu-mulate "hits" and "false alarms" (see below)within single tests only. Subject AXP's dataare described in the text.The records of probe trials in all CA tests

of equivalence have their origin on the lowestline; probes assessing transitivity begin on the

0 18 JLR7

w C B 1 12mIo SYMM.

5z BR 9 11co SIMM.

H r zSY". . . ....._

16 17

> TRANS.1-4F_ .................................

13 14 15

D' CA I8 1r EQUIV. } r6 8 19 121

CUMULATIVE FALSE ALARMS ON PROBES

Fig. 3. Cumulative records of Subject JLR's responseson probe trials. Each "hit" (response consistent with therelation being tested) causes the line to move one verticalstep. Each "false alarm" (response consistent with one ofthe relations not being tested) causes the line to move onestep to the right. Hits and false alarms cumulate withineach test; the scale is shown at the upper left. The numbersdirectly above each record indicate the sequence of tests.Two records with the same number indicate a test thatincluded probes for both relations.

line labeled AC; and probes assessing sym-metry begin either on the line labeled BA orCB, depending on the relation tested. The or-igin of each cumulative record is displaced anarbitrary distance along the appropriate testaxis.On each trial, the subject's choice of a com-

parison stimulus that was consistent with therelation being tested was considered a "hit,"and caused the line to move up one notch; aperfect performance produced a vertical lineas in Test 7 (Figure 3). Every choice incon-sistent with the relation being tested was con-sidered a "false alarm," (not an incorrect re-jection, because no choice was incorrect), andcaused the line to move one notch to the right;the lower the slope of the line, the greater thenumber of selected comparisons inconsistentwith the relation being tested.

Because each record includes both high-toneand low-tone probes, an intermediate slope(e.g., Test 1 in Figure 3) could have repre-sented a subject's consistent selection of com-parisons indicative of relations under the con-trol of only one tone. For example, the subjectmight have responded as though the tone werealways high. In fact, this pattern never oc-curred, so intermediate slopes always indicate

35

KAREN M. BUSH et al.

0 18 JXTLO 4 5 6

w iSi,M

z

'.

B R 9 10

J8ii 13 14

I..CR 12 15

.) EQUIV..I|

...

CUNULATIVE FALSE ALARMS ON PROBES

Fig. 4. Cumulative records of Subject JXT's responseson probe trials. Each "hit" (response consistent with therelation being tested) causes the line to move one verticalstep. Each "false alarm" (response consistent with one ofthe relations not being tested) causes the line to move one

step to the right. Hits and false alarms cumulate withineach test; the scale is shown at the upper left. The numbersdirectly above each record indicate the sequence of tests.Two records with the same number indicate a test thatincluded probes for both relations.

a mixture of hits and false alarms on probeswith both high and low tones.

Subject JLRSubject JLR received 17 tests (Figure 3).

The first was the CA test of equivalence. Wouldthe CA conditional discriminations, not ex-plicitly taught to the subject, emerge under thecontrol of the tones, as diagrammed in theupper and lower sections of Figure 2? Thestep-like record, with only 21 hits in the 36probe trials, indicates a failure of equivalenceto emerge. Repeated in Tests 2 and 3, the CAprobes continued to show no convincing evi-dence of equivalence.

Test 4 checked the explicitly taught AB re-lations for symmetry by probing with BA trialsin the presence of one or the other tone. Thelow slope of the line during the early trials ofTest 4 showed that symmetry was not im-mediately present, but the abrupt change to anearly vertical line showed symmetry emerg-ing suddenly. Test 5, a repetition of the BAtest, produced 35 hits in the 36 trials.

Might the emergence of the BA conditionaldiscriminations, indicating AB symmetry, have

brought in equivalence? A repetition of theCA probes in Test 6 indicated that it had not;only 15 of the subject's 36 choices were hits.

Test 7 yielded a perfect score on 36 CBprobes, indicating symmetry of the BC rela-tions, but in Test 8, a score of only 10 hits in36 CA probes indicated that the positive sym-metry tests had not been sufficient to generateequivalence. To ensure that both sets of ex-plicitly taught relations, AB and BC, had re-tained their symmetric properties, BA and CBsymmetry probes were mixed in Test 9. Sym-metry was intact in both, but Test 10 stillshowed no equivalence. Test 11 confirmed thatthe emergent BA and CB relations endured.

Symmetry of the AB and BC relations hadnever been shown at the same time that theCA relations were being probed. Test 12,therefore, included CB symmetry probes withthe CA equivalence probes. Subject JLR'schoices were hits on all 18 of the CB probes.Her first five choices on the CA trials werefalse alarms, but 12 of her remaining 13 choiceswere hits; equivalence emerged during this test.Also, after a few hits on the CA probes, evenwithout beeps or points, Subject JLR said, "Ittook me long enough, but I've got it now."

Tests 13, 14, and 15 confirmed the emer-gence and maintenance of the CA conditionaldiscriminations indicative of equivalence.Then, AC probes in Tests 16 and 17 dem-onstrated that the AB and BC relations weretransitive, a property that was required (alongwith symmetry) if the emergence of the CArelations was to be confirmed as a valid in-dicator of equivalence.

In her verbal reports, Subject JLR gavenames to all the stimuli and was able to de-scribe all of the sample-comparison relationsand their derivations, in accordance with Fig-ure 2.

Subject AXPSubject AXP had 43 tests (not shown), dur-

ing which he showed symmetry for the trainedAB and BC relations but never showed tran-sitivity (AC) or equivalence (CA) under con-textual control of the tones. Nor was his re-sponding consistent with stimulus classesgenerated by one tone alone. A full graphicalpresentation of Subject AXP's extensive testdata would be more distracting than illumi-nating.

In Tests 1 through 5 (CA probes for equiv-

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

alence), he never scored more than 11 hits in36 probes. The AB and BC conditional dis-criminations had not generated equivalence re-lations. The AB and BC relations were thentested for transitivity by presenting the subjectwith AC probes in Tests 6 and 7; the ACrelations did not emerge.

Subsequent tests yielded evidence neither oftransitivity (AC) nor of AB symmetry (BA).The BA conditional discriminations indicativeof AB symmetry under tonal control didemerge, however, when tested with only ABtrials in the baseline. Then, a return to thefull baseline of AB and BC trials confirmedthat the AB relations had become symmetric,as had the BC relations.A long series of tests then presented various

combinations of probes, but equivalence (CA),although tested 18 more times, still did notemerge. Nor did transitivity emerge, althoughit was reassessed four more times with the ACprobes. Testing came to a halt when personalcircumstances kept Subject AXP from con-tinuing the experiment.

Subject AXP's verbal reports did not indi-cate any consistent names for the stimuli, nordid he describe any of the emergent sample-comparison relations. He stated that he wasunable to describe what he was doing, butcould draw it and, subsequently, drew a dia-gram of the samples and specific comparisonshe had been choosing. Neither his statementsnor his drawings outlined any general rules.

Subject JXTThe data for Subjects JLR and AXP had

suggested that the testing sequence and thecombinations of baseline trials and probes caninfluence the emergence of new relations, eventhough the tests are carried out in extinction.A previous study (Sidman et al., 1985) hadgiven rise to a similar suggestion. Accordingly,in an attempt to facilitate the emergence ofcontextually controlled equivalence, SubjectJXT was given a different teaching and testingsequence. It is not possible, at present, to de-termine whether these procedural modifica-tions had any effect on the subject's perfor-mance.

After Subject JXT met the learning crite-rion on the AB conditional discriminations anddemonstrated continued accuracy in extinc-tion, she received BA symmetry probes mixedwith a baseline of AB trials. Her nearly 100%

hit rate in Tests 1 through 3 (Figure 4) showedsymmetry of the AB relations. Subject JXTthen learned the BC conditional discrimina-tions and demonstrated continued accuracy inextinction. The subsequent CB probes in Tests4 through 6, mixed with a baseline of BC trials,showed symmetry of the BC relations.AB and BC trials were then reviewed sep-

arately until Subject JXT met criterion oneach. Then she was given the mixed baselineof AB and BC trials until she met the learningcriterion and maintained her accuracy in ex-tinction. Testing for emergent relations thenresumed with the full AB and BC baseline.

In Test 7, Subject JXT scored 100% hitson CB probes for symmetry of the BC rela-tions, with the full baseline. In Tests 8 through10, the BA probes for AB symmetry (also withthe full baseline) showed progressive improve-ment and stabilization of the hit rate.

