JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

CONDITIONAL RELATIONS BY MONKEYS: REFLEXIVITY,SYMMETRY, AND TRANSITIVITY

KENNETH D. MCINTIRE, JAMES CLEARY, AND TRAvis THOMPSON'

UNIVERSITY OF WISCONSIN-EAU CLAIRE AND UNIVERSITY OF MINNESOTA

Two cynomolgous macaques categorized six colors into two groups of three after conditional discrim-ination training (zero-delay symbolic match-to-sample). The procedures resulted in the establishmentof relations among the elements of each set-relations that were not specifically trained and that canbe characterized by the properties of reflexivity, symmetry, and transitivity. Each set of colors wasrelated to a characteristic pattern of responding: One response pattern involved temporal duration(press and hold the response keys); the second response pattern entailed repeated pressing and releasingof the response keys (fixed ratio 8). Six combinations of two colors were trained, three combinationsfrom each set. After discriminative performance stabilized for each monkey, they were tested with 10additional color combinations, all of which differed from the training combinations. The conditionalrelations established between test combinations can be characterized as stimulus equivalence. Thetraining procedures were analogous to the procedure of using category names, and have implicationsfor understanding the function of language in the formation of equivalence classes.Key zords: stimulus equivalence, conditional relations, discrimination training, reflexivity, symmetry,

transitivity, key press, monkeys

The logical properties of reflexivity, sym-metry, and transitivity underlie much of math-ematics and are routinely taught to grammarschool children as principles defining arith-metic operations on number systems. Transi-tivity requires a set of at least three elements.If element a bears a particular relation to ele-ment b (aRb) and the same relation is foundbetween elements b and c (bRc), then transi-tivity requires that aRc be true. Symmetry re-quires two elements: If aRb, then bRa. Re-flexivity or identity requires only one element:aRa. These three properties, formalized withinthe context of logic and mathematics, form thebasis of larger systems that require them asbasic operations. At least since Kant (1781/1929), logic systems have been proposed asrules explaining the interaction of people withtheir environments. An enduring question has

1 Kenneth D. McIntire is at the University of Wiscon-sin-Eau Claire; James Cleary and Travis Thompson areat the University of Minnesota. This research was con-ducted while K. D. McIntire was an Honorary Fellow atthe University of Minnesota. He is grateful to the Uni-versity of Wisconsin-Eau Claire and to the University ofMinnesota for the many courtesies extended to him. Grat-itude is also extended to two anonymous reviewers fortheir constructive evaluation of this paper.

Requests for reprints should be sent to Kenneth D.McIntire, Psychology Department, University of Wiscon-sin-Eau Claire, Eau Claire, Wisconsin 54702.

concerned the natural status of such logic sys-tems when incorporated into behavioral the-ories. In the present case, we have posed thefollowing question: Are reflexivity, symmetry,and transitivity purely formal, logical con-structions, or do they develop in the absenceof specific rule training as an organism re-sponds in organized (or even preorganized)ways to sets of events in its environment? Ifthe latter, what are the necessary and sufficientconditions for development of such relation-ships within an organism's repertoires?There is a relation between certain discrim-

ination-training procedures and the develop-ment of functional reflexive, symmetrical, andtransitive stimulus relations by adult, child,nonhandicapped, and retarded human popu-lations (Sidman, 1971; Sidman & Cresson,1973; Sidman, Kirk, & Willson-Morris, 1985).During conditional discrimination training, ifa consistent relationship aRb and bRc is es-tablished between three otherwise dissimilarstimuli, the relation aRc occurs in the absenceof specific training, as does cRa, cRb, bRa andaRa, bRb, cRc. For example, assume stimulusa to be the written word "six," b to be "6,"and c to be "XXXXXX." By establishing therelations, six -- 6 and 6 -- XXXXXX, usingconditional discrimination-training proce-dures, the relation six -- XXXXXX is estab-lished, as are the other untrained, and thus

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1987, 479 279-285 NUMBER 3 (MAY)

KENNETH D. McINTIRE et al.

UNRELATED STIMULIXXXXXX

6SIX

TRAINED RELATIONSXXXXXX_- 6

6 SIX

EMERGENT RELATIONSXXXXXX *XXXXXX

6 -6SIX _-SIX

6 XXXXXX

SIX -46

XXXXXX SIX

SIX XXXXXX

Fig. 1. Schematic of the relations that may emergeamong a set of three stimuli as a result of conditionaldiscrimination training. Implementation of the trainingprocedure requires the use of at least one set of threestimuli.

