Stimulus class formation and stimulus-reinforcer relations

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

STIMULUS CLASS FORMATION AND STIMULUS-REINFORCERRELATIONS

WILLIAM V. DUBE, WILLIAM J. MCILVANE, RUSSELL W. MAGUIRE,HARRY A. MACKAY, AND LAWRENCE T. STODDARD

EUNICE KENNEDY SHRIVER CENTER, NORTHEASTERN UNIVERSITY, ANDNEW ENGLAND CENTER FOR AUTISM

This study examined stimulus class membership established via stimulus-reinforcer relations. Men-tally retarded subjects learned conditional discriminations with four two-member sets of visual stimuli(A, B, C, and D). On arbitrary-matching trials, they selected comparison stimuli Bi and B2 condi-tionally upon samples Al and A2, respectively, and Cl and C2 conditionally upon Bi and B2,respectively. On identity-matching trials, they selected all stimuli as comparisons conditionally uponidentical stimuli as samples. Throughout training, correct selections of Al, BI, Cl, and Dl werefollowed by one reinforcer, RI, and those of A2, B2, C2, and D2 were followed by another, R2.Subsequent tests documented the formation of two four-member stimulus classes, Al-Bl-Cl-Dl andA2-B2-C2-D2. The class membership of the A, B, and C stimuli could have been based on equivalencerelations that resulted from the arbitrary-matching training. Dl and D2 had never appeared onarbitrary-matching trials, however. Their class membership must have been based on relations withRl and R2, respectively. Results thus confirm a previous finding that stimulus classes can be expandedvia stimulus-reinforcer relations. They also define more precisely the potential nature of those classesand the conditions under which class membership can be established.

Key words: conditional discrimination, matching to sample, stimulus classes, stimulus-reinforcerrelations, pointing, mentally retarded adults

An operant is defined as a class of responsesfunctionally related to a given consequence(Skinner, 1953, p. 65). Given appropriate con-text, such responses are mutually substitut-able. For example, when deprived of water,one is likely to turn on faucets, open waterbottles, ask for water, and so on. If a numberof different stimuli each individually occasiona given response, then those stimuli can bemembers of a functional stimulus class. Par-alleling response classes, the defining charac-teristic is mutual substitutability of class mem-bers within a given context (cf. Sidman, 1977;Spradlin, 1977). The stimulus class concept isespecially appropriate when a variable appliedto one class member subsequently affects other

This research was supported in part by NICHD GrantsHD 22218, HD 17445, and HD 10210. Special thanksto Murray Sidman for this thoughtful comments on thisresearch. Thanks also to Joanne Kledaras for editorialhelp in preparing the manuscript. We gratefully acknowl-edge the cooperation of Vincent Strully and the staff ofthe New England Center for Autism (formerly EfficacyResearch Institute). Russell Maguire is currently withAmego, Inc. Reprint requests should be addressed to Wil-liam V. Dube, Behavioral Neurology Department, E. K.Shriver Center, 200 Trapelo Road, Waltham, Massachu-setts 02254.

members without explicit conditioning (e.g.,de Rose, Mcllvane, Dube, Galpin, & Stod-dard, 1988; Galloway & Petre, 1968; Silver-man, Anderson, Marshall, & Baer, 1986).

Current studies of stimulus class formationgenerally examine some form of conditionalstimulus control (Sidman, 1986). The focus istypically on stimulus-stimulus relations in-volving conditional and discriminative stimuliin matching-to-sample procedures (Fields &Verhave, 1987; Sidman & Tailby, 1982; Stod-dard & Mcllvane, 1986). For example, sub-jects may be trained to select comparison (dis-criminative) stimuli B1 and B2 conditionallyupon sample (conditional) stimuli Al and A2,respectively (AB matching), and also to selectcomparison stimuli Cl and C2 conditionallyupon samples B1 and B2, respectively (BCmatching). The left portion of Figure 1 illus-trates the four-term behavioral units estab-lished by this type of training (cf. Sidman,1986); Al, A2, BI, B2, Cl, and C2 representarbitrary visual stimuli (e.g., Greek letters),and RI represents a reinforcing stimulus (e.g.,food). In representing these units, we showboth the comparison stimulus selected and theone not selected. Without explicit tests, onecannot assume that the latter is irrelevant to

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NUMBER 1 (JANUARY)1989, 51, 65-76

WILLIAM V. DUBE et al.

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Fig. 1. Training and testing paradigm for a demonstration of stimulus class formation. Nonspecific reinforcementcontingencies are shown on the left, and performance-specific contingencies are shown on the right. The large lettersA, B, and C represent two-member sets of arbitrary visual stimuli. Arrows point from samples to comparison stimuli.Solid arrows represent performances established through direct training; dashed arrows represent emergent matchingperformances. The smaller letters (Al, A2, etc.) show four-term behavioral units that may result from AB and BCtraining. Sample stimuli are shown to the left of the vertical lines, and simultaneously displayed comparison stimuliare shown to the right. Selections of a comparison are shown by an encircled "R" (for "response") to the right of thestimulus selected. Stimuli that follow selections are shown to the right of the encircled "R." See text for details.

stimulus control of the response (see McIlvaneet al., 1987; Sidman, 1987; Stromer & Os-borne, 1982). In Figure 1, the trained perfor-mances are represented by solid arrows. If sub-jects then demonstrate BA, CB, AC, and CAmatching performances without explicit train-ing (as shown by the dashed arrows in Figure1), then the formation of two stimulus classesis documented (Al-Bl-Cl and A2-B2-C2).Stimulus class members are mutually substi-tutable with respect to their conditional (sam-ple) and discriminative (comparison) stimulusfunctions.

At this level of analysis, response-reinforcerrelations that define operants are rarely em-phasized. Under some circumstances, how-ever, relations of stimuli with reinforcers maybe critical to complete analysis of stimulusclasses. Such circumstances may occur whenmatching-to-sample procedures are pro-grammed with performance-specific reinforce-ment contingencies (cf. Peterson, 1984; Tra-pold, 1970), as illustrated in the right portionof Figure 1. With performance-specific con-tingencies, correct selections of B1 and C1 arefollowed by Rl (e.g., food), and correct selec-tions of B2 and C2 are followed by a differentreinforcing stimulus, R2 (e.g., water).

With both types of procedures-nonspecific(Figure 1, left portion) and performance spe-cific (Figure 1, right portion)-the resultingstimulus classes are defined by stimulus-stim-ulus relations among conditional and discrim-inative stimuli. However, with performance-specific procedures, one may ask if the classesalso are defined by stimulus-reinforcer rela-tions. If so, then the classes may be expandedto include new stimuli by establishing similarstimulus-reinforcer relations between thereinforcers, RI and R2, and the new stimuli(Dube, McIlvane, Mackay, & Stoddard, 1987).

In the present study, we examined the ex-pansion of stimulus classes with performance-specific reinforcement procedures like thoserepresented in the right portion of Figure 1.This study was a systematic replication andextension of our earlier work with mentallyretarded subjects (Dube et al., 1987). Figure2 illustrates the procedures of the present study,showing behavioral units that were establishedby baseline training and those that emergedon probe trials. (Procedures for our earlierstudy were similar to those in Figure 2. Dif-ferences will be noted below.) During training(Figure 2A), four pairs of visual stimuli weredisplayed on identity-matching trials (AA, BB,

66

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STIMULUS-REINFORCER RELATIONS

CC, and DD matching). The A, B, and Cstimuli were also displayed on arbitrary-matching trials; subjects were trained to per-form AB and BC matching tasks. Perfor-mance-specific reinforcement contingencieswere in effect throughout. Correct selectionsof Al, B1, C1, and D1 were followed by R1,and correct selections of A2, B2, C2, and D2were followed by R2.When the baseline performances were es-

tablished, probe sessions tested for the emer-gence of new behavior that had not been ex-plicitly conditioned (Figures 2B and C).Emergent arbitrary-matching performanceswith the A, B, and C stimuli (Figure 2B) weretested first. Emergence of these performanceswould indicate the formation of two stimulusclasses (AI-BI-CI and A2-B2-C2) similar tothose shown in Figure 1. Such class formationmight have at least two bases, either by itselfsufficient and not mutually exclusive of theother. The first is the trained arbitrary-match-ing performances AB and BC. The formationof stimulus classes after these relations havebeen established among sample and compar-ison stimuli has been demonstrated many timesbefore (e.g., Sidman & Tailby, 1982; Stoddard,1986). The second basis for class formation iscommon relations between the stimuli in eachclass and the specific reinforcers (i.e., Al, Bi,and Cl with RI; and A2, B2, and C2 withR2).

Emergence of the behavior shown in Figure2C would indicate that the D stimuli were alsomembers of classes with the A, B, and C stim-uli. Class membership of the D stimuli wouldhave to be based solely on specific stimulus-reinforcer relations, because the D stimuli hadnever been displayed simultaneously with theA, B, or C stimuli. Prior to the probe trials,the D stimuli had appeared only on DD iden-tity-matching trials.

After the probe sessions were completed, wereversed the contingencies for the identity-matching trials with the D stimuli (not shownin Figure 2). Correct selections of Dl werenow followed by R2 and those of D2 by Rl.This reversal provided a stringent control forD stimulus class membership based on somevariable other than the performance-specificreinforcement contingencies (e.g., primarystimulus generalization; cf. Sidman, 1987). Ifclass membership of the D stimuli dependedupon stimulus-reinforcer relations, a reversal

of those contingencies might disrupt-and per-haps reverse-that class membership (Dube etal., 1987). A new series of probe sessions ex-amined this possibility.As previously noted, the design of our earlier

study (Dube et al., 1987) was similar to thatshown in Figure 2. A major procedural dif-ference involved the history of food reinforcersRl and R2. In our previous study, the fooditems had explicitly defined discriminativefunctions, serving as matching-to-sample stim-uli along with spoken names, printed symbols,and junk objects. Testing revealed that allstimuli, including the food items, were mem-bers of stimulus classes. The present studyexamined whether class membership based onstimulus-reinforcer relations depended on therestricted set of conditions of our previous study.Specifically, we asked whether such member-ship could be shown even if reinforcers had noexplicit matching-to-sample functions.

METHODSubjectsTwo moderately mentally retarded males

(PN and JDB) served as subjects. They were20 and 14 years old, respectively. On the Pea-body Picture Vocabulary Test, their age-equivalent scores were 4.1 years and 3.8 years,respectively.

Apparatus and SettingTwo Macintosh® (Apple) computers were

used. Their screens (19 by 14 cm) displayedstimuli, and the subject responded by touchingthem. One computer was fitted with a touch-sensitive screen (MicroTouch Systems, Inc.)that permitted automatic data recording (Dube& McIlvane, in press). Modula-2 programscontrolled stimulus presentation and data col-lection.

Sessions were conducted 4 or 5 days perweek in a quiet room of the residential schoolwhere both subjects lived. The Macintosh ap-paratus was placed on a table, and the subjectsat facing it. The experimenter sat behind andslightly to one side, so that the subject couldnot observe the experimenter and the appa-ratus at the same time. Food reinforcers weredelivered manually by the experimenter froma supply kept on a small table next to him.With the apparatus that lacked a touch-

sensitive screen, the experimenter recorded the

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WILLIAM V. DUBE et al.

EMERGENT BEHAVIOR

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encircled "R" (for "response") to the right of the stimulusselected. Stimuli that followed selections are shown to theright of the encircled "R." Rl and R2 are reinforcingstimuli. See text for details.

subject's responses. Whenever the subjecttouched a response area on the screen (seematching-to-sample procedures, below), theexperimenter pushed a corresponding buttonon the computer's keyboard. When data re-cording was done manually, all sessions werevideotaped to permit reliability assessment.Reliability scores (agreements/trials) were ob-tained for about one third of the sessions, andscores were always 98% or better. The manualrecording method was used for all of PN'ssessions and for about half of JDB's baselinesessions; JDB's remaining baseline sessions andall of his probe sessions were conducted withthe touch-sensitive screen.

Reinforcer Preference TestingThis preliminary step determined two food

reinforcers of approximately equal preference.Through such tests, we sought to avoid re-sponse biases that can influence respondingwhen performance-specific reinforcers are used(Litt & Schreibman, 1981). Four food itemswere displayed two at a time in all possible

combinations; each combination was displayedfour times. On every such preference-test trial,the experimenter said "Take one" and thenrecorded the subject's choice. For both subjects,two foods were about equally preferred: ForPN, they were approximately 0.5 oz of cola(Rl) and a cheese puff (R2); for JDB, theywere cola (R1) and a piece of candy (R2).These tests also identified a third food itemthat each subject would take and eat reliably.These items, a fruit drop for PN and a pretzelfor JDB, were used in a pretraining phase.

Matching-to-Sample ProceduresThe matching-to-sample display consisted

of five "keys," 4.5 by 4.5 cm white squares ona gray field. One key was centered on the com-puter's screen and one key appeared in eachcorner. Sample and comparison stimuli ap-peared on the center key and on the four cornerkeys, respectively.

Every trial began when a sample stimulusappeared on the center key. A required sampletouch was followed immediately by the pre-sentation of comparison stimuli on two of thefour outer keys. The remaining keys wereblank, and the locations of comparison stimulivaried unsystematically across trials. Addi-tional touches of the sample, present through-out the trial, had no programmed conse-quences. A touch of a comparison stimulus wasfollowed by the disappearance of all stimulifrom the keys and consequences as follows.

Reinforcement ProceduresContinuous and intermittent reinforcement

schedules were used at different points in theexperiment. With continuous reinforcement,all correct selections were followed by melodictones, a flashing display on the computer screen,and a food item. The tones and visual displaypresented with food item Rl had very differentphysical characteristics from those presentedwith R2. These stimuli, also performance-spe-cific consequences, were judged to be highlydiscriminable from one another. A third visualdisplay-tone complex followed correct selec-tions during pretraining.

During the intertrial interval, all keys wereblank. The experimenter initiated the next trial(by means of a hand switch) only after thesubject had consumed the food (about 20 s forPN and 15 s for JDB). After incorrect selec-tions, the screen went black for 5 s and the trial

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ended. Thereafter, the keys were redrawn, anda 15- to 20-s intertrial interval began.With intermittent reinforcement, about one

fourth of the subjects' correct selections werefollowed only the intertrial interval (VR 1.3).Also, no blackout followed incorrect selections.

StimuliThe lower left portion of Figure 2 illustrates

the stimuli (approximately 2.5 by 2.5 cm) thatwere displayed on training and test trials.Stimuli used in pretraining were line drawingsof common objects (e.g., car, house, etc.) orsymbols (e.g., arrow, cross, etc., or Greek let-ters).

Matching-to-Sample Training ProceduresTwo methods were used to teach matching-

to-sample performances. One was a delayedprompting method (Sidman, 1977; Touchette,1971) in which correct comparison selectionwas prompted by the disappearance of the in-correct comparison. Over trials, the promptwas delayed progressively by 0.5 s followingeach correct matching selection; incorrect se-lections decreased the delay by 0.5 s. For eacharbitrary-matching performance, the learningcriterion was 16 consecutive trials on whichthe subject responded correctly before the dis-appearance of the incorrect comparison stim-ulus.The second method used stimulus fading

and was modeled after one described by Ro-senberger, Stoddard, and Sidman (1972). Cor-rect comparison selections were prompted bydisplaying the incorrect comparison less dis-tinctly. The apparent intensity of the S- stim-ulus was reduced by masking out an evenlydistributed portion of its pixels; on successiveprogram steps 0%, 25%, 50%, 75%, and finally100% of the pixels were displayed. The pro-gram advanced one step after three consecutivecorrect selections; the program backed up tothe previous step following any error. Again,the learning criterion was 16 consecutive un-prompted selections.

PretrainingIn introductory sessions, a simple discrim-

ination task was used to teach the subjects toscan and to touch stimuli on the screen. Theseprocedures, modeled after those of Sidman andStoddard (1966), have been described exten-sively elsewhere (Dube & McIlvane, in press).

Subjects next learned simultaneous identitymatching with pretraining stimuli. Every se-lection of the comparison stimulus that wasidentical to the sample was followed by thepretraining reinforcer. PN's identity-matchingperformances were accurate immediately, butJDB's were not. For the latter, the delayedprompting procedure was used to establishidentity matching. Identity-matching trainingcontinued until subjects performed errorlesslyfor at least one session.

Baseline TrainingIdentity matching to sample. Subjects first

performed identity matching with all stimuli(Sets A-D). Reinforcer-specific contingencieswere in effect on a continuous-reinforcementschedule. All correct selections of Al, B1, Cl,and Dl were followed by Rl, and those of A2,B2, C2, and D2 were followed by R2.

Arbitrary matching to sample. After four (forPN) or three (for JDB) sessions of identitymatching, subjects were taught the arbitrary-matching performances. On AB trials, Al andA2 were sample stimuli and Bl and B2 werecomparison stimuli. Selections of BI and B2conditionally upon Al and A2, respectively,were followed by RI and R2, respectively. OnBC trials, B1 and B2 were samples and C1and C2 were comparisons. Selections of C1and C2 conditionally upon Bi and B2, re-spectively, were followed by Rl and R2, re-spectively.

After the arbitrary-matching performanceswere learned, AB and BC trials were inter-mixed with identity-matching trials (AA, BB,CC, and DD trials), and the intermittent-re-inforcement schedule was introduced. A pos-sible advantage of intermixing trial types wasto establish a context in which there were twobases on which comparison stimuli could beselected, identical physical features or arbi-trarily defined relations with the sample. Thiscontext might prove helpful when D stimuliwere presented on arbitrary-matching trialsfor the first time (see below).

Stimulus Class ProbesA series of probe sessions tested for for-

mation of two stimulus classes: Al-Bi-Cl-DIand A2-B2-C2-D2. Two probe procedureswere used; they will be termed the "repeated-probe" and the "unique-probe" procedures.Subject PN received seven repeated-probe ses-

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WILLIAM V. DUBE et al.

Table 1

Results of baseline training. Where more than one trial type is reported on a single line (e.g.,AA, BB, CC), the number of trials of each type is equal. The number of training trials isshown, but not included in the correct/error (C/E) totals.

Subject Sessions Relation C/E Training trials

PN 1-4 AA, BB, CC, DD 143/15-8 AA, BB, CC 37/3

DD 20/0AB 100/4 28 delayed cue

9-15 AA, BB, CC 42/0DD 58/0AB 78/0BC 116/8 34 delayed cue

JDB 1-3 AA, BB, CC, DD 144/04-7 AA, BB, CC 24/0

DD 24/0AB 133/11 18 stimulus fading

8-14 AA, BB, CC 42/0DD 58/0AB 92/0BC 126/0 18 stimulus fading

sions. Results of these sessions led to the de-velopment of the unique-probe procedure; thisprocedure was used for PN's remaining probesessions and all of JDB's probe sessions. Fur-ther details and the rationale for the changewill be explained with the results. Additionalbaseline sessions were programmed occasion-ally as a review (e.g., when several days elapsedbetween experimental sessions).

Repeated-probe sessions. In each such ses-sion, six unreinforced probe trials were inter-spersed among 42 intermittently reinforcedbaseline trials. Baseline trials included 13 AB,13 BC, and 16 identity-matching trials. Inprobe sessions in which only A, B, and C stim-uli were displayed on probe trials, identity-matching trials included two AA, two BB, twoCC, and 10 DD trials; in probe sessions inwhich D stimuli were also displayed on probetrials, only 16 DD identity-matching trialswere included. All probe trials in a sessiontested potentially emergent relations involvingonly one set of samples and one set of com-parisons. In a CA probe session, for example,C1 and C2 were sample stimuli on three probetrials each, and Al and A2 were comparisonstimuli on all six trials. A given relation wasconsidered demonstrated when all of the sub-ject's probe selections within a session wereclass consistent (i.e., three selections of Al whenCl was the sample and three selections of A2when C2 was the sample).

Unique-probe sessions. In these sessions, agiven probe trial display appeared only once,and thus each probe trial tested a differentemergent relation. For example, PN's firstunique-probe session tested for the followingemergent relations: BlAl, B2A2, AlC1, A2C2,ClA1, and C2A2. Probe sessions could containtwo, four, or six probe trials. Probe trials wereinterspersed among 42 to 46 intermittentlyreinforced baseline trials which included 14 to16 AB trials, 14 to 16 BC trials, and two AA,two BB, two CC, and eight DD identity-matching trials. The criterion for demonstrat-ing probed relations was either six of six orseven of eight consecutive class-consistent re-sponses for each emergent arbitrary-matchingtask. With the unique-probe procedure, ofcourse, this criterion could be met only acrosssessions.

Reversed Reinforcement Contingencies for DStimuliAs outlined previously, the performance-

specific reinforcement contingencies were re-versed on all DD identity-matching trials.Correct selections of Dl were followed by R2,and those of D2 by RI. All other contingenciesremained as before. Thus, the baseline con-sisted of AA, BB, CC, AB, and BC trials withthe original performance-specific contingen-cies, and DD identity-matching trials with re-versed contingencies. Reinforcement was con-

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tinuous for the first session and intermittentin the second and subsequent sessions. Afterthree additional baseline sessions, stimulus-class probe sessions were conducted using theunique-probe procedure.

RESULTSPretraining

Both subjects learned the simple discrimi-nation without error in the first session. In twoidentity-matching sessions, PN responded cor-rectly on 76 of 80 trials. He met the pretrainingcriterion in his second session. Subject JDBmade six errors on 14 identity-matching trialsin his first pretraining session. The delayedprompting method was then used to teach theperformance directly, and he met the criterionin his fifth pretraining session. He then wasgiven 16 sessions of additional identity-match-ing pretraining.

Baseline TrainingIdentity matching to sample. The upper por-

tion of Table 1 summarizes the baseline train-ing. Both subjects displayed generalized (frompretraining) identity matching with the ex-perimental stimuli, performing virtuallyerrorlessly in four (PN) and three UDB) ses-sions.

Arbitrary matching to sample. PN learnedthe AB task in Sessions 5 through 8 and theBC task in Sessions 9 through 12, receiving28 and 34 delayed prompting trials, respec-tively. Intermittent reinforcement was intro-duced in Session 13. During baseline devel-opment, PN responded correctly on 178 of 182unprompted AB trials and on 116 of 124 un-prompted BC trials. He performed withouterror in Sessions 13 through 15.JDB's arbitrary-matching training was

conducted with the stimulus fading procedure.He learned the AB task in Sessions 4 through7 and the BC task in Sessions 8 through 10,both after 18 fading trials. Intermittent rein-forcement was introduced in Session 12. Dur-ing training, JDB responded correctly on 225of 236 unprompted AB trials and on each of126 unprompted BC trials. He performedwithout error in Sessions 12 through 14.

Stimulus Class ProbesSubject PN was given seven repeated-probe

sessions, 17 unique-probe sessions, and six ad-

Table 2

Results of repeated-probe sessions with Subject PN. Foreach session, the type of probe trial displayed is given inparentheses (see text for details). For each probe trial, theplus (+) or minus (-) indicates that a response was con-sistent or inconsistent, respectively, with stimulus classformation.

Probe Probe trialsession(type) 1 2 3 4 5 6

1 (CA) + + + + + +2 (BD) + + + - + +3 (BD) + + + + + -4 (BD) + + + - + -5 (DB) + + + - + -6 (CB) + - + + + -7 (CA) + + + + - +

ditional baseline sessions. JDB was given 14unique-probe sessions and two baseline ses-sions. During the probe sessions, both subjectsresponded virtually without error on baselinetrials.

Subject PN: Repeated-probe sessions. Resultsof PN's repeated-probe sessions are shown inTable 2. In Table 2, a plus (+) or minus (-)indicates a probe response that was consistentor inconsistent, respectively, with stimulus classformation. For example, class-consistent proberesponses were selections of Al and A2 con-ditionally upon C1 and C2, respectively; class-inconsistent responses were selections of A2 orAl conditionally upon Cl and C2, respec-tively. The first probe session included six CAprobes, and all probe responses were class con-sistent. Emergent CA matching provided evi-dence for the formation of the A-B-C classes.Four subsequent sessions examined the statusof the D stimuli, which had so far appearedonly on identity-matching trials. Initial testsexamined potential BD and DB relations. Ta-ble 2 (Probe Sessions 2-5) shows that PN didnot consistently select D1 and D2 conditionallyupon Bi and B2, respectively, and vice versa.Thus, these results did not document D stim-ulus class membership. Moreover, results ofsubsequent CB and CA sessions (Table 2, Ses-sions 6 and 7) were also not perfectly consistentwith class formation.

Data analysis suggested that the inconsistentresponding may have been an unintended re-sult of our probe methods. The left portion ofTable 2 shows that 20 of 21 selections on thefirst three probe trials of each session were

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WILLIAM V. DUBE et al.

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Fig. 3. Results of unique-probe sessions for SubjectsPN and JDB. Each bar represents the percentage of proberesponses that was consistent with stimulus class forma-tion. Letters below each bar show the emergent perfor-mance tested (sample comparison). Numbers in paren-theses below each bar show the number of probe trials foreach performance. See text for details.

class consistent. However, only 13 of 21 trialswere class consistent on the final three probes(Table 2, right portion). These data suggestedshifts in stimulus control as the session pro-gressed, perhaps because probe selections werenever reinforced. The unique-probe methodwas devised to circumvent this apparent prob-lem in measurement. We reasoned that effectsof nonreinforcement might be reduced if eachprobe display was presented only once in asession.

Subject PN: Unique-probe sessions. In thefirst four unique-probe sessions, probe trialsdisplayed only A, B, and C stimuli; probesdisplaying the D stimuli were included in sub-sequent sessions. PN's probe results are shownin the upper portion of Figure 3. The barsshow percentage of class-consistent selections;the total number of probe trials given is shownin parentheses below each bar. Class consis-tency was shown on 77 of 80 probe selections.Thus, the results documented formation of theA-B-C classes and expansion of those classesto include the D stimuli.

Subject JDB. The lower portion of Figure3 shows Subject JDB's probe results, all ob-tained with the unique-probe procedure. Inthe first five sessions, probe trials displayedonly A, B, and C stimuli; probes displaying

the D stimuli were included in subsequentsessions. With one exception, results for allprobed relations immediately met the criteriafor class formation (six of six or seven of eightconsecutive class-consistent selections). Theexception occurred on his first eight CD probes,when only six of eight selections were classconsistent. The final eight CD probe trialswere presented in a baseline in which the pro-portion of trials displaying C stimuli was in-creased (two AA, two BB, 10 CC, eight DD,10 AB, and 12 BC trials per session); all re-sponses were class consistent on these probes.In all, Figure 3 shows that 74 of 78 selectionswere class consistent, documenting class for-mation and expansion.

Reversed Reinforcement Contingencies for DStimuli

Both subjects were errorless in the first threebaseline sessions following reversal of the per-formance-specific contingencies on DD iden-tity-matching trials. Subject PN received 19probe sessions and three additional baselinesessions. JDB received 15 probe sessions andthree additional baseline sessions. Baselineperformances remained virtually errorlessthroughout probing. Probe session results forSubjects PN and JDB are shown in the upperand lower portions, respectively, of Figure 4.For both subjects, responses on BA, CB, AC,and CA probes remained class consistent.

Results of D stimulus class probes are plot-ted as the percentage of selections that wereconsistent with the reversed stimulus-reinforc-er relations (e.g., selecting Dl and D2 con-ditionally upon A2 and Al, respectively). Eachbar is divided in two. The left and right por-tions show results from equal numbers of probetrials in early and later probe sessions, re-spectively. For both subjects, initial probe re-sults showed immediate disruption of previousD stimulus class membership. (Maintainedclass membership would have produced 0%consistency with the prevailing D stimulus-reinforcer relations.) Moreover, as probingcontinued, results became increasingly moreconsistent with reversed D stimulus classmembership. The right portions of the bars inFigure 4 show class consistency on 30 of PN's32 selections and on all 24 of JDB's selections.PN's DA and DC performances were excep-tions initially, as suggested by the larger num-ber of probe trials that were given. In each

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case, the final eight probe trials were given ina baseline that was changed to increase thenumber of trials displaying A and C stimuli,respectively (for DA probes: 12 AA, one BB,one CC, 10 DD, six AB, and six BC trials persession; for DC probes: one AA, one BB, 12CC, 10 DD, six AB, and six BC trials persession).

DISCUSSIONThis study systematically replicates and ex-

tends our earlier work on stimulus classes andperformance-specific consequences (Dube etal., 1987). Stimulus-reinforcer relations servedas the basis for stimulus class membership ina context in which the reinforcers had no ex-plicitly developed sample or comparison func-tions. Thus, such class membership does notdepend on the restricted set of procedures ofour previous study. Indeed, findings from otherareas of our research program suggest thatthese results may be only one example of a

much broader phenomenon (cf. de Rose et al.,1988; de Rose, Mcllvane, Dube, & Stoddard,1988).The reversal of D stimulus class member-

ship provided a stringent control for artifactualresults due to primary stimulus generalization(cf. Sidman, 1987) or arbitrary class assign-ment (Saunders, Saunders, Kirby, & Spradlin,1988; Stromer, 1986). When performance-specific reinforcement contingencies for the Dstimuli were reversed, subsequent probe re-

sults showed that the stimulus class member-ship of those stimuli also reversed. This resultstrongly supports a conclusion that D stimu-lus class membership depended on specificstimulus-reinforcer relations. The reversalprocedure used here can be contrasted with themore typical control for stimulus-reinforcerrelations wherein stimuli and reinforcers arerandomly (procedurally) associated (Rescorla,1967). One may ask whether the latter mayoffer an advantage, that of demonstrating con-ditions under which reinforcers do and do notbecome class members. The random controlcondition is not straightforward in matching-to-sample contexts, however. In the presentexperiment, for example, it would require cor-rect selections of Dl or D2 on identity-match-ing trials to be followed equally often by Rland R2 (cf. Litt & Schreibman, 1981). Suchnonspecific contingencies would provide no ba-

1 1 PN

f50

BA CB AC CA AD DA BD e8 CD DC(10) (10) (10) (10) (8) (16) (8) (8) (8) (16)

BA CB AC CA AD D M 6 ) D(10) (11) (11) (10) (8) (8) (8) (8) (8) (8)

EMERPENTPERFOPIMCESTSTED(NUMBER OF PROBE TRIALS)

Fig. 4. Results of probe sessions for Subjects PN andJDB following reversal of specific reinforcement contin-gencies for D stimuli on baseline trials. Each bar repre-sents the percentage of probe responses that was consistentwith stimulus class formation (see text). Letters beloweach bar show the emergent performance tested (samplecomparison). Numbers in parentheses below each bar showthe number of probe trials for each performance. Barsdivided in two show results of the first half (left portion)and second half (right portion) of the probe trials. See textfor details.

sis for selection on subsequent probe trialstrials which nonetheless demand some re-sponse. Consistent conditional behavior couldemerge based on primary stimulus general-ization or arbitrary assignment. However, therandom condition could be very useful in ana-lyzing stimulus classes that were defined orig-inally by performance-specific reinforcementcontingencies. Also, a design that included both(a) alternation of specific and nonspecific re-inforcement conditions and (b) repeated re-versals of specific reinforcement contingenciesmay be useful for the analysis of stimulus classmembership that is conditional upon prevail-ing stimulus-reinforcer relations.The present study also defined more pre-

cisely the classes established via the perfor-mance-specific reinforcement procedure. Ourprevious study did not document the formationof equivalence classes, because the use of au-ditory stimuli in training precluded some testsnecessary to document equivalence accordingto criteria outlined by Sidman and Tailby(1982); the use of all-visual stimuli in the pres-ent study permitted the full complement oftests, as follows. Typical stimulus-equivalence

73

WILLIAM V. DUBE et al.

research has used matching-to-sample meth-ods to show that the relations (r) among classmembers possess the logical properties of re-flexivity (e.g., ArA), symmetry (e.g., if ArB,then BrA), and transitivity (e.g., if ArB andBrC, then ArC). According to these criteria,the A-B-C classes were clearly equivalenceclasses. Both subjects displayed generalizedidentity matching with the experimental stim-uli, a test of reflexivity. Both subjects givenAB and BC training then proved immediatelycapable of BA and CB performances, tests ofsymmetry. The same training also establishedthe basis for the AC performance, a test oftransitivity, and its symmetric counterpart, CA.Were the D stimuli also members of the

equivalence classes? Apparently, they were.Generalized DD identity matching demon-strated reflexivity. Although no arbitrary-matching performances involving the D stim-uli were trained directly, the emergentmatching performances indicate stimulusequivalence. All relations between the D stim-uli and the A-B-C class members were sym-metric. No cases were seen in which, for ex-ample, ArD did not imply DrA. Further, therelations were always transitive. No cases wereseen in which, for example, ArB and BrD didnot imply ArD.

Given the preceding facts, one is led next toask about the status of the reinforcers R1 andR2 in the A-B-C-D equivalence classes. Somestatus must be inferred, because D stimulus-class membership depended on relations withthose reinforcers. Because reinforcers werenever displayed as sample or comparison stim-uli, the usual tests for equivalence were notpossible. Nonetheless, it may be meaningful toinfer that the reinforcers were also membersof the equivalence classes. The inferential pathparallels that for combined tests of symmetryand transitivity in sample-comparison rela-tions (Sidman & Tailby, 1982). Such tests ex-amine the status of, for example, BC and CBrelations after the AB and AC relations areestablished by direct training. Emergence ofthe transitive BC performance requires ArBsymmetry: If BrA (ArB symmetry) and ArC(established by the training contingencies), thenBrC (transitivity). Similarly, emergence of CBrequires ArC symmetry: if CrA (ArC sym-metry) and ArB (established by the trainingcontingencies), then CrB (transitivity). Notethat these tests never present the A stimuli as

comparison stimuli; BrA and CrA relationsare derived from the emergence of BC and CBperformances. Now consider the emergent ADand DA conditional performances in the pres-ent experiment. The relevant history was, ofcourse, the relations of the A and D stimuliwith the performance-specific reinforcers (R).One may express these as relations ArR andDrR. By the logic of transitivity, the AD per-formance seems to require relations ArR andRrD (the symmetric counterpart of the directlyconditioned DrR). By the same reasoning, theDA performance would seem to require re-lations DrR and RrA (the symmetric coun-terpart of the directly conditioned ArR). Thus,the emergence of AD and DA performancesindicates that the ArR and DrR were bothsymmetric and transitive; similar cases may bemade with respect to BrR and CrR in relationto DrR. Viewed in this way, the stimulus-reinforcer relations meet the requirements forequivalence relations, even though the rein-forcers never appeared as matching-to-samplestimuli.One implication of stimulus-reinforcer

equivalence relations is that they might haveprovided a sufficient basis for all of the emer-gent arbitrary-matching performances that weobserved. Applying the reasoning outlined inthe preceding paragraph, the AA, BB, CC,and DD identity-matching performances andthe specific consequences by themselves mighthave established the A-B-C-D classes; the ABand BC training might have been redundant.However, one can argue plausibly that AB andBC training might have been critical to theemergent arbitrary-matching performances,including those that involved D stimuli. It ispossible that it was necessary to establish theA-B-C equivalence classes first and only thencould the D stimuli be added via the stimulus-reinforcer route. It is also possible that the ABand BC training was necessary because it es-tablished the arbitrary-matching context. Hadthe subjects experienced only identity match-ing with specific consequences, then the probetrials would for the first time display samplesand comparison stimuli that were all physi-cally dissimilar from one another. (This secondpossibility might indicate only the need for arecent history of arbitrary matching with anystimuli, and not necessarily with those usedfor the experimental tests.)Further study willbe necessary to clarify these issues.

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STIMULUS-REINFORCER RELATIONS 75

Mackay and Sidman (1984) have suggestedthat studies of stimulus classes and equivalencerelations can help in formulating an accountof some types of linguistic processes. The pres-ent line of inquiry may prove relevant to thisenterprise, because of a possibly importantparallel with functional analysis of verbal be-havior (Skinner, 1957). We refer to the dis-tinction between mands and tacts. A mandcharacteristically specifies its consequences(e.g., "Give me water"), but the tact does not(e.g., "That's water"). Our work suggests thatequivalence-class membership can be based oncommon relations with specific consequences.Do such classes differ qualitatively from thoseestablished with nonspecific reinforcementprocedures? If so, behavioral processes under-lying the reported functional independence ofmands and tacts (Lamarre & Holland, 1985)might be amenable to analysis with condi-tional-discrimination procedures. Moreover,stimuli can be members of different classes indifferent contexts (cf. Lazar & Kotlarchyk,1986; Wulfert & Hayes, 1988). It seems pos-sible that a member of a class defined by spe-cific consequences could at other times be amember of a class that was not so defined. Ifso, then analyses of processes underlying func-tional interdependence of mands and tacts(Skinner, 1957, p. 188) would also be feasible.

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Received October 6, 1987Final acceptance September 12, 1988