Having shown symmetry for each of thedirectly taught relations, Subject JXT wasgiven the CA probes for equivalence with thefull baseline (Test 1 1). Although the first partof the test gave no evidence of equivalence, thehit rate did increase at the end. Test 12 thenconfirmed the emergence of equivalence, withthe subject scoring 31 hits in 36 choices on theCA probes.An injury prevented SubjectJXT from par-

ticipating in the experiment for the next sev-eral weeks. When she returned, she once moreshowed AB and BC symmetry in Tests 13 and14, which inserted BA and CB probes into thefull baseline. Test 15 reaffirmed the emergenceof equivalence. Subject JXT did not return forfurther testing; transitivity was never testeddirectly, and no verbal reports were obtained.

DISCUSSIONOf 3 subjects who were explicitly taught AB

and BC conditional discriminations with con-textual control by tones, 2 showed that theteaching and testing had generated contex-tually controlled equivalence relations. NewCA, BA, CB, and AC conditional discrimi-nations emerged under tonal control. One sub-ject demonstrated tonal control in BA and CBsymmetry tests but gave no evidence of tran-sitivity or equivalence in the AC and CA tests.

Teaching 2 subjects the AB and BC con-ditional discriminations created six three-member classes of equivalent stimuli, with the

37

KAREN M. BUSH et al.

high tone common to one set of three classesand the low tone common to the other. Controlby the tones made multiple-class membershippossible for the visual stimuli, each one be-coming a member of two classes. For example,in the presence of the low tone, stimulus Alparticipated in one equivalence class along withB1 and C1 and, in the presence of the hightone, participated in another class along withB2 and C3 (Figure 2).

If some kind of contextual control did notdetermine the class membership of stimulusAl at any particular moment, stimuli B1, Cl,B2, and C3 would all have become equivalentto each other because of their shared equiva-lence relation with Al; the subjects would havehad no basis for performing the new condi-tional discriminations as they did. The toneskept the classes from interacting. These find-ings provide an affirmative answer to the majorquestion that initiated the study: If conditionaldiscriminations are brought explicitly undercontextual control, will new conditional dis-criminations that define equivalence relationsalso emerge under contextual control?The data also raise several questions that

remain unanswered. For example, why didSubject AXP not show the same results as theothers? His academic competence indicated thathe was perfectly capable of forming equiva-lence relations. Perhaps the answer is to befound in his verbal report, in which he neithergave names to the stimuli nor described anyrules for relating the stimuli. Still, it has notyet been demonstrated that verbal mediationis necessary for equivalence relations to emergefrom conditional discriminations. The oppo-site-that equivalence relations are necessaryfor verbal rules to emerge-is, at present,equally likely.

Another unanswered question concerns thenature of the contextual control. One possi-bility is that the high and low tones functionedas second-order conditional stimuli, with theexplicitly arranged contingencies placing eachin control of the original first-order conditionaldiscriminations (depicted by the solid arrowsin Figure 2), and each then coming to controlthe emergent relations also (depicted by thedashed and dotted arrows in Figure 2).An alternative interpretation does not at-

tribute second-order control to the tones. It ispossible that the tones never developed an in-dependent function of their own but simply

entered into stimulus compounds with the vi-sual stimuli. They may have merely changedthe stimuli in the first-order conditional dis-criminations from purely visual to auditory-visual compounds. For example, instead ofmatching the visual sample Al to visual com-parison B1 under the control of the high toneand the same visual sample to visual compar-ison B2 under the control of the low tone, thesubjects may have been matching one com-pound sample (Al + high tone) to a compoundcomparison (Bl + high tone) and anothercompound sample (Al + low tone) to a com-pound comparison (B2 + low tone). If thesecompounds had formed, the subjects could besaid to have learned only first-order and notsecond-order conditional discriminations.

It is clear that the A and B stimuli did notsimply form stimulus compounds with eachother; the AC and CA tests showed the Astimuli to be effective in the absence of theexplicitly related B stimuli, and the CB testsshowed the B stimuli to be capable of func-tioning independently of the A stimuli. Simi-larly, the AC, CA, and BA tests showed thatthe B and C stimuli did not have to functiontogether as compounds. A tone, however, waspresent in every test; the tones, therefore, werenever shown to function independently of vi-sual samples and comparisons with which theyhad been explicitly combined. Contextual con-trol by the tones may have come about solelybecause one tone or the other was an elementof every stimulus.The tones, then, may not have served as

second-order conditional stimuli. They maysimply have made the specification of the first-order conditional stimuli more complex, andfor that reason never have exerted independentcontrol over emergent equivalence relations.Would it be possible to establish second-orderconditional control by stimuli that were ca-pable of functioning independently? Thisquestion helped shape the next experiment.

EXPERIMENT 2The first purpose of Experiment 2 was to

determine whether emergent contextual con-trol could be confirmed with another subject.The second purpose, an attempt to produceunequivocal second-order control over theemergent conditional discriminations, dictateda more complex procedure. Experiment 2 was

38

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

123I x d 4-MI

ll l CLASS

A 0 _ #1*#2

1 1 1 #3r A 11

EMBER STIMULUS CLASSES

High Tone

Dl,Al,Bl,Cl

D2MA2,B2,C2

D3,A3,B3,C3

Low Tone

Dl,Al,82,C2

D2MA2,MB3C3

D3,A3,Bl,Cl

RELATIONS TAUGHTHIgh Tone Low Tone No Tone

AB Al B 1, A2B2, A3B3 A 1 B2, A2B3, A3B 1CB ClBl, C2B2, C3B3DA DAl1, D2A2, D3A3

RELATIONS TESTEDHigh Tone Low Tone No Tone

BlAl,B2A2,B3A3 BiA3,B2Al,B3A2

BlCl,B2C2,B3CSAlDl,A2D2,A3D3

DlBl,D2B2,D3B3

BDl1,B2D2,B3D3AlCI,A2C2,A3C3DICI,D2C2,D3C3ClAl,C2A2,C3A3CIDI,C2D2,C3D3

D1B2,D2B3,D3Bl

B1D3,B2Dl,B3D2AlC2,A2C3,A3ClD1C2,D2C3,D3ClCIA3,C2Al,C3A2CiD3,C2Dl,C3D2

Fig. 5. Procedure for Experiment 2. The upper left portion diagrams DA, AB, and CB, the relations taughtdirectly; the letter H denotes relations in the high tone, and L denotes the low tone. The upper right portion showsthe expected stimulus classes contextually controlled by tones. The middle portion shows the relations taught with andwithout tones. The bottom shows the tests for symmetry, transitivity, and equivalence with and without tones.

an attempt at systematic, rather than direct,replication of Experiment 1, in that it requiredthe emergence not of three-member but of four-member classes under contextual control.True second-order control required that the

tones exert contextual control independentlyof the particular visual stimuli with which theyhad been combined during the original teach-ing. One way to validate such independencewould be to generate emergent conditional dis-criminations that involved new combinations

of tones and visual stimuli. These would beanalogous to the emergent relations betweenvisual stimuli that had never been explicitlyrelated to each other during teaching. The pro-cedure illustrated at the top of Figure 5 wasdesigned to permit such definitive tests for truesecond-order control over emergent condi-tional discriminations. As before, the AB con-ditional discriminations were taught in thepresence of either the high or the low tone.Stimuli C and D were related to stimuli B and

D

A

B

SYMMBCADBA

TRANSDB

EQUIVBDACDCCACD

39

KAREN M. BUSH et al.

A, respectively, in the absence of the tones.Would the tones then control the class mem-bership of the C and D stimuli with whichthey had never before been combined?As in Experiment 1 with the tones present,

arrows in Figure 5 point from sample (A stim-uli) to comparisons (B stimuli), with the high(H) or low (L) tone indicated beside each ar-row. For example, when Al was the sample,the subject learned to select comparison B1 inthe presence of a high tone and comparisonB2 in the presence of a low tone. The tonesalso determined the comparison he was to se-lect when the sample was A2 or A3.The subject learned the CB and DA con-

ditional discriminations without any tones. Withthe B stimuli as comparisons, he was taughtto select B1 whenever Cl was the sample, B2with C2 as the sample, and B3 with C3. Sim-ilarly, with the A stimuli as comparisons, helearned to select Al whenever Dl was thesample, A2 with D2, and A3 with D3. Allrelations that were explicitly taught are listedin the center section of Figure 5.

If the explicit teaching had generated equiv-alence relations, the DA and CB conditionaldiscriminations would be symmetric; emergentAD and BC conditional discriminations wouldbe independent of the tones (bottom section ofFigure 5). AB symmetry, however, would gen-erate two sets of BA conditional discrimina-tions, one set accompanied by the low tone andthe other set by the high tone (as in Experiment1). All other emergent conditional discrimi-nations would have to include C or D stimulias samples or comparisons and would also haveto involve the AB or BA relations.

In the DB transitivity test, the tone would,for example, determine whether Dl as thesample would lead the subject to select com-parison BI or B2. It is of particular interesthere that while the original conditional dis-criminations were being taught, no tones ac-companied the D stimuli. Similarly, in the CAequivalence test (because this test requiressymmetry of the AB relations, it is more thanjust a transitivity test), the tones would controlthe emergent CA conditional discriminations,even though the C stimuli and the tones hadnot been presented together during the originalteaching. The CD and DC tests for four-mem-ber equivalence classes are the most demand-ing, because the original teaching had involved

neither the samples nor the comparisons inconditional discriminations that included tones.The four-member stimulus classes under

tonal control are shown in the upper rightsection of Figure 5. Given equivalence, six four-member classes will form, each tone control-ling three classes. The subject would be ableto match any member of a class to any other,even without having been directly taught to doso.

All of the new relations that could be ex-pected to emerge after the explicit teaching arelisted in the bottom section of Figure 5. Controlby the tones over emergent conditional dis-criminations in which C or D stimuli servedas samples or comparisons would suggest thatthe tones could function independently of theA and B stimuli with which they had beencombined during the original teaching. This,in turn, would suggest that the tones had notsimply entered into compounds with the visualstimuli but instead were exerting second-ordercontextual control over the emergent equiva-lence relations.

METHODSubject

Subject EXY was a 25-year-old male for-eign student enrolled as an undergraduate ina local school of music.

ApparatusAll equipment was identical to that of Ex-

periment 1, except that there was no touchscreen to identify responses. Instead of touch-ing the screen to indicate the stimulus he wasselecting, the subject pressed one of five keyson the numerical data pad on the keyboardbelow the monitor on which the stimuli ap-peared. The keys, arranged in a cross, corre-sponded in position to the stimuli. The subjectwas told to "choose one of these [stimuli onthe monitor] by pressing the corresponding oneof these [keys on the keyboard]-the one thatis in the same relative position as those upthere."

ProcedureThe preteaching and teaching contingen-

cies, the delayed-cue procedure, the proceduralparameters, and the standard learning crite-rion were the same as in Experiment 1. SubjectEXY tended to work for longer sessions than

40

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

the subjects in Experiment 1 and rarely earnedless than $15 per session. He participated infour teaching and three testing sessions.

After preteaching, Subject EXY first learnedthe AB conditional discriminations with thetones, as illustrated in Figure 5. With anysample (an A stimulus), the tone (high or low)determined the comparison (one of the Bstimuli) that the subject was to select. Afterreaching the learning criterion, the subjectcontinued to review the AB conditional dis-criminations at the start of subsequent ses-sions.The subject then learned the CB conditional

discriminations without any tones present. ABtrials (with tones) and CB trials (without tones)were then mixed. Next, the DA conditionaldiscriminations were taught without tones. Thefinal baseline, reviewed at the start of eachsession, contained trials of all the explicitlytaught conditional discriminations-AB withhigh tone, AB with low tone, and CB and DAwithout any tone.The subject then received the extinction pre-

test, meeting the learning criterion on the base-line without any beeps or points. Finally, hewent through a series of tests for emergentconditional discriminations. As in Experiment1, trials that assessed emergent relations werepresented as probes mixed with baseline trials.Again, all testing was done in extinction.The sequence of tests will be described with

the results. After the tests were completed, ver-bal reports were requested, taped, and tran-scribed.

RESULTSFigure 6 presents Subject EXY's probe data,

obtained in 20 tests that had 18 or 36 probesinterspersed among AB, CB, and DA baselinetrials. Baseline accuracy remained above 95%.Again, hits and false alarms are cumulatedwithin single tests only.