"emergent," relations indicated in Figure 1.By training two combinations of the threestimuli (aRb and bRc), all relations emergeapparently defined by the logical properties ofreflexivity, symmetry, and transitivity. As allthree stimuli stand in the same set of relation-ships with one another, they are mutually sub-stitutable, or equivalent, under these condi-tions. Stimulus equivalence classes are thusformed when stimuli bear a consistent rela-tionship with one another and are mutuallysubstitutable as defined by reflexivity, sym-metry, and transitivity. For example, one cansubstitute the spoken word "six" for the arrayXXXXXX or write the number 6 or six. Sub-sequently, this allows one to do arithmetic(4 + 2 = 6) and to write and talk about it("four plus two equals six"). Not all possiblecombinations of stimuli need to be trained.Once a stimulus becomes an element in an

equivalence class, the relationships of its useneed not be taught if the relationships havebeen taught with repsect to the other elements.

The conditions that are essential for devel-opment of equivalence classes remain unclear.It is possible that stimulus equivalence is sim-ply an emergent property of conditional dis-crimination training procedures. A second pos-sibility is that equivalence classes are relatedto verbal behavior and, as such, are probablylimited to humans. These possibilities havebeen evaluated in a series of experiments thatattempted to establish equivalence classes inmonkeys (D'Amato, Salmon, Loukas, &Tomie, 1985; Sidman et al., 1982). Except forone study showing that monkeys with "mas-sive" exposure to conditional discriminationprocedures demonstrate transitivity whentransitive relations are reinforced during test-ing (D'Amato et al., 1985), there is no evidencethat monkeys formed equivalence classes. In-asmuch as procedures similar to those usedwith the monkeys result in the development ofrobust equivalence classes in children (Sidmanet al., 1982), this suggests that the formationof equivalence classes is a uniquely humancharacteristic.

It is, however, possible that the previousfailures to develop robust equivalence classesin monkeys resulted from procedural ratherthan organismic limitations. If this is so, aprocedure resulting in the establishment ofstimulus equivalence in nonhumans may helpclarify how humans form equivalence classes.Many studies of the establishment of equiva-lence classes in human subjects used verbalstimuli (spoken or heard by the subjects) dur-ing discrimination training and/or equiva-lence testing. Moreover, even in the studiesthat used only visual stimuli, the subjects mayhave devised their own linguistic codes for thestimuli. Stated simply, the subjects may havetalked to themselves and created names for thenonsense figures, and those names may havehelped the formation of equivalence classes.This suggestion is supported by observationsof children creating names for nonsense stimuliused during discrimination training in the ab-sence of specific instructions to do so (Lazar,Davis-Lang, & Sanchez, 1984).Naming is a complex phenomenon, often

involving social functions and social conse-quences. However, its basis involves the per-formance of some arbitrary response in thepresence of a specific discriminative stimulus.It is possible that the discriminated emissionof differential response topographies is itselfof functional significance in the establishment

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of stimulus equivalence. As such, organismswould be expected to form equivalence classesonly to the extent that their behavioral rep-ertoires allow them functionally to "name"stimuli. We report here that cynomolgous ma-caques, when given a simple two-word namingsystem, are capable of forming two three-ele-ment equivalence classes with the propertiesof reflexivity, symmetry, and transitivity.

METHOD

SubjectsRang and Manley are female, wild-born

cynomolgous macaques (Macaca fascicularis)approximately 15 years of age. Neither hadbeen used for research for several years. Theypreviously had been exposed to procedures in-volving the discrimination of response durationbut had no experience with procedures similarto those of the present study. They were main-tained at their preexperimental body weightsof 3.2 and 4.0 kg, respectively. Both were feddaily rations of monkey biscuits in their homecages when sessions were completed.

ApparatusCentered on one wall of the primate test

chamber, approximately 10 cm above the gridfloor, a small food hopper caught the raisins,currants, chopped dates, dried banana chips,carob bits, and occasional dried papaya thatwere presented in small amounts as reinforc-ers. Three translucent plastic response keys(3.0 cm diameter) were mounted in a hori-zontal line 30 cm above the food hopper. