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NODAL STRUCTURE AND STIMULUS RELATEDNESS IN EQUIVALENCE CLASSES:POST-CLASS FORMATION PREFERENCE TESTS

PATRICIA MOSS-LOURENCO

WESTCHESTER INSTITUTE FOR HUMAN DEVELOPMENT

AND

LANNY FIELDS

QUEENS COLLEGE OF THE CITY UNIVERSITY OF NEW YORK

Three experiments used postclass formation within-class preference test performances to evaluate theeffects of nodal distance on the relatedness of stimuli in equivalence classes. In Experiment 1, two 2-nodefour-member equivalence classes were established using the simultaneous protocol in which all of thebaseline relations were trained together, after which all emergent relations probes were presentedtogether. All training and testing was done using match-to-sample trials that contained two comparisons.After class formation, the effects of nodal distance were evaluated using within-class preference tests thatcontained samples and both comparisons from the same class. These tests yielded inconsistentperformances for most participants. Experiment 2 replicated Experiment 1, but a third null comparisonwas used on all trials during class formation. Thereafter, virtually all of the within-class probes, for allparticipants, evoked performances that were consistent with the predicted effects of nodal distance, thatis, the selection of comparisons that were nodally closer to the samples. It appears, then, that theestablishment of the equivalence classes with a third null comparison induced control by nodal structureof the classes. Experiment 3 demonstrated the generality of these findings with larger classes thatcontained more nodal separations, that is, three-node five-member classes. Emergent-relations testsconducted immediately after the within-class tests showed the classes to be intact. Thus, the differentialrelatedness of stimuli in a class or their interchangeability depended on the content of a test trial: within-class probes occasioned responding indicative of differential strength among the stimuli in the class, whilecross-class tests occasioned responding indicative of interchangeability of stimuli in the same class.

Key words: equivalence class, nodal structure, nodal distance, within-class preference, matching-to-sample, college students

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An equivalence class contains a finite num-ber of physically disparate stimuli all of whichbecome related to each other after thetraining of some conditional discriminationsamong the stimuli. Assuming the stimuli in apotential class are represented by the letters,A, B, C, D and E, a five-member equivalenceclass can be established by training fourbaseline relations such as AB, BC, CD, and

DE. The formation of such a class would thenbe documented when the presentation of onestimulus in the set occasions the selection ofany other stimulus in the set (Fields &Verhave, 1987). This can be accomplishedwith the presentation of the untrained probesBA, CB, DC, ED, AC, AD, AE, BD, BE, CE, CA,DA, EA, DB, EB, and EC (Fields & Verhave,1987; Sidman, 1994; Sidman & Tailby, 1982).If two classes are being established, each probewould contain a sample stimulus from oneclass and at least two comparison stimuli, onefrom each class. The selection of the compar-sion from the same class as the sample wouldindicate control of behavior by class member-ship. That sort of selection by all probes woulddocument the formation of the equivalenceclasses. Such a pattern of conditional selectionwould also indicate that the stimuli in the classare functionally interchangeable or substitut-able for each other (Sidman, 1994). Thesubstitutability of the stimuli documented by

This research was conducted with support from PSC-CUNY Research Award 61669-00-39 and CUNY Collabora-tive Research Grant 80209-09-13. Portions of these dataappeared in a doctoral dissertation submitted by the firstauthor to The Graduate Center of The City University ofNew York. We thank Xiqiang Zhu for his assistance in thedevelopment of the software used to conduct theexperiment.

Correspondence may be addressed to Patricia Moss-Lourenco, Department of Psychology, Queens College/CUNY, 65-30 Kissena Blvd., Flushing, NY 11367 (e-mail:[email protected]) or Lanny Fields at the same address (e-mail: [email protected]).

doi: 10.1901/jeab.2011.95-343

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR 2011, 95, 343–368 NUMBER 3 (MAY)

343

these tests also implies that the members of anequivalence class are equally related to eachother (Fields & Verhave, 1987). Of note, theseresults are obtained from trials that containstimuli in the same and different classes.

An alternative view is that stimuli in anequivalence class are not equally related toeach other (Fields & Moss, 2007). This notionhas its roots in the findings described inexperiments that have explored the learningof derived lists (Ebbinghaus, 1913), seriallearning (Slamecka, 1985), and semanticmemory networks (Collins & Loftus, 1975;Collins & Quillian, 1969). In all of these cases,the stimuli in a list or network were separatedby a variable number of nodal stimuli and thelikelihoods of responding were inversely relat-ed to the number of nodes that separated thestimuli in the lists or the networks. In all ofthese experiments, differential responding wasoccasioned by relations between stimuli in thesame class.

These results led Fields and Verhave (1987)to opine that under some conditions, therelatedness of stimuli in the same equivalenceclass should also be an inverse function of thenodal distance that separates the stimuli in anequivalence class. In the example above, thetraining of AB, BC, CD, and DE would lead tothe establishment of a five-member equiva-lence class with a nodal structure representedas ARBRCRDRE (Fields, Adams, & Verhave,1993a; Fields & Verhave, 1987). In thisstructure some stimuli are related to otherstimuli by training to a common stimulus. Anode is defined as any stimulus that links atleast two other stimuli in an equivalence class.Furthermore, nodal distance is defined as thenumber of nodes that link two stimuli withinan equivalence class (Fields & Verhave, 1987).Thus, one node (C) separates B and D whilethree nodes (B, C, D) separate A and E.According to the associative distance view ofrelatedness of stimuli in equivalence classes,because fewer nodes separate the stimuli in BDthan AE, the relational strength of BD shouldbe greater than that of AE, and likewise forother relations with different nodal spreads.

These predictions have been supportedusing performances obtained under a rangeof testing conditions. Specifically, when thedelayed emergence of equivalence classes wasdemonstrated, during the initial test block, thedegree of class-consistent responding pro-

duced by derived-relations probes was aninverse function of the nodal distance thatseparated the stimuli in each derived relation(Bentall, Jones, & Dickins, 1998; Fields, Ad-ams, Verhave, & Newman, 1990; Kennedy,1991; Kennedy, Itkonen, & Lindquist, 1994;Sidman, Kirk, & Willson-Morris, 1985; Spencer& Chase, 1996). In addition, the order inwhich the derived relations reached criterionwas a direct function of nodal distance (Fieldset al., 1990; Kennedy et al., 1994). Further-more, latency occasioned by derived relationswas a direct function of nodal distance(Bentall et al.,1998; Kennedy et al., 1994;Spencer & Chase, 1996; Tomanari, Sidman,Rubio, & Dube, 2006; Wulfert & Hayes, 1988).In another study, Fields, Adams, Verhave, andNewman (1993b) first established three-nodefive-member equivalence classes. They thentrained a response to one of the classmembers, and finally presented the remainingclass members in repeated test blocks untiltransfer of responding was complete. For someparticipants, that response generalized gradu-ally to the other class members. For theseparticipants, on the first test block, the degreeof generalization was an inverse function ofnodal distance that separated the trainingstimulus from the other class members. Withrepeated testing, the accuracy of respondingincreased to 100% in an order that was aninverse function of nodal distance.

In these studies, the effects of nodal distancethat were observed during the delayed emer-gence disappeared once the classes were fullyformed. This could mean that the effects ofnodal distance could have been transient,disappearing permanently after the formationof the equivalence classes. Alternatively, theeffect of nodal distance could have beenpermanent, but no longer influenced theperformances occasioned by the prevailingtest conditions. In such a case, nodal distanceshould still influence responding in postclassformation tests, a position supported by theresults of the following experiments.

Before describing these studies, it is impor-tant to note two potential factors that wereconfounded with nodal distance in the previ-ously mentioned studies. The baseline rela-tions were trained in a serial manner thatcorresponded to the nodal separation of thestimuli in the classes. In addition, due toserialized training, the number of presenta-

344 PATRICIA MOSS-LOURENCO and LANNY FIELDS

tions of each baseline relation was alsocorrelated with nodal distance. Thus, theeffects attributed to nodal distance might havebeen driven by either of these factors alone orin combination. These problems were avoidedin the next two experiments by the establish-ment of equivalence classes using the simulta-neous protocol, a procedure in which allbaseline relations were trained on a concur-rent basis (i.e., in the same blocks), werepresented an equal number of times, and allderived-relations probes were introduced on aconcurrent basis.

Dual-Option Function Transfer Tests

Fields, Landon-Jimenez, Buffington, andAdams (1995) used the simultaneous protocol(SIM) to establish two 5-member equivalenceclasses by training AB, BC, CD, and DE.Equivalence classes were formed by only 2 ofthe 12 participants. After class formation, theywere trained to emit different and incompat-ible responses in the presence of the Astimulus and the E stimulus in the same class.Finally, all class members were then presentedseparately and without feedback. Under thoseconditions, the frequency with which the A-based response was occasioned by the B, C,and D stimuli was an inverse function of nodaldistance. Similarly, the frequency with whichthe E-based response was occasioned by the D,C, and B stimuli was an inverse function ofnodal distance. This pattern of respondingremained stable with test repetition, and thusprovided a postclass formation steady-statemeasure of the effects of nodal distance onresponding. These performances could haveoccurred only if nodal structure was theprimary determinant of relational strengthamong the stimuli in the parent equivalenceclasses.

Fields and Watanabe-Rose (2008) extendedthese findings by the establishment of two 4-node six-member equivalence classes throughthe training of AB, BC, CD, DE, and EF underthe simultaneous protocol. After testing forthe emergence of all derived relations, differ-ent responses were trained to the C and Dstimuli of each class using a successive discrim-ination procedure. Finally, all 12 stimuli in thetwo classes were presented singly, many times,and in randomized order with no informativefeedback. Only 4 of 15 participants in theexperiment formed the equivalence classes.

For both classes for 2 participants and oneclass for 1 participant, the response trained tothe C stimulus in a class, then, generalizedessentially completely to the A and B stimulibut rarely to the D, E, and F stimuli in thatclass. Likewise, the response trained to the Dstimulus generalized essentially completely tothe E and F stimuli but rarely to the A, B, andC stimuli. Therefore, the two 6-memberequivalence classes were bifurcated into two3-member equivalence classes each: A1-B1-C1,A2-B2-C2, D1-E1-F1, and D2-E2-F2 as predictedby nodal structure. These results could haveoccurred only if the stimuli in each equiva-lence class were related to each other on apermanent basis and the relational strengthamong the class members was a function ofnodal distance. Results for one class for 1participant and for both classes for anotherparticipant, however, did not demonstratebifurcation by nodal structure. These resultsindicate that nodal structure was not the onlydeterminant of responding in the dual-optiontransfer tests.

To summarize, both of these studies estab-lished equivalence classes using the simulta-neous protocol, which eliminated the con-founding of the effects of serial order ofpresentation and number of presentations ofstimuli with nodal distance. On the negativeside, however, the use of the simultaneousprotocol reduced the percentage of partici-pants who formed classes and were then ableto provide data that could be used to evaluatethe differential relatedness of stimuli in theequivalence classes.

Within-Class Preference Tests

Within-class preference testing is anothermethod for showing the permanent postclassformation effects of nodal distance. Presentedin a matching-to-sample format, these testspermit direct comparisons of the relativestrengths of any two relations in an equiva-lence class that share the same samplestimulus. Fields, Adams, and Verhave (1989;as cited in Fields et al., 1993b) established two3-node five-member classes by training AB, BC,CD, and DE. The formation of two equivalenceclasses with a nodal structure represented asARBRCRDRE was documented by class-consistent responding on the derived relationsprobes. Thereafter, within-class preferencetests were presented in a match-to-sample

WITHIN-CLASS PREFERENCE NODAL DISTANCE EFFECTS 345

format in which each trial contained onesample and two comparisons from the sameclass. For example, in a BDE test for class 1, theB1 stimulus was presented as a sample with theD1 and E1 stimuli as comparisons. Therelation between B1 and D1 constituted aone-node transitive relation, while B1 and E1constituted a two-node transitive relation. Themany trials that were presented evaluateddifferent nodal spreads between each compar-ison and the sample on that trial. Participantsvirtually always selected the comparison thatwas nodally closer to the prevailing sample.Thus, in an ABC probe, B was preferred to C,in an ACD probe, C was preferred to D, in anACE probe, C was preferred to E, etc. Thesedata then demonstrated that preferences werean inverse function of nodal distance thatseparated the stimuli in the structure of theclass; that is, the differential relatedness ofstimuli in an equivalence class was determinedby nodal structure.

In the above study, the equivalence classeswere formed using the simple-to-complex(STC) protocol (Fields, Reeve, Rosen, Varelas,Adams, Belanich, & Hobbie, 1997). Thisprotocol involves the systematic presentationof training and testing trials. Specifically, thebaseline relations were established in a serialorder that was completely correlated with thenodal distances that separated the stimuli in aclass. In addition, the number of training trialspresented during class formation was alsocorrelated with nodal distance. Thus, theresults of the within-class preference tests,which were attributed to nodal distance, couldalso have reflected serial order and/or thenumber of trials used to establish eachbaseline relation. Alligood and Chase (2007)addressed the issue of unequal number oftraining trials by the establishment of four-node six-member equivalence classes wherethe number of training trials was held constantfor each of the baseline relations. The post-class formation within-class preference teststypically occasioned the selection of nodallyproximal stimuli which supported the viewthat the relational strengths among stimuli inan equivalence class are inversely related tonodal distance. As with Fields et al. (1989; ascited in Fields et al., 1993b), however, theequivalence classes were established using aserialized training and testing protocol. Thus,the results reported by Alligood and Chase

(2007) could still have reflected the effects ofserial order rather than nodal distance. Tosummarize, there is still no measure of theunconfounded effects of nodal distance on theperformances evoked by postclass formationwithin-class preference tests.

EXPERIMENT 1

As noted earlier, the establishment ofequivalence classes under the simultaneousprotocol eliminates the confounding effects ofnodal distance and the serially orderedtraining of baseline relations. In this experi-ment, participants attempted to form equiva-lence classes using the simultaneous protocolbefore assessing the effects of nodal distanceusing postclass formation within-class prefer-ence tests. When, however, equivalence classesare established using the simultaneous proto-col, only a small percentage of participantsform classes (Buffington, Fields, & Adams,1997; Fields et al., 1997; Fields et al., 1995).Thus, any effects of nodal distance might belimited to the small percentage of individualswho can form equivalence classes under thesimultaneous protocol. The issue of yield andthus representativeness of outcome was ad-dressed by the incorporation of a yield-enhancing procedure described by Fields etal. (1997). Specifically, they increased thepercentage of participants who formed equiv-alence classes under the simultaneous proto-col (yield) by having participants learn otherequivalence classes using the simple-to-com-plex protocol before attempting to learn newequivalence classes under the simultaneousprotocol. A similar approach was used in thepresent experiment to increase the percent-age of participants who would form newequivalence classes under the simultaneousprotocol. Thus, the effects of nodal distancecould be evaluated with a representativesample of participants drawn from the generalpopulation.

METHOD

Participants

The participants were 10 undergraduatestudents enrolled in a course in IntroductoryPsychology at Queens College/CUNY. Partici-pation in the experiment fulfilled one of thecourse requirements. All students read and


signed the informed consent statement beforeparticipating in the experiment, which wasconducted in one 2.5- to 3.5-hr session.

Apparatus

Hardware and software. The experiment wasconducted with an IBM-compatible computerthat displayed all stimuli on a 15-inch VGAmonitor. Responses consisted of touchingspecific keys on a standard keyboard. Theexperiment was controlled by custom softwarethat programmed all stimulus presentationsand recorded all keyboard responses.

Stimuli. Ten nonsense syllables were usedduring preliminary training. In class 1, theywere BAK (U1), NUC (V1), WEX (W1), HUZ(X1), SIV (Y1); in class 2 the stimuli were REJ(U2), TUD (V2), GIP (W2), DIH (X2), andMEL (Y2). Eight nonsense syllables were themembers of the equivalence classes formedunder the simultaneous protocol. In class 1,they were QIJ (A1), TUW (B1), COH (C1),MEP (D1); in class 2, they were VIF (A2), KUY(B2), XOL (C2), and GEZ (D2). All stimuliwere presented on a computer monitor asblack letters centered in white 5-cm 3 5-cmsquares with black borders.

Procedure

Trial format and contingencies. All trials in theexperiment were presented in a simultaneousmatching-to-sample format (Cumming & Ber-ryman, 1965). Each trial involved the presen-tation of a sample and two comparison stimuli.The samples were drawn from one of two sets.The positive comparison (Co+) was from thesame set as the sample on that trial and thenegative comparison (Co2) was from theother set. The sample was presented on theupper portion of the monitor and was cen-tered horizontally. The positive and negativecomparisons were presented below the sampleand to the left and right of the sample. Theupper edges of the comparisons were belowthe lower edge of the sample. The right edgeof the left comparison was to the left of the leftedge of the sample, and the left edge of theright comparison was to the right of the rightedge of the sample. The location of thepositive comparison was randomly assignedwith the stipulation that it was presented thesame number of times on the left and on theright in a block of trials.

Trial block organization and feedback reduction.Each phase of the experiment consisted ofblocks of trials. In all phases, the trials in ablock were presented in a randomized orderwithout replacement. A trial began when‘‘Press ENTER’’ appeared on the screen.Pressing the ENTER key cleared the screenand a sample stimulus was displayed. Pressingthe space bar added the two comparisonstimuli to the display. During a trial, thecomparisons on the left and the right wereselected by pressing the 1 or 2 key, respective-ly. A comparison selection cleared the screenand immediately displayed a feedback messagecentered on the screen.

When informative feedback was presented, a‘‘RIGHT’’ or ‘‘WRONG’’ message appearedon the monitor, and depended on theaccuracy of the comparison selection. Themessage remained on the screen until theparticipant pressed the R key (R for RIGHT)in the presence of the word ‘‘Right’’ or the Wkey (W for WRONG) in the presence of theword ‘‘Wrong.’’ These responses demonstrat-ed that the participant discriminated thefeedback information. During some trainingand all testing trials, uninformative feedbackwas presented after a comparison selection.On these occasions a dashed line that brack-eted the letter E (i.e., - - E - -) appeared on themonitor and remained on until the participantpressed the E key, which served as anobserving response for the uninformativefeedback. The occurrence of an appropriateR, W, or E response cleared the monitor,ended the trial, and enabled the start of thenext trial (Fields et al. 1995).

At the start of training, all of the trials in ablock resulted in the presentation of informa-tive feedback after each comparison selection,that is, 100% feedback. The block was present-ed repeatedly with 100% feedback until alltrials occasioned the selection of correctcomparisons, that is, produced 100% correctresponding which was the mastery criterion.Thereafter, the percentage of trials in a blockthat produced informative feedback was re-duced to 75%, 25%, and finally to 0% as longas the mastery criterion was maintained in ablock. During feedback reduction, a randomgenerator determined the trials that producedinformative feedback. Each block ended withthe on-screen message, ‘‘Press ENTER tobegin the next block.’’ If 100% correct


responding was not achieved within threeblocks at a given feedback level duringtraining, the participant was returned to theprevious feedback level during the next block.

Experimental Phases

Phase 1: Instructions and keyboard familiariza-tion. The experiment began with the presen-tation of the following on-screen instructions:

Thank you for volunteering to participate inthis experiment. PLEASE DO NOT TOUCHANY OF THE KEYS ON THE KEYBOARDYET! In this experiment you will be presentedwith many trials. Each trial contains three orfour CUES. These will be familiar and unfa-miliar picture images. YOUR TASK IS TODISCOVER HOW TO RESPOND CORRECT-LY TO THE CUES. Initially, there will also beINSTRUCTIONS that tell you how to respondto the cues, and LABELS that will help you toidentify the cues on the screen. The labels andthe instructions that tell you which KEYS topress will slowly disappear. Your task will be toRESPOND CORRECTLY to the CUES and theINSTRUCTIONS by pressing certain keys onthe computer’s keyboard. The experiment isconducted in phases. When each phase ends,the screen will sometimes tell you how you did.If you want to take a break at any time, pleasecall the experimenter. PRESS THE SPACEBARTO CONTINUE.