Subject EXY started with two CD tests,each containing 36 probe trials. Tones hadnever before accompanied the C samples orthe D comparisons. If the original teachinghad established the prerequisites for the emer-gence of tonal control over four-member classesof equivalent stimuli (Figure 5), sample CGwould lead the subject to select comparison D1in the presence of the high tone and compar-ison D3 in the low tone; with sample C2, the

EXY0 36

BC 20

ADM

to 3BA

tY 17Q DBz TRANS] . . . i8

° BD 18(en EQUIV.I. .J...I- 19I AC liI

EOUIVY....I

> DCII|_ EQUIV. .J. .....-LJ i s

GJ CRA leiD EQUIV ......... ..12 1ECD 11.15EQUJY L-.:r- , ..I.

CUMULATIVE FALSE ALARMS ON PROBES

Fig. 6. Cumulative records of Subject EXY's re-sponses on probe trials. Each "hit" (response consistentwith the relation being tested) causes the line to move onevertical step. Each "false alarm" (response consistent withone of the relations not being tested) causes the line tomove one step to the right. Hits and false alarms cumulatewithin each test; the scale is shown at the upper left. Thenumbers directly above each record indicate the sequenceof tests. Two records with the same number indicate a testthat included probes for both relations. Note change inscale from previous graphs.

subject would select comparison D2 in the hightone and Dl in the low tone; and with sampleC3, he would select D3 in the high tone andD2 in the low tone.The first two tests did not fulfill these ex-

pectations; the low, step-like slopes of Curves1 and 2 (Figure 6) indicate a failure of equiv-alence to emerge. Tests 3 (36 trials) and 4 (18trials) probed the AB conditional discrimina-tions for symmetry by presenting BA trialswith the tones. The AB relations proved sym-metrical, but CD conditional discriminationsindicative of equivalence still did not appearin Test 5. Tests 6 and 7 combined BA andCD probes (18 trials of each), but the resultsdid not change; the AB relations maintainedtheir symmetry, but the CD relations still didnot emerge. Test 8, which presented 18 ADprobe trials without any tones, showed thatthe DA relations were symmetric, but anotherCD probe in Test 9 still yielded no evidenceof equivalence.

41

KAREN M. BUSH et al.

If CD relations indicative of four-memberequivalence classes are to emerge, AB sym-metry (under tonal control) and DA symmetry(independently of the tones) are required (Fig-ure 5). BA and AD tests had already docu-mented these necessary symmetries. Also re-quired are the BD and CA relations that wouldsignify two sets of three-member equivalenceclasses (ABD and ABC); the four-memberclasses could not be expected to emerge in theabsence of either set of smaller classes. Giventhe AB and DA symmetry that the emergentBA and AD relations had already demon-strated, transitivity of BA and AD would bringabout the necessary BD relations. Given theexplicitly taught CB relations and the AB sym-metry that the emergent BA relations had dem-onstrated, transitivity of CB and BA wouldbring about the necessary CA relations.

Because probes of the BD and CA condi-tional discriminations test simultaneously forsymmetry and transitivity, they are equiva-lence tests. The BD probes for the ABD classrequire both the BA and AD relations to besymmetric if equivalence is to emerge, but theCA probes for the ABC class require only BAsymmetry. The presumably simpler CA re-lations were therefore tested next.

After the first three false alarms at the be-ginning of Test 10, Subject EXY said, "Oh, Ithink I have something," and the remainingprobes documented the existence of the three-member ABC class. In Test 11, the subjectagain scored mainly hits on the CA probes.

In Test 12 the subject was again given theCD probes; this time, the 36 trials containedonly one false alarm. Six previous tests hadfailed to yield CD relations indicative of four-member ABCD classes, but after the three-member ABC classes had emerged, the CDrelations showed themselves immmediately.

Tests 13 through 20 included two replica-tions of the CD probes (Tests 14 and 15) andprobed all of the previously untested condi-tional discriminations that were necessary todocument four-member equivalence classes.Tests 13 and 16 confirmed the four-memberclasses by demonstrating the necessary DC re-lations; the DB relations in Test 17 showedthat the DA and AB relations were transitive,and the BD relations in Test 18 confirmed thethree-member equivalence class ABD. Test 19probed the AC relations, confirming the three-member ABC class that Tests 11 and 12 had

shown by means of CA probes; and in Test20, BC probes demonstrated the symmetry ofthe CB relations.

In his verbalizations elicited after the tests,Subject EXY used names for each of the stim-uli and described the relations among stimuliexactly as they are illustrated in Figure 5.

DISCUSSIONOnce more, the question that initiated the

study received a positive answer: Classes ofequivalent stimuli that emerge from contex-tually controlled conditional discriminationswill themselves be under contextual control.The contextual control permitted stimuli tobecome members of more than one class with-out causing the classes to combine. Experiment2 confirmed this finding with a third subject,extending it to the more complex case of emer-gent four-member classes.

There remains the secondary question ofwhether the contextual control could be at-tributed to second-order conditional discrimi-nations. Although tones had never been pres-ent while Subject EXY was explicitly beingtaught conditional discriminations that in-volved C or D stimuli, the emergent CD, DC,CA, AC, DB, and BD conditional discrimi-nations did depend on the tones. For example,with C1 as the sample and the D stimuli ascomparisons, the subject selected D1 in thepresence of the high tone and D3 in the lowtone. Similarly, in each emergent conditionaldiscrimination, the tone controlled the classmembership of the C and D stimuli.On the face of it, the tones seemed to be

controlling equivalence relations even betweenvisual stimuli that had never been presentedwith tones while conditional discriminationswere being explicitly taught. If this were cor-rect, true second-order conditional controlwould have been demonstrated. The reason forthe tentative nature of this conclusion lies inthe subject's descriptions of the rules he wasfollowing during probes for emergent condi-tional discriminations. (Because it was rec-ognized that the subject's verbal descriptionmight itself influence what he subsequentlydid, reports were not elicited until all of theconditional-discrimination procedures had beencompleted.)

In a CD trial, for example, with only thelow tone and sample C1 present (D3 was thecorrect choice after the subject produced the

CONTEXTUAL CONTROL OF EQUIVALENCE RELATIONS

comparisons), Subject EXY was asked, "Whatare you going to do?" He said the following(paraphrased, and with the alphanumericstimulus designations shown in Figure 5 sub-stituted for the names he used): "When I seeCl [the sample], I immediately think aboutB1. And a low tone, with B1, connects to A3. IfI push C1, A3 will be on one of the squares.If A3 is not there, D3 is connected to A3, soI will push D3. D3 is connected to A3, andA3 with a low tone makes B 1, which is connectedto Cl." (Subject then pressed the sample toproduce the comparisons, and selected D3.)

Even though the tone was present from be-ginning to end, the subject mentioned it onlywhile describing the AB and BA relations,never while referring to the CB or DA rela-tions. He spoke of D3 being related to A3 andC1 to B1 without including the tone in hisdescription. The tone was noted only in de-scribing AB relations. Could he have learnedto disregard the tone in conjunction with theC and D stimuli and to take it into accountonly in conjunction with the AB relations? Ifso, that might invalidate the assumption thatthe tones exerted direct second-order controlover the emergent CD relations. The subject'sperformance can be described as a chain inwhich his verbal rule, interacting with the ex-perimental stimuli, acted as a complex set ofdiscriminative stimuli (Skinner, 1969, pp. 122,142-148) to determine his final choices. Thetones might have controlled the emergence onlyof the segment of the rule that dealt with theAB conditional discriminations.Whether the verbal rules stated by the sub-

ject played a pivotal role in the emergence ofequivalence relations is, of course, only con-jectural, depending on several assumptionswhose validity has not yet been demonstrated.These can only be outlined briefly here. First,does equivalence, in general, require that theindividual be able to verbalize the relation-ships? Second, even if such verbalization provesnot generally necessary, might it be requiredfor the emergence of larger classes, and par-ticularly for multinodal classes (Fields & Ver-have, 1987)?

Third, were the emergent (or directly taught)conditional discriminations in this experimentactually rule governed? The reports were ret-rospective, created perhaps by the experi-menter's very act of requesting them and there-fore not even existing during the previous

experimental procedures. Fourth, although thecontingencies outlined in Figure 5 did generatethe stated rules, it cannot be known whetherthose rules, if they did exist before the re-quested verbal reports, then operated inde-pendently of the contingencies that generatedthem. And finally, one can ask the chicken-and-egg type of question: Which comes first,the rules or the equivalence relations? If oneis indeed necessary for the other, which is pri-mary?To discuss potential solutions for these

problems is not appropriate here. Yet, evenwith these unanswered questions about pos-sible interactions between equivalence rela-tions and rule-governed behavior, it is unwiseat this juncture to ignore the likelihood thatthe formulation of a helpful set of rules becamepossible only when the subject learned to dis-regard the tones except when considering theAB relations. This may have occurred duringthe CA probes in Test 10 (Figure 6), when hesaid "I think I have something," and was per-haps more likely to happen during a test forthree-member than for four-member classes.In that event, the tones could not be said anymore definitely than in Experiment 1 to havefunctioned as second-order conditional stimuliin exerting their contextual control.

GENERAL DISCUSSIONIn the present experiments, we sought to

determine whether contextually controlledconditional discriminations can produce emer-gent equivalence relations that are also undercontextual control. Three of 4 subjects gave apositive answer to this question, even thoughit could not be determined unequivocallywhether the tones exerted contextual controlas independent second-order conditional stim-uli or simply as common elements ofcompoundfirst-order conditional and discriminativestimuli.A major impetus for the present study came

from an analysis of the potential role of second-order conditional stimuli in accounting for thecontextual control of emergent equivalenceclasses (Sidman, 1986). This analysis raisedthe question of why the context itself does notbecome a member of all the emergent classesand, by virtue of its common membership, con-dense all of the classes into one. In the presentstudy, for example, if the tones exerted inde-

43

44 KAREN M. BUSH et al.

pendent second-order control over the directlytaught and the emergent conditional discrim-inations, why did the tones not enter intoequivalence relations with the A and B stim-uli? If they did, all stimuli would be relatedto the tones and therefore to each other andwould become members of a single equivalenceclass. Why did this not happen?The most likely reason is that the contin-

gencies themselves prevented it. Differentialstimulus control-discrimination-requiresthat the controlling stimuli be different. If allstimuli became equivalent to each other, thesubjects would have no basis for respondingdifferentially; neither the simple nor the con-ditional discriminations that the reinforcementcontingencies specified would have been pos-sible for the subjects. A conflict therefore existsbetween the reinforcement contingencies thatcall for differential stimulus control and theformation of equivalence classes that impartthe same function to all members of a class.As the most likely winners of such a conflict,the reinforcement contingencies perhaps coun-teract the tendency of the stimuli to combineinto one large equivalence class.A similar consideration arises in conjunction

with the observation that different reinforcerscorrelated with each sample-comparison pairbring the reinforcers into the sample-compar-ison equivalence class (Dube, Mcllvane,Mackay, & Stoddard, 1987). In the more com-mon experimental procedure in which all con-ditional discriminations share a common rein-forcer, one might expect all of the stimuli tobecome related to each other because of theirrelation to the same reinforcer. Again, as inthe case of a common second-order conditionalstimulus, one can appeal to the incompatibilitybetween class formation and the reinforcementcontingencies to explain why the use of a com-mon reinforcer does not preclude the estab-lishment of conditional discriminations or theemergence of independent equivalence classes.The considerations just noted assume sec-

ond-order conditional control by the contex-tual stimulus. The incompatibility betweenclass formation and the contingencies does notarise when a subject is learning simple dis-criminations or first-order conditional discrim-inations. It becomes a problem only when sec-ond-order control is being established. Anotherreason that a common element (tone or rein-forcer) might not bring all the stimuli into a

single equivalence class comes from the pos-sibility, discussed in conjunction with Exper-iments 1 and 2, that the common elementssimply enter into stimulus compounds witheach visual sample and comparison. In thepresent experiments, the tones would then nothave become second-order conditional stimuli.In that case, the conflict between second-orderconditional control and the formation of equiv-alence classes would not have arisen, or, if itdid, would have resolved itself. This potentialconflict may even increase the likelihood thatthe formation of stimulus compounds willpreempt the establishment of second-orderconditional discriminations.

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Received October 21, 1987Final acceptance July 23, 1988