After pressing the space bar, participantswere trained to emit the appropriate keyboardresponses to complete a trial. This phaseinvolved the repeated presentation of a blockof 16 trials. Trials contained three Englishwords, such as KING, QUEEN, and CAMEL.The semantic relation between the sampleword (e.g., KING) and one of the comparisons(e.g., QUEEN) was used to prompt theselection of the correct comparison. Thewords RIGHT or WRONG followed eachcomparison selection. Correct responding tothe stimuli in a trial was facilitated by thepresentation of instructional prompts (e.g.,‘‘Make your choice by pressing 1 or 2’’, ‘‘PressR to continue’’, ‘‘Press W to continue’’, or‘‘Press E to continue’’) which was systemati-cally deleted across trials as long as theparticipant made correct responses. For fur-ther details, see Fields et al. (1990) or Fields etal. (1997). Phase 1 ended when the sampleand comparison stimuli were presented with-out prompts, and performance was at 100%accuracy during a single block.

Phase 2: Preliminary training using the simple-to-complex protocol. Preliminary training involvedthe formation of two 3-node five-memberequivalence classes using a variation of asimple-to-complex protocol which is detailedin Table 1. In this protocol, the serial estab-lishment of the baseline relations was inter-leaved with tests to assess the emergence of thenew relations that could be derived from thealready documented baseline relations. Afterthe acquisition of each baseline relation,participants were presented with two blocksof overtraining. If responding in a test blockwas less than 87% accurate, the block wasrepeated with informative feedback presentedon all trials and at the end of the test block,until responding on that block met the abovementioned mastery criterion. If Phase 2 wascompleted within 2 hr, the participant ad-vanced to Phase 3. Participants who spentmore than 2 hr in Phase 2 were excused fromthe experiment.

Phase 3: Equivalence class formation under thesimultaneous protocol. The aim of this phase wasto establish two new four-member equivalenceclasses with an ARBRCRD nodal structure.The protocol began with the concurrenttraining of the baseline conditional discrimi-nations for Class 1 (A1–B1, B1–C1, and C1–D1) and Class 2 (A2–B2, B2–C2, and C2–D2).During each training block, each samplestimulus was presented on two trials (thepositive comparison appeared on the left onone trial and on the right on the other trial).The training block was repeated until oneblock produced 100% accuracy. Thereafter,feedback was reduced until the baselinerelations were maintained in the absence offeedback. Once all baseline relations wereestablished and maintained with no informa-tive feedback, the participants were presentedwith an emergent relations test that containedall of the baseline, symmetrical, one- and two-node transitive and equivalence relationsprobes. Four trials were presented for eachrelation; two trials for the relation from Class 1and two from Class 2 in which the position ofthe Co+ was on the right for one trial and theleft for the other trial. All of the trials thatmade up the emergent relations test werespread across four test blocks, 12 trials per testblock, for a total of 48 trials. Each blockconsisted of one trial for each relational typeso that each of the four trials mentioned above


occurred one time across all four blocks.Within a block all trials were presented in arandomized order without replacement. Thistest (combination of four blocks) was repeatedup to four times or until the participantperformed with at least 92% accuracy on eachof the four blocks.

Phase 4: Within-class preference tests. Once theparticipant passed the emergent relations test,the effects of nodal distance were assessed.The differential strength of relations in thetwo-node four-member equivalence classes wasmeasured using within-class preference teststhat involved the presentation of trials thatcontained a sample and two comparisons fromthe same class. The comparisons differed interms of the nodal distance that separatedeach from the sample. Each combination of aspecific sample and two comparisons will becalled a probe type. Each probe type wasdesignated with three letters, the first of whichrepresents the sample, the second of whichdesignates the comparison that was nodallyproximal to the sample, and the third letterdesignates the comparison that was nodallydistal to the sample. For example, a probe typedesignated as ACD contained A as the samplewith C and D as the comparisons, where C andD were one and two nodes removed from thesample stimulus, respectively.

The within-class preference tests consistedof the presentation of four within-class probeblocks. Each probe block consisted of thepresentation of two probe types which arereferred to as a probe pair. The same probepair was presented in a block for both Class 1and Class 2. Trials for each probe type for agiven class were presented four times for atotal of 16 trials per test block. Trials for allfour probe types were presented in a random-ized sequence in the same test block.

The four within-class test blocks that werepresented to assess the effects of nodaldistance on preference among the membersof each of the two-node four-member classesare presented in Table 2. This table lists thewithin-class probe pairs in their order ofpresentation: ABD/DCA, ACD/ABC, DCB/ABC, and DBA/DCB. Each within-class probeblock was presented up to two times. If theparticipant selected the nodally proximalcomparisons on at least 94% of the trials inthe first test block, the block was not repeated.Performances that did not meet this criterion

resulted in a second presentation of the sametest block.

Although there were many probe types thatcould have been used in the within-classpreference test, we included those listed inTable 2 for three reasons. First, we wereworking under a time constraint that limiteda participant’s involvement in the experiment.Second, we were concerned that the presenta-tion of the totality of the within-class probetypes would result in a degrading in perfor-mance. Third, some of the probe typesevaluated the same nodal spreads as otherprobe types. With these constraints, we select-ed the probe types listed in Table 2 becausethey represented a broad range of nodalspreads.

In each probe pair, one of the probe typeswas of primary interest and the second probetype was included so that the performancesproduced by both probe types would bemaximally interpretable. Each probe block isdescribed next with a listing of all possibleoutcomes and interpretations.

The first test block contained ABD and DCAprobes. In both of these probes, maximalnodal spreads separated the two comparisonsfrom the sample stimuli. If participants did notrespond in accordance with nodal proximityon these probes, it would be unlikely that theparticipant would respond in accordance withnodal proximity for lesser nodal spreads. Thisfirst block contained ABD probes which pitteda 0-node baseline relation (AB) against a two-node transitive relation (AD) and the DCAprobes which pitted a 0-node symmetricalrelation (DC) against a two-node equivalencerelation (DA). The selection of B in the ABDprobe and C in the DCA probe woulddemonstrate conditional control of compari-son selection based on nodal proximity.

The second test block contained ACD andABC probes. The ACD probes pitted a one-node transitive relation (AC) against a two-node transitive relation (AD). The ABC probespitted a 0-node baseline relation (AB) againsta one-node transitive relation (AC). Bothprobes contained the same sample, while theC comparison acted as the nodally proximalstimulus on one trial and the nodally distalstimulus on the other. The ACD probe was ofprimary interest because it pitted two relationsof the same type (transitive) against each otherwhere the only difference was in terms of


Table 1

Training and testing trials using the simple-to-complex protocol to train two 3-node five-memberequivalence classes. Sa 5 sample; Co+ 5 positive comparison; Co2 5 negative comparison.

Step Relation%

Feedback

Class 1 Class2

# of trialsSa Co+ Co2 Sa Co+ Co2

Train AB Baseline 100 A1 B1 B2 A2 B2 B1 12Train AB Baseline 75, 25, 0 A1 B1 B2 A2 B2 B1 8Test BA Symmetry 0 B1 A1 A2 B2 A2 A1 8

0 A1 B1 B2 A2 B2 B1 4Train BC Baseline 100 B1 C1 C2 B2 C2 C1 12Train BC Baseline 75, 25, 0 B1 C1 C2 B2 C2 C1 8Test CB Symmetry 0 C1 B1 B2 C2 B2 B1 4

0 A1 B1 B2 A2 B2 B1 40 B1 C1 C2 B2 C2 C1 8

Test BA/CB Symmetry 0 A1 B1 B2 A2 B2 B1 40 B1 C1 C2 B2 C2 C1 40 B1 A1 A2 B2 A2 A1 80 C1 B1 B2 C2 B2 B1 8

Test AC Transitivity 0 A1 B1 B2 A2 B2 B1 40 B1 C1 C2 B2 C2 C1 40 A1 C1 C2 A2 C2 C1 8

Test CA Equivalence 0 A1 B1 B2 A2 B2 B1 40 B1 C1 C2 B2 C2 C1 40 C1 A1 A2 C2 A2 A1 8

3 MIX test S, T, 0 B1 A1 A2 B2 A2 A1 20 A1 C1 C2 A2 C2 C1 20 C1 A1 A2 C2 A2 A1 2

Train CD Baseline 100 C1 D1 D2 C2 D2 D1 12100 A1 B1 B2 A2 B2 B1 4100 B1 C1 C2 B2 C2 C1 4

Train CD Baseline 75, 25, 0 C1 D1 D2 C2 D2 D1 8Test DC Symmetry 0 C1 D1 D2 C2 D2 D1 4

0 D1 C1 C2 D2 C2 C1 8Test BD 1-NODE 0 C1 D1 D2 C2 D2 D1 4

Transitivity 0 B1 D1 D2 B2 D2 D1 8Test AD 2-NODE 0 C1 D1 D2 C2 D2 D1 4

Transitivity 0 A1 D1 D2 A2 D2 D1 8Test DB 1-NODE 0 C1 D1 D2 C2 D2 D1 4

Equivalence 0 D1 B1 B2 D2 B2 B1 8Test DA 2-NODE 0 C1 D1 D2 A2 A1 84MIX test BL, S, T, E 0 D1 C1 C2 D2 C2 C1 4

0 B1 D1 D2 B2 D2 D1 40 A1 D1 D2 A2 D2 D1 40 D1 B1 B2 D2 B2 B1 40 D1 A1 A2 D2 A2 A1 4

Train DE Baseline 100 D1 E1 E2 D2 E2 E1 8100 A1 B1 B2 A2 B2 B1 4100 B1 C1 C2 B2 C2 C1 4100 C1 D1 D2 C2 D2 D1 4

Train DE Baseline 75, 25, 0 D1 E1 E2 D2 E2 E1 8Test ED Symmetry 0 D1 E1 E2 D2 E2 E1 4

0 E1 D1 D2 E2 D2 D1 8Test CE 1-NODE 0 D1 E1 E2 D2 E2 E1 4

Transitivity 0 C1 E1 E2 C2 E2 E1 8Test BE 2-NODE 0 D1 E1 E2 D2 E2 E1 4

Transitivity 0 B1 E1 E2 B2 E2 E1 8Test AE 3-NODE 0 D1 E1 E2 D2 E2 E1 4

Transitivity 0 A1 E1 E2 A2 E2 E1 8Test EC 1-NODE 0 D1 E1 E2 D2 E2 E1 4

Equivalence 0 E1 C1 C2 E2 E2 E1 8Test EB 2-NODE 0 D1 E1 E2 D2 E2 E1 4

Equivalence 0 E1 B1 B2 E2 B2 B1 8


nodal spread. The selection of the C stimulusin the ACD probe could reflect control bynodal proximity or possibly an unconditionalpreference for the C stimulus. The ABC probewas used as a foil to produce comparisonselections that would disambiguate the sourceof control that was the determinant ofresponding in the ACD probe. In the ABCprobe, the C stimulus was nodally distal to thesample. If C was selected in the ABC probe, itwould imply that the selection of C in the ACDprobe reflected control by simple preferenceto the C stimulus rather than control by nodalproximity. On the other hand, the selection ofB in the ABC probe would imply that C was notsimply a preferred stimulus. Thus, the selec-tion of C in the ACD probe would have to bebased on nodal proximity.

The third test block consisted of the DCBand ABC probes. The DCB probes pitted a 0-

node symmetrical relation (DC) against a one-node equivalence relation (DB). The ABCprobes pitted a 0-node baseline relation (AB)against a one-node transitive relation (AC).Both of these contain the same stimuli in thecomparison set (B and C). Thus, each com-parison is nodally proximal on one probe andis nodally distal on the other probe. Theselection of C in the DCB probes and B on theABC probes would demonstrate conditionalcontrol of comparison selection based onnodal proximity, and would rule out controlby an unconditional preference for eithercomparison. In contrast, the uniform selectionof the B comparison in both probes woulddemonstrate a simple unconditional prefer-ence for B, and likewise for the uniformselection of the C comparison.

The fourth test block contained DBA andDCB probes. The DBA probes pitted a one-

Step Relation%

Feedback

Class 1 Class2

# of trialsSa Co+ Co2 Sa Co+ Co2

Test EA 3-NODE 0 D1 E1 E2 D2 E2 E1 4Equivalence 0 E1 A1 A2 E2 A2 A1 8

5 MIX test S,T,E 0 E1 D1 D2 E2 D2 D1 40 C1 E1 E2 C2 E2 E1 40 E1 C1 C2 E2 C2 C1 40 B1 E1 E2 B2 E2 E1 40 E1 B1 B2 E2 B2 B1 40 A1 E1 E2 A2 E2 E1 40 E1 A1 A2 E2 A2 A1 4

Table 1

(Continued)

Table 2

Within-class preference probes for Experiments 1 and 2. The first letter (Sa) depicts the samplein the trial, the second letter (CoP) depicts the nodally proximal stimulus, and the third letter(CoD) depicts the nodally distal stimulus for that probe. Under TYPES the left and right columnsdepict relations between the sample and nodally proximal comparison and the sample andnodally distal comparison, respectively. The number indicates the nodal distance between thesample and comparison, while the letter indicates the relational type (i.e. BL is baseline, S issymmetry, T is transitivity, and E is equivalence).

Pair (in order) Sa CoP CoD TYPES

1 A B D 0-BL 2-TD C A 0-S 2-E

2 A C D 1-T 2-TA B C 0-BL 1-T

3 A B C 0-BL 1-TD C B 0-S 1-E

4 D B A 1-E 2-ED C B 0-S 1-E


node equivalence relation (DB) against a two-node equivalence relation (DA). The DCBprobes pitted a 0-node symmetrical relation(DC) against a one-node equivalence relation(DB). Both probes contained the same sam-ple, while the B comparison acted as thenodally proximal stimulus on one probe andthe nodally distal stimulus on the other. TheDBA probe was of primary interest because itpitted two relations of the same type (equiva-lence) against each other where the onlydifference was in terms of nodal spread. Theselection of the B stimulus in the DBA probecould reflect control by nodal proximity orpossibly an unconditional preference for the Bstimulus. The DCB probe was used as a foil toproduce comparison selections that woulddisambiguate the source of control that wasthe determinant of responding in the DBAprobe. In the DCB probe, the B stimulus wasnodally distal to the sample. If B was selectedin the DCB probe, it would imply that theselection of B in the DBA probe reflectedcontrol by simple preference for the Bstimulus rather than control by nodal proxim-ity. On the other hand, the selection of C inthe DCB probe would imply that B was notsimply a preferred stimulus. Thus, the selec-tion of B in the DBA probe would have to bebased on nodal proximity.

Phase 5: Emergent relations test. The mainte-nance of the two equivalence classes wasevaluated with the re-administration of theemergent relations test described in Phase 3.

RESULTS AND DISCUSSION

Equivalence Class Formation under the Simple-to-Complex Protocol

Of the 10 participants who began Experi-ment 1, 8 formed two 3-node five-memberequivalence classes during preliminary train-ing under the simple-to-complex (STC) pro-tocol. The 2 remaining participants formedfour-member classes during preliminary train-ing but did not have enough time to completethe entire experiment.

Equivalence Class Formation under theSimultaneous Protocol

After forming the two 5-member classesunder the STC protocol, the simultaneousprotocol was used to establish two new two-node four-member equivalence classes for the

8 remaining participants. All 8 participantsacquired the baseline relations, and 7 passedthe emergent relations tests which document-ed the formation of two 2-node four-memberequivalence classes.

Within-Class Probes

Figure 1 depicts the data for each of thewithin-class preference probe types. Theprobe blocks are listed on the abscissa fromleft to right in their order of presentation.Although each probe block was presented upto two times, the data in Figure 1 includethe performances evoked by the last presen-tation of each probe block. Each sectordepicts the data for one participant. Thetop and bottom panels in each sector depictdata for the probes in Classes 1 and 2,respectively. In addition, the clustered col-umns within each graph depict data fromthe two probe types that were presentedtogether in a probe pair. The values on theordinate represent the percentage of trialsthat occasioned selection of the nodallyproximal stimulus. The particular featuresof the probe pair that controlled respondingcan be inferred from the pattern of respond-ing evoked by the two probe types for eachclass in a probe block.

Control by Nodal Proximity

Conditional control of responding based onnodal proximity is defined as the selection ofthe nodally proximal stimulus on at least sevenof eight trials for a given probe pair, asillustrated by the ABC–ACD probe pair forClass 2 for Participant 1, among others. Eightwithin-class probe pairs (indicated by the pairsof bars) were presented to each participant.Conditional selection reflective of control bynodal proximity was evoked by 88% of probepairs (7 of 8) for 1 participant (1), by 75% ofthe probe pairs (6 of 8) for 2 participants (2and 3), by 25% of probe pairs (2 of 8) for 1participant (6), and by 0% of the probe pairsfor 3 participants (4, 5, and 7). As a group,these performances indicate that nodal struc-ture was not a strong determinant of related-ness among the stimuli in multinodal equiva-lence classes. When viewed by probe typeacross participants, 38% of the probe pairsevoked performances reflective of control bynodal proximity.


Fig. 1. Performances on all within-class preference probes for all participants in Experiment 1. Each type of probe isrepresented by one bar. The two probe types that were included in a given probe block are presented as a clustered pairof bars. The clusters of probes are depicted on the abscissa in their order of presentation. The values on the ordinate arethe percentage of trials that occasioned selection of the nodally proximal stimulus (CoP).


Other Sources of Stimulus Control

Many of the probe pairs occasioned perfor-mances indicative of other forms of stimuluscontrol such as nodal distality, preferences forparticular comparisons, or avoidance of aparticular comparison. These are describednext.

Control by nodal distality. Control of respond-ing based on nodal distality, was demonstratedby the selection of the nodally distal stimuluson at least seven of the eight trials for a givenprobe pair. This is illustrated with the ABD–DCA probes in Classes 1 and 2 for Participant5. Responding on 16% of probe pairs (9 of 56)produced performances reflective of this formof stimulus control.

Discriminative control by a comparison stimulus:stimulus preference. In many probe blocks, thesame stimulus served as the nodally proximalcomparison in one probe and the nodallydistal comparison in the other probe. Theselection of the constant comparison on atleast seven of the eight trials in the probe pairwould indicate that comparison selectionreflected the unconditional discriminativecontrol by, or preference for, a particularstimulus. Preferences for the B comparison areillustrated with the DCB–DBA probes forClasses 1 and 2 for Participant 6. The B andC comparisons were preferred in 12 and 4 ofthe cases, respectively. In all 16 cases, the samecomparison was usually selected in the pres-ence of two different samples. Thus, theperformances could not have been deter-mined by a conditional relation between thesample and comparison stimuli. To summa-rize, responding on 29% (16 of 56) of theprobe pairs indicated selection of a particularcomparison stimulus which reflected uncondi-tional control by a preferred stimulus.

Avoidance or rejection of a comparison. In someprobe blocks, such as ABC–ACD, a participantcould select the comparisons that were uniqueacross the two probes; for example, B in theABC probe and D in the ACD probe. Thisoccurred in the ABC–ACD probe block forParticipant 5. A performance such as this canbe interpreted in a few ways. First, respondingcould have been controlled by rejection oravoidance of the constant comparison, the Cstimulus. Alternatively, these performancesmight reflect control by proximity on theACD probe and distality on the ABC probe.Based on parsimony, we support the former

interpretation. Performances on 7% (4 of 56)of the probe pairs indicated respondingreflective of control by rejection of a particularstimulus.

Preference or rejection of a comparison. In someprobe blocks, such as DCB–ABC, a participantcould respond by selecting the same compar-ison stimulus on all trials. Since both of thecomparisons were the same for both of theprobe types in this pair (e.g., B and C in theDCB–ABC probe pair), it cannot be deter-mined whether the participant was respondingbased on a preference for the stimulusselected or rejection of the comparison stim-ulus that was not selected.

Indeterminate control and equal relatedness. Inthe remaining 5% (3 of 56) of the probe pairs,the nodally proximal comparisons in the twoprobes were selected on approximately 50% ofthe trials, as illustrated by the ABD–DCAprobes for Classes 1 and 2 for Participant 7,among others. In these cases, we could notdiscern a specific source of stimulus control.This finding would imply an equality ofstrength between each comparison and thesample for these particular probes. If findingssuch as these were obtained for most of theprobes, it would support the view that thestimuli in the equivalence classes were equallyrelated to each other. Since that was not thecase, these results provide weak support, atbest, for the view that the stimuli in anequivalence class are equally related to eachother.

Within-Participant Commonality of TestPerformances across Classes

As can be seen in Figure 1, performances onthe within-class preference tests varied acrossand within participants. Nonetheless, eachparticipant demonstrated similar patterns ofresponding for each probe pair in Classes 1and 2. This occurred for most participants,suggesting that participants preferred to re-spond using the same stimulus control topog-raphy for relations in the same probe pairacross classes. Thus, even if nodal structuremight have influenced the selection of aproximal comparison in one class and anothersource of control influenced comparisonselection in the other class, only one of thesepatterns of responding would have prevailed.This interpretation will be considered in moredepth in the Introduction of Experiment 2.


Sources of Stimulus Control by Probe Type

Table 3 enumerates the frequency of occur-rence of particular stimulus control topogra-phies that influenced the performancesevoked by each of the four within-class probepairs. Data were aggregated across classes andparticipants. All four probe pairs occasionedperformances controlled by nodal proximity.Three of the probe pairs led to performancescontrolled by nodal distality. One probe paireach led to performances that were controlledby a preference for the B or C stimuli orrejection of the B or C stimuli. For three of theprobe pairs, it was not possible to identify thesources of stimulus control that determinedresponding. Finally, for some of the presenta-tions of the DCB–ABC probe pairs, which wereindicated by *, the predominant selection wasthe B stimulus. This performance could havebeen determined either by preference for theB stimuli, since B was present on all trials inthe block, or rejection of the C stimuli, since Cwas present on all trials but was never selected.In general, then, there was no apparentsystematic relation between particular probepairs and the stimulus control topographiesthat determined test performances.

Maintenance of Equivalence Classes

As just noted, the within-class tests resultedin substantial levels of variability in respond-ing, which might raise questions about theintegrity of the previously established equiva-lence classes. This possibility was addressed byconsidering the performances in the cross-class emergent-relation tests presented afterthe completion of the within-class preferencetests. During these cross-class tests, all partic-ipants responded in a class-consistent manner

on at least 95% of the test trials. Theseperformances demonstrated the maintenanceof the two originally established equivalenceclasses. Thus, the within-class tests did notdisrupt the integrity of the underlying equiv-alence classes, regardless of the responsesevoked by the within-class probes.

Summary

Seven of 10 participants formed equiva-lence classes under the simultaneous proto-col. Thereafter, only 1 of the 7 participantsshowed test performances in the within-classpreference tests that reflected control bynodal proximity, and thus the differentialrelatedness of stimuli in the equivalenceclasses. When aggregated across probe types,classes, and participants, 38% of the within-class probe pairs evoked the selections ofnodally proximal comparisons. The remainingprobes occasioned responding controlled bystimulus preferences, rejection of compari-sons, or nodal distality. These results, then,did not provide a strong demonstration of theeffects of nodal distance on the differentialrelatedness of stimuli in multinodal equiva-lence classes. Rather, they indicated that manyforms of stimulus control influenced respond-ing and thus precluded drawing definitiveconclusions about the differential relatednessof stimuli in equivalence classes. In addition,the notion that the stimuli in the equivalenceclass were equally related to each other wasalso not supported because the actual out-comes of the experiment did not match thoserequired by the predictions of equal related-ness.

The literature mentioned in the Introduc-tion indicated that nodal structure influencedtest performances in a systematic manner in a

Table 3

The number of probe pairs that evoked comparison selections based on one of the listedstimulus control topographies.

ProbePairs

Stimulus Control Topographies

Proximal Distal Pref. for B Pref. for C Reject B Reject C ??

ABD-DCA 7 4 x x x x 3ABC-ACD 5 - x 4 x 4 1DCB-ABC 6 1 5* - - 5* 2DCB-DBA 3 4 5 x 2 x -

Totals 21 9 10 4 2 4 6

* Performances could reflect preferences for the B stimuli or rejection of the C stimuli.


number of different testing conditions. InExperiment 1, however, only 38% of thewithin-class preference probes yielded perfor-mances that were controlled by nodal proxim-ity. This disparity in outcome suggests that theexpression of the effects of nodal structureusing procedures like those specified inExperiment 1 could be enhanced with theaddition of some as yet unspecified variable.Experiment 2 was designed to identify such avariable.

EXPERIMENT 2

In Experiment 1, the equivalence classeswere formed using trials that contained twocomparisons, one from each class. During exitinterviews, a large number of participantsreported that they learned relations amongthe stimuli in one class, and also learned torespond to the stimuli in the other class byresponding away from the stimuli in thelearned class. Specifically, during an emer-gent-relations test trial, the presentation of asample from the ‘‘unlearned’’ class led theparticipant to respond away from the compar-ison from the ‘‘learned’’ class; thus, respond-ing that appeared to reflect the presence ofthe other class really involved rejection of the‘‘learned’’ class. The stimuli in the other‘‘class’’, then, were not being treated asmembers of a class.

The literature cited in the Introductionsupports the view that when an equivalenceclass is formed, participants also learn aboutthe nodal structure of the class. If, however,participants formed only one class (as report-ed by some of the participants in Experiment1), as they acquired the baseline relationsamong the stimuli in the ‘‘learned’’ class, theywould also have learned of the nodal structureof that class. In addition, because they did notlearn the baseline relations among the stimuliin the other set, they could not have learned ofthe nodal structure of that set. Thus, nodalstructure could not have controlled behaviorin a systematic manner for the latter class. Asalready noted, the participants responded in asimilar manner to the probes in both classes,and in general did not respond in accordancewith nodal proximity. These results suggestthat any control of behavior by nodal proxim-ity for the stimuli in the class that was actuallyformed was overshadowed by a preference for

responding in a similar manner to stimuli inthe same probe pair in both classes.

It follows from this argument that a proce-dure which would guarantee the formation ofboth classes should also induce control ofbehavior by nodal structure in each of theclasses, and thereby give rise to performancesin the preference tests that were correlatedwith nodal proximity. According to Sidman(1987), to insure that participants form allexperimenter-defined equivalence classes, atleast three comparisons should be used duringthe establishment of the baseline relations.This occurs because the inclusion of threecomparisons minimizes the selection of class-consistent comparison selection by the rejec-tion of another comparison stimulus, andmaximizes selection based on within-classrelations for all trained classes. Thus, the useof three comparisons ensures the explicitformation of all specified equivalence classes(Carrigan & Sidman, 1992; Johnson & Sidman,1993; Sidman, 1987; Sidman, 1994). If allclasses are formed using this sort of procedure,it is also possible that control by nodalstructure would be induced for all classes andpreference tests should occasion selections inaccordance with nodal proximity.

Although researchers have implementedthis three-comparison strategy by the establish-ment of three equivalence classes, others havedemonstrated the formation of two equiva-lence classes with the use of three compari-sons: one from each class and a null stimulusthat was not a member of either class(Dougher, Augustson, Markham, Greenway,& Wulfert, 1994). If two explicit classes areestablished, the nodal relations among thestimuli in each class should also influenceresponding. Thus, in Experiment 2, trainingof the baseline relations and testing for theemergence of derived relations were conduct-ed using trials that contained one comparisonfrom each class along with a third nullcomparison. If participants respond in aclass-indicative manner to the stimuli in bothclasses, they must be attending to relationsamong all stimuli in a class and for bothclasses. It is our hypothesis that equivalenceclass formation conducted with a null compar-ison must also establish stimulus control by thenodal structure of equivalence classes andevoke the selection of nodally proximal stimuliduring within-class tests.


METHOD

Participants

Twelve undergraduate students enrolled ina Psychology 101 course at Queens Collegeserved as the participants to fulfill a courserequirement. All participants read and ac-knowledged the Informed Consent Statementgiven to them before the start of the experi-ment. The experiment lasted from 2.5 to 3.5 hrand was conducted in one session.

Apparatus

Hardware, software, and stimuli were thesame as those used in Experiment 1. Inaddition, the stimuli used for the thirdcomparison were: PIB (A3), DUR (B3), SOF(C3), JEH (D3).

Procedure

Phases 1 and 2. Instructions and keyboardfamiliarization and preliminary training using thesimple-to-complex protocol. Both phases were thesame as in Experiment 1.

Phase 3: Equivalence class formation using thesimultaneous protocol. This was the same as inExperiment 1 with one exception. Each train-ing and testing trial contained three instead oftwo comparison stimuli: the positive compari-son which was from the same class as thesample, the negative comparison which camefrom the class not represented by the sample,and a null comparison. During initial trainingblocks, each sample stimulus was presented onsix trials, with each comparison stimulus ap-pearing two times in each of the left, middle,and right positions. Therefore, each trainingblock contained 36 trials. During feedbackreduction each sample stimulus was presentedon three trials, with each comparison stimulusappearing once in each of the left, middle, andright positions. Once all baseline relations wereestablished and maintained with no informativefeedback, the participants were presented withan emergent- relations test that contained all ofthe baseline, symmetrical, one- and two-nodetransitive and equivalence-relations probes. Sixtrials were presented for each relation; threetrials for the relation from Class 1 and threefrom Class 2 in which the position of the Co+was on the right for one trial, the middle forone trial, and the left for the other trial. All ofthe tests that made up the emergent-relationstest were spread across three test blocks, with

one trial for each relation for each classpresented in a test block. Therefore, 24 trialswere presented in a test block for a total of 72trials. Within a block all trials were presented ina randomized order without replacement. Thistest (combination of three blocks) was repeatedup to four times or until the participantperformed with at least 92% accuracy on eachof the three blocks.

Phase 4: Within-class preference tests. Once theparticipant passed the emergent- relations test,participants were presented with the samewithin-class preference test trials used inExperiment 1. These trials contained onlytwo comparisons and no null comparison.

Phase 5: Emergent-relations test 2. This phaseevaluated the maintenance of the two equiva-lence classes with the re-administration of theemergent-relations test described in Phase 3.


Equivalence Class Formation under theSimple-to-Complex Protocol

During preliminary training, the STC pro-tocol was used to establish two 3-node five-member equivalence classes. These classeswere formed by 10 of the 12 participants,who then continued into the main part ofExperiment 2. The 2 remaining participantsformed four-member classes during exposureto the STC protocol and ran out of time beforeexpanding class size to five members. Thus,these 2 participants did not continue in thepresent experiment.


Of the 10 participants who formed the two5-member classes under the STC protocol, 7formed two new 2-node four-member equiva-lence classes under the simultaneous protocol.Of the 3 participants who did not form theclasses, 1 did not acquire the baselines in theallotted time, and 2 acquired the baselines butran out of time before the administration ofthe emergent- relations test blocks.


All 7 participants were given the within-classpreference tests, the results of which aredepicted in Figure 2. All of the within-classprobes evoked the selection of the nodallyproximal comparison stimuli on at least seven


of eight trials in each probe. A comparison ofsome outcomes showed that a 0-node baselinerelation was preferred to a one-node transitiverelation, and that was preferred to a two-nodetransitive relation (0nB . 1nT . 2nT). Acomparison of other outcomes showed that a0-node symmetrical relation was preferred to aone-node equivalence relation, and that waspreferred to a two-node equivalence relation(0nS . 1nE . 2nE).

The nearly unanimous selection of nodallyproximal comparison stimuli across all of thewithin-class probes strongly supports the viewthat the strength of relations among thestimuli in an equivalence class is an inversefunction of the nodal distance that separatesthe stimuli among the trained relations thatare the prerequisites of an equivalence class.This result stands in striking contrast to theresults obtained in Experiment 1, and iscorrelated with the use of the null comparisonduring equivalence class formation in thepresent experiment and its absence duringclass formation in Experiment 1. Thus, thesedata suggest that the inclusion of the nullcomparison during equivalence class forma-tion was responsible for enhancing sensitivityto the nodal structure of the equivalenceclasses in all participants.


When reexposed to the cross-class emer-gent-relation tests, all participants respondedin a class-consistent manner on at least 95% ofthe test trials. Thus, the within-class tests didnot disrupt the integrity of the underlyingequivalence classes. A necessary corollary ofthis finding is that the underlying equivalenceclasses existed during the administration ofthe within-class preference tests. This matterwill be considered in more detail in theGeneral Discussion.

Effect of the Null Comparison

The inclusion of the null comparison in thetraining and testing trials used to establish anddocument the formation of equivalence classesdid not influence the percentage of partici-pants who formed equivalence classes. It did,however, have a profound effect on thecontrol exerted by nodal structure on theselection of comparisons during virtually allwithin-class probes. These results suggest that

the inclusion of the null comparison duringthe formation of equivalence classes results inthe establishment of two distinct equivalenceclasses where the nodal structure is learnedbetween the relations in both of the classes.Therefore, the establishment of nodal struc-ture in both classes results in performancesindicative of control by nodal structure. Theeffect of the null comparison was shown in abetween-participant preparation. Additionalresearch would be needed to determinewhether similar effects would be obtained ona within-subject basis.

EXPERIMENT 3

In Experiment 2, the range of nodalcomparisons that could be evaluated waslimited by class size. In addition, many of thewithin-class probes had procedural factors thatwere correlated with nodal proximity. Onesuch procedural factor that occurred for theDBA and ACE probes was that each sample–comparison relation differed in terms of nodalnumber as well as the number of functionsacquired by each comparison during training.For example, in the DBA probe, the B stimulusserved as a sample on the BC trials and as acomparison on AB trials, thus B serves twobehavioral functions; that is, the B stimulusserved as a node. Conversely, the A stimulusonly served as a sample on AB trials, thus Aserves only one behavioral function, that is, theA stimulus served as a single. Therefore, theselection of the nodally proximal comparisoncould have been based on the selection of thecomparison that had acquired two functionsand not the comparison that acquired onefunction, that is, the participant could haveselected the comparison that served as a nodeinstead of a single. The other proceduralfactor that was correlated with nodal proximityon the ABC and DCB probes was that eachsample–comparison relation differed in termsof relational type. For example, on the ABCprobes both comparisons bore different typesof relations to the sample stimulus, that is, a 0-node baseline relation for AB and a one-nodetransitive relation for AC. Thus, the selectionof the B comparison could be attributed to apreference for a baseline relation over atransitive relation. Finally, on the ABD andDCA probes, nodal proximity was correlatedwith both relational type and number of


Fig. 2. Performances on all within-class preference probes for all participants in Experiment 2. The format is thesame as in Figure 1.


functions acquired by the comparisons. Someof these factors can be eliminated by theestablishment of larger equivalence classeswith a greater number of nodal stimuli. Thus,Experiment 3 involved the establishment oftwo 3-node five-member classes, followed bythe administration of some within-class probesin which nodal proximity was not confoundedwith the procedural factors mentioned above.

METHOD

Participants

Twelve undergraduate students enrolled ina Psychology 101 course at Queens Collegeserved as the participants to fulfill a courserequirement. All participants read and ac-knowledged the Informed Consent Statementgiven to them before the start of the experi-ment. The experiment lasted from 2.5 to 3.5 hrand was conducted in one session.

Apparatus

The hardware and software were the same asthose used in all aspects of Experiments 1 and2. The stimuli used during preliminary train-ing and during equivalence class trainingunder the simultaneous protocol were thesame as in Experiment 1. The stimuli in thetwo 5-member classes formed under thesimultaneous protocol in Experiment 3 wereQIJ (A1), TUW (B1), COH (C1), MEP (D1),and RAB (E1); in Class 2, they were: VIF (A2),KUY (B2), XOL (C2), GEZ (D2), and NAS(E2). In addition, the stimuli used for thethird comparison were: PIB (A3), DUR (B3),SOF (C3), JEH (D3), and LAV (E3).

Procedure

Phases 1 and 2. Instructions and keyboardfamiliarization and preliminary training using thesimple-to-complex protocol. Both phases were thesame as in Experiment 1.

Phase 3: Equivalence class formation under thesimultaneous protocol. In this phase equivalenceclasses were established with stimuli thatdiffered from those used in Phase 2, and bythe concurrent training of the AB, BC, CD,and DE baselines for two 3-node five-memberequivalence classes that would produce anodal structure represented by ARBRCRDRE. The baseline relations that were trainedbetween the Class 1 stimuli were A1–B1, B1–C1, C1–D1, and D1–E1. The baseline relations

that were trained between the Class 2 stimuliwere A2–B2, B2–C2, C2–D2 and D2–E2. Eachtrial consisted of the presentation of thesample stimulus along with a stimulus fromthe same class, the stimulus with the sameletter designation from the other class, and athird comparison from the third stimulus setwith the same letter designation as the othertwo comparisons.

During initial training blocks, each samplestimulus was presented on six trials, with eachcomparison stimulus presented two times eachon the left, middle, and right positions. Eachtraining block consisted of 48 trials. Duringthe maintenance phase, when block feedbackwas 75, 25, and 0%, each sample stimulus wasonly presented three times and each compar-ison was presented one time in each position,for a total of 24 trials per block.

Thereafter, all of the baseline relations,symmetrical relations, one-, two-, and three-node transitive and equivalence relations werepresented in a set of test blocks. Six trials werepresented for each relation. Each set of testblocks contained three trials for a given relationfrom Class 1 and three trials from Class 2, inwhich the positions of the comparisonschanged on each trial so that each stimuluswas presented once in each position (i.e., left,middle, right). Although the test consisted of120 trials, they were presented in a set of threetest blocks, each of which contained 40 trials.Each block included one trial for each rela-tional type for Classes 1 and 2. Within a block,all trials were presented in a randomized orderwithout replacement. This set of three blockswas repeated up to four times or until theparticipant performed with at least 92% accu-racy on each of the three blocks in the a set.

Phase 4: Within-class preference tests. Once theparticipant passed the emergent relations test,the within-class preference test was adminis-tered to assess the effects of nodal distance. Inthe preference tests, each trial contained asample and two comparisons, all from thesame class. The comparisons differed in termsof the nodal distances that separated eachfrom the sample.

Table 4 lists the within-class probes used toassess the effects of nodal distance on prefer-ence among the members of each of the three-node five-member classes. Time constraintsprevented us from administering all of thepossible probes. Instead, we selected a variety of


probes to evaluate the effects of many nodalspreads and minimize the effects of possibleconfounds on test performances. As in Exper-iment 1, the first block consisted of probes thatcontained the largest nodal spread between thetwo comparisons and the sample stimulus.

Test Block 1 contained ABE and EDAprobes. The ABE probe pitted a 0-nodebaseline relation against a three-node transi-tive relation. The EDA probe pitted a 0-nodesymmetrical relation against a three-nodeequivalence relation. In both probes maximalnodal spreads separated the comparisons fromthe samples. Test Block 2 contained ACD andEDC probes. The ACD probes pitted one- andtwo-node transitive relations against eachother. The EDC probes pitted a 0-nodesymmetrical relation against a one-node equiv-alence relation. Test Block 3 contained ECBand ABC probes. The ECB probes pitted one-and two-node equivalence relations againsteach other. The ABC probes pitted a 0-nodebaseline relation against a one-node transitiverelation. Test Block 4 contained ACE and ABCprobes. The ACE probes pitted one- and three-node transitive relations against each other.The ABC probe pitted a baseline relationagainst a one-node transitive relation. TestBlock 5 contained DBA and DCB probes. TheDBA probes pitted one- and two-node equiva-lence relations against each other. The DCBprobe pitted a 0-node symmetrical relationagainst a one-node equivalence relation.

Phase 5: Emergent-relations test 2. The mainte-nance of the two equivalence classes wasevaluated with the re-administration of theemergent relations test described in Phase 3.


Equivalence Class Formation under the Simple-to-Complex Protocol

Ten of the 12 participants formed two 3-nodefive-member equivalence classes using the STCprotocol. The 2 remaining participants formedfour-member classes but ran out of time beforeexpanding class size to five members.


Of the 10 participants who formed the two 5-member classes under the simple-to-complexprotocol, 7 formed two new three-node five-member equivalence classes under the simulta-neous protocol. Of the 3 participants who didnot form the classes, 1 did not acquire thebaselines during the allotted time, and 2acquired the baselines but ran out of timebefore the administration of the emergentrelations test blocks. Due to time constraints,only 4 of the participants who formed three-node five-member classes under the simulta-neous protocol were given the within-classpreference tests.


Figure 3 presents the results of the within-class preference tests for the 4 above- men-tioned participants. The format of Figure 3 waslike that used for Figures 1 and 2 but withdifferent probe types. With one exception, thetrials in all of the within-class probes evoked theselection of the nodally proximal comparisonstimuli on at least seven of eight trials in eachprobe. A comparison of some outcomes showedthat a 0-node baseline relation was preferred toa one-node transitive relation, and that waspreferred to a two-node transitive relation. Inaddition, a one-node transitive relation waspreferred to a three-node transitive relation(0nB . 1nT . 2nT) and (1nT . 3nT).

A comparison of other outcomes showedthat a 0-node symmetrical relation was pre-ferred to a one-node equivalence relation, andthat was preferred to a two-node equivalencerelation (0nS . 1nE . 2nE). In addition, a 0-node symmetrical relation was preferred to athree-node equivalence relation (0nS . 3nE),and a one-node equivalence relation waspreferred to a two-node equivalence relation(1nE . 2nE). The nearly unanimous selectionof nodally proximal comparison stimuli across

Table 4

Within-class preference probes for Experiment 3. Seedescription for Table 2.

Pair(in order) Sa CoP CoD TYPES

1 A B E 0-BL 3-TE D A S-0 3-E

2 A C D 1-T 2-TE D C 0-S 1-E

3 E C B 0-S 2-EA B C 0-BL 1-T

4 A C E 1-T 3-TA B C 0-BL 1-T

5 D B A 1-E 2-ED C B 0-S 1-E


all of the within-class probes strongly supportsthe view that the strength of relations amongthe stimuli in an equivalence class is an inversefunction of the nodal distance that separates

the stimuli among the trained relations thatare the prerequisites of an equivalence class.The one exception to this general outcomeoccurred with the ECB and ABC probes forClass 1 for Participant 18. In these probes, alltrials evoked selection of the B stimulus.Therefore, responding on these probes dem-onstrated control by preference for B orrejection of the C stimulus.


When reexposed to the cross-class emer-gent-relations tests, all participants respondedin a class-consistent manner on at least 95% ofthe test trials. These performances demon-strated the maintenance of the two originallyestablished equivalence classes. Thus, thepresentation of within-class tests between thetwo sets of cross-class tests did not disrupt theintegrity of the underlying equivalence classes.As in Experiment 2, these results support theview that the underlying equivalence classesexisted during the administration of thewithin-class preference tests.

Coexistence of Equal and Graded Relatedness

Responding indicative of class integrity andthe equal relatedness of stimuli was expressedwith the presentation of cross-class tests. Re-sponding in accordance with nodal distance orgraded relatedness was expressed immediatelyupon the presentation of within-class tests. Bothof these performances were expressed immedi-ately in successively presented test blocks, all ofwhich provided no informative feedback forany of the comparisons selected on a trial.These results showed that both between- andwithin-class sources of stimulus control coexist-ed but were expressed separately by thepresentation of test trials that contained stimulifrom different classes or from the same class.

GENERAL DISCUSSION

Effect of Null Comparison on Class Formation andNodal Distance Effects

Three experiments assessed the strength ofrelations among the stimuli in equivalenceclasses by use of post-class formation within-class preference tests. In Experiment 1, 7 ofthe 10 participants formed two 2-node four-member classes using trials that contained twocomparisons each. In post-class formation

Fig. 3. Performances on all within-class preferenceprobes for all participants in Experiment 3. The formatis the same as in Figure 1.


preference tests, only 1 of the 7 participantsresponded to all of the probes in a mannerindicative of control by nodal proximity. Only38% of the probe pairs in the within-classpreference tests presented to the totality of theparticipants evoked responding indicative ofcontrol by the nodal separation of stimuli inthe classes. Although a relatively large percent-age of participants formed the equivalenceclasses, nodal distance exerted a minimaleffect on within-class test performances.

In Experiments 2 and 3, a similar percentageof participants formed equivalence classes, butthe two classes were formed using trials thatcontained one comparison from each class anda third null comparison. When the within-classpreference tests were administered, virtually allof the test trials presented to all participantsevoked responding that reflected control by thenodal proximity of the stimuli in the previouslyestablished classes. Thus, the strength ofrelations among the stimuli in each multinodalequivalence class was an inverse function of thenumber of nodes that separated the stimuli inthe class. This increase in control exerted bynodal structure from Experiment 1 to Experi-ments 2 and 3 can be attributed to the inclusionof a third null comparison on all trials used toestablish the underlying equivalence classes.Although the inclusion of a null comparisonincreased sensitivity to the effects of nodalproximity, it did not influence the likelihood offorming equivalence classes under the simulta-neous protocol.

Generality of Nodal Distance Effects

In two earlier studies (Fields et al., 1995;Fields & Watanabe-Rose, 2008), nodal distanceeffects were demonstrated by participants whowere exposed to tests used to assess the post-class formation effects of nodal distance. Thepercentage of participants in these studies whoshowed the effects was very low because only asmall number of them formed equivalenceclasses under the SIM protocol. Thus, thegenerality of the nodal distance effect in largerpopulations could be questioned.

In the present experiments, however, muchhigher percentages of participants formedequivalence classes under the SIM protocolbecause of the prior establishment of otherequivalence classes under the STC protocol.Thus, a relatively large percentage of partici-pants were eligible to engage in the preference

tests used to measure the effects of nodaldistance. All of the participants in Experi-ments 2 and 3 showed control of respondingby nodal structure during the within-classpreference tests. Thus, the control of behaviorby nodal structure for a large proportion ofparticipants was achieved by the combinationof two procedures: (1) the prior establishmentof equivalence classes under the STC protocol,and (2) the subsequent establishment of newequivalence classes under the simultaneousprotocol with trials that contained null com-parison stimuli. The results of Experiments 2and 3, then, extend the generality of theeffects of nodal distance on the differentialrelatedness of stimuli in equivalence classes.

Nodality Effects Primed by Initial Probe Pairs?

In Experiments 2 and 3, the first set ofprobes in the preference test sequence in-volved the presentation of trials in which thecomparison stimuli bore maximally differentnodal spreads from the sample. These initialprobes, then, might have signaled that thecomparison to be selected is the one ‘‘mostsimilar’’ to a trained relation. Since similarityto a trained relation is indexed by nodalseparation, the presentation of these initialprobes might have primed the selections ofthe nodally proximal comparisons in thesubsequently presented probes. Regardless ofthe status of the priming function served bythe initial trials, responding on virtually allpreference tests was a direct function of nodalproximity. Of necessity, such an outcomemeant that the participants must have learnedthe nodal structure among the stimuli in theclasses during the formation of the classes.Therefore, the capability of responding to thestimuli in the equivalence class based ondifferential relatedness was present and couldhave been activated by the content of the testtrials or possibly by combination of thepresentation of the initial probe pair and thecontent of the test trial.

Although the current data cannot be used todetermine whether the initial probes primedresponding based on nodal structure, thatpossibility could be evaluated by future re-search that would replicate the within-classpreference tests used in the present experi-ment but without exposure to the initial probepairs. The outcome of such an experiment,however, would not invalidate the results


obtained in Experiments 2 and 3. At best, itwould identify an additional variable thatactivated the effects of nodal structure on therelatedness of stimuli in equivalence classes.

Scope and Robustness of Nodal Distance Effects

Previous research has shown that nodalstructure influenced the delayed emergenceof equivalence classes (Bentall et al., 1998;Fields et al., 1990; Kennedy, 1991; Kennedy etal., 1994; Sidman et al., 1985; Spencer &Chase, 1996), response latency and speedduring and after class formation (Bentall etal.,1998; Kennedy, 1991; Spencer & Chase,1996; Tomanari et al., 2006; Wulfert & Hayes,1988), and the gradual transfer of respondingafter class formation (Fields et al., 1993b). Inaddition, nodal distance influenced the bifur-cation of previously formed equivalence classesin accordance with nodal structure (Fields etal., 1995; Fields & Watanabe-Rose, 2008). Theresults of Experiments 2 and 3 demonstratedyet another post-class formation effect of nodalstructure: the selection of nodally closercomparisons in within-class preference tests.

In addition to extending the range ofconditions that show the effects of nodaldistance, the results of Experiments 2 and 3also address some criticisms that have beenraised regarding the robustness of the effectsof nodal distance (Sidman, 1994, 2000). Thesecriticisms include: (1) Nodal distance hadtransient effects during the delayed emer-gence of equivalence classes and the gradualtransfer of responding among the members ofequivalence classes. (2) The tests used to assessnodal distance effects forced outcomes indic-ative of nodal distance. (3) The effects ofnodal distance were diminished when morethan two classes were established on a concur-rent basis. (4) There could have been poten-tial biases, based on different reinforcementhistories acquired by stimuli, that were con-founded with nodal distance.

None of these criticisms were relevant to thedata reported in Experiments 2 and 3. Withregard to these four criticisms: (1) the effectsof nodal distance were demonstrated in asteady state after the formation of the classes.Thus, the effects of nodal distance were nottransient. The same can be said of the resultsreported by Fields and Watanabe-Rose (2008)and Fields et al. (1995). (2) The design of thewithin-class preference tests permitted a par-

ticipant to respond independently of, or inaccordance with nodal structure. Therefore,the test performances that matched thepredictions based on nodal distance couldnot be attributed to a forcing of the outcomebased on design biases embedded in the testtrials themselves. The same can be said of theresults reported by Fields and Watanabe-Rose(2008) and Fields et al. (1995). (3) The resultsof the preference tests were obtained with awide range of nodal spreads after the forma-tion of two equivalence classes using a thirdnull comparison during training and testing.Rather than a diminution, a maximal effect ofnodal distance was demonstrated for the set oftwo equivalence classes established in eachexperiment. (4) The use of the simultaneousprotocol to establish the equivalence classesminimized differences in stimulus–reinforcerbiases that could have been correlated withnodal distance. To summarize, the results ofthe preference tests in Experiments 2 and 3could not be accounted for by any of thepotential confounding factors mentioned inthe previous paragraph. Therefore, the resultsof the Experiments 2 and 3 support the viewthat nodal distance exerted a stable and robusteffect on the differential relatedness of stimuliin an equivalence class that was not confound-ed by the factors mentioned above.

Possible Confounds with Nodal Distance in thePreference Tests

The present experiments demonstrated thatnodal structure influenced the selection ofnodally proximal stimuli as measured usingwithin-class preference tests conducted in amatching-to-sample format. The performancesevoked by the ACD and ECB probes inExperiment 3 provided unambiguous andunconfounded demonstrations of the effectsof nodal distance on relational preferencesafter class formation. For other probes in thepresent experiments, however, nodal proxim-ity was sometimes correlated with relationaltype and/or the number of functions served bythe comparisons. Thus, performances thatwere correlated with nodal proximity couldalso have been influenced by these lattervariables instead of, or in addition to nodalproximity. These possibilities are illustratedwith the ABC, DBA, and EDA probes.

In the case of the ABC probes, differenttypes of relations existed between the sample


and each comparison along with differences innodal spread. Specifically, AB was a 0-nodebaseline relation while AC was a one-nodetransitive relation. Thus, the preference forthe nodally proximal stimulus might have alsoreflected control by a trained relation ratherthan an emergent relation. In the case of theDBA probes, a different number of functionshad been acquired by the two comparisons.Specifically, the B stimulus had acquired botha sample function during BC training and acomparison function during AB training,while the A stimulus had acquired only asample function during AB training. There-fore, DB, the one-node equivalence relationwas correlated with a comparison that servedtwo functions while DA, the two-node equiva-lence relation, was correlated with a compar-ison that served only one behavioral function.Thus the preference for the nodally proximalcomparison might have been controlled by apreference for a comparison that served twoinstead of one behavioral function. Finally, inthe case of the EDA probes, the sample andcomparisons differed in terms of relationaltype (ED being a symmetrical relation and EAbeing an equivalence relation) and in numberof functions served by each comparison (Dserved as a node and A served as a single).Therefore, the preference for the nodallyproximal comparison might have been con-trolled by a preference for a comparison thatserved as a node or for a symmetrical relationinstead of an equivalence relation.

In summary, the performances evoked bythe within-class preference probes, which werecorrelated with nodal proximity, might havebeen controlled by other variables. Thatnotion, however, can be ruled out for thefollowing reasons. If these nominally con-founded variables were responsible for selec-tion instead of nodal proximity, probes thatdid not have these confounds (i.e., ACD andECB) would have produced random selectionof comparisons. That, however, did not occur:Instead, virtually all probes occasioned theselection of the nodally proximal comparisonsregardless of the presence or absence of theseconfounds. Since these formally confoundedvariables were not correlated with test perfor-mances, these factors did not account for theperformances evoked by the totality of thewithin-class probes. Nodal proximity was theonly factor that was present in all types of

probes and was systematically correlated withtest performances. Therefore, nodal proximityhad to be the variable that was the primarydeterminant of the relatedness of stimuli inthese classes in the present experiments.

Intactness of Equivalence Classes during and afterPreference Testing

In all three experiments, after completingthe within-class preference test, participantswere presented with a final cross-class emer-gent relations test block. Virtually all of theprobes in this block evoked respondingindicative of the intactness of the equivalenceclasses. This occurred regardless of the perfor-mances evoked by the within-class preferencetests (i.e., in Experiments 1, 2, and 3). Thus,the underlying equivalence classes, which weredocumented in the emergent-relations testsconducted prior to preference testing musthave remained intact during the administra-tion of the within-class preference probes. Ofinterest, the integrity of the classes was alsomaintained regardless of the performancesoccasioned by the within-class preference tests.Similar results were reported by Fields andWatanabe-Rose (2008) who found that equiv-alence classes remained intact after demon-strations of class bifurcation in dual-optionresponse transfer tests. The results of the latterexperiment then demonstrated that the integ-rity of an equivalence class is maintainedfollowing a variety of procedures used tomeasure differential relatedness of stimuli inthe classes.

These results have important implicationsfor Sidman’s interpretation of the existence ofequivalence classes (Sidman, 1994, 2000). Henoted that for the stimuli in a set to befunctioning as members of an equivalenceclass, they must demonstrate the property ofinterchangeability or substitutability. He wenton to state that, ‘‘Without [this] commoncharacteristic … the class does not exist.’’(1994, p. 543). The data collected during theemergent relations tests conducted after theadministration of the within-class preferencetests raise questions about this analysis. Whenthe participants in Experiments 2 and 3 wereexposed to the emergent relations test afterthe administration of the preference probes,virtually all of the emergent relations probesevoked responding that demonstrated theintactness of the equivalence classes. Accord-


ing to Sidman’s analysis, the classes did notexist—could not be defined—during thepreviously conducted within-class preferencetests (Sidman, 1994, p. 543). The class-consis-tent responding seen during the final emer-gent relations tests then could have occurredonly with the instant re-creation of the classeswithout benefit of any training. Because this isimplausible, it is far more likely that, onceformed, equivalence classes remain intactduring the administration of the within-classpreference tests. These results then imply thattwo stimulus control topographies coexistamong the stimuli in an equivalence class:one class-based and reflective of equal related-ness among class members, and the othernodally-based and reflective of differentialrelatedness among the class members. Theessential issue, then, is not whether these twostimulus control topographies exist but ratherhow these topographies come to controlresponding in different test trials.

Theoretical Integration

Many experiments have shown that a num-ber of stimulus control topographies can gaincontrol of responding when training is con-ducted using trials presented in a matching-to-sample format (Fields, Garruto, & Watanabe,2010; Iversen, 1997; Iversen, Sidman, & Carri-gan, 1986; McIlvane & Dube, 2003). Whetherintended or not, these topographies acquiredcontrol because of their planned or adventi-tious correlation with the contingencies ofreinforcement that established the experi-menter-defined relations. These findings makeplausible the assumption that training condi-tions designed to ensure the formation of allexperimenter-defined equivalence classes alsoresult in the acquisition of control by morethan one relation among the stimuli in a class,specifically, class-based and nodally-based stim-ulus control topographies.

When a set of linked conditional discrimi-nations are established, they define a nodalstructure among the stimuli in the relations.When this is done, the relatedness amongstimuli in the set will be an inverse function ofthe number of nodes that separate the stimuliin the trained relations. This assumption isdriven by the extensive literature on therelatedness of stimuli in semantic memorynetworks (Branch, 1994; Collins & Loftus,1975; Collins & Quillian, 1969; Fields &

Verhave, 1987). If established, this differentialrelatedness is maintained even in the presenceof tests devised to assess the formation ofequivalence classes or the relatedness ofstimuli in the class. In addition, the contin-gencies embedded in the matching-to-sampletrials reinforce differential responding tostimuli in different sets, that is, discriminationbetween sets, also called class-based stimuluscontrol topographies.

After the establishment of the linked base-line relations, the formation of the equiva-lence class is evaluated with the presentationof derived relations probes, each of whichcontains a sample stimulus from one set (Sa),one comparison stimulus from the same set(i.e., the positive comparison or Co+), and atleast one other stimulus from other sets (i.e.,the negative comparisons or Co-s). The Sa andCo+ are linked by a set of intervening nodeswhile any Co2 is explicitly not linked bytraining to the sample stimulus of that trial.Thus, the contingencies of reinforcementshould result in the selection of comparisonsfrom the same set as the sample rather thanstimuli in sets that differ from the samplestimuli. These emergent-relations test perfor-mances would show a discrimination betweenclasses and thus document the formation ofequivalence classes.

When each stimulus in a class results in theselection of all other stimuli in the class, all ofthe stimuli would be functioning as stimuli thatare substitutable for each other. When anyemergent-relations probe is presented, anycomparison from a given set is ‘‘closer’’ to thesample stimulus from the same set than anystimulus in another set. Therefore, the selectionof a comparison from the same set is most likely,regardless of the nodal separation between thesample and comparison stimuli. On the otherhand, a within-class preference probe containsboth comparison stimuli from the same class.Because some stimuli are ‘‘closer’’ to each otherbased on the training structure, participants aremore likely to select the comparison that isnodally closer to the sample.

In Experiments 2 and 3, participants werepresented with a battery of cross-class emer-gent relations probes, followed immediately bya battery of within-class preference probes,followed immediately by a second battery ofcross-class emergent relations probes. Al-though they were not accompanied by any


instructions or reinforcement for responding,the cross-class probes evoked respondingindicative of the presence of two classes ofsubstitutable stimuli where nodal separation ofstimuli did not influence test performances. Incontrast, the preference probes evoked re-sponding indicative of stimuli that weredifferentially related in accordance with nodaldistance. These essentially instantaneous shiftsin performance, which coincided with achange in test type, strongly suggest that thecontent of the trials were discriminative for theexpression of each type of performances.

Indeed, the trials had features that weredistinguishable from each other. The cross-class trials contained a sample from one class,a comparison from the same class and anothercomparison from a different class. The within-class probes contained a sample and twocomparisons, all from the same class. Thus,the two types of trials were formally discrimi-nable from each other in terms of thepresence or absence of stimuli from the sameor different classes. The cross-class probes thenfunctioned as discriminative stimuli for per-formances controlled by the discriminability ofthe stimuli between classes, while the within-class probes functioned as discriminative stim-uli for performances controlled by nodalproximity. These results support the notionthat the content of the probes were discrimi-native for the occurrence of class-based ornodally-based responding (Fields et al., 1993a;Fields & Moss, 2007; Fields et al., 1995; Fields& Watanabe-Rose, 2008). This analysis isconsistent with Sidman’s view that differentpartitions of the stimuli in an equivalence classcan be governed by contextual stimuli (Sid-man, 1994, pp 548–549).

Although it sounds contradictory for stimuliin a class to be interchangeable and also to bedifferentially related to each other, the datadescribed in the present experiments attest tosuch a circumstance. The immediate switchesin performance imply that both stimuluscontrol topographies had been establishedduring the training of the baseline relationsthat linked the stimuli in each set and weremaintained after class formation. Although thedefinition of an equivalence class involves ademonstration of the interchangeability of thestimuli in a set, and by implication their equalrelatedness, the procedures used to establishan equivalence class also establish other

relations among the stimuli in the set. Theserelations are indicative of a graded relatednesswhich is governed by the nodal separation of thestimuli in the set. While these two forms ofstimulus control coexist, the expression of eachform of stimulus control is determined by thetwo types of test trials which are discriminablefrom each other: one being sensitive to cross-class discriminative control and the other beingsensitive to the nodal structure of the class.Performances that demonstrate equal related-ness as documented by between-class discrimi-nations do not negate performances that dem-onstrate differential relatedness as documentedby within-class preference tests, and vice versa.

A single set of reinforcement contingenciesestablishes discrimination between classes anddifferential relatedness among the stimuli ineach class. Performances indicative of eachstimulus control repertoire cannot be mea-sured at the same time. Each, however, can beexpressed or measured in the presence of adifferent environmental setting. Each setting isdefined by the content of a given test trial.These test trials serve discriminative functionsthat occasion the expression of the tworelations that coexist among the stimuli in aclass. The results of Experiments 2 and 3support this integrated interpretation of therelations that exist among the members of anequivalence class.

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Received: March 1, 2010Final Acceptance: December 21, 2010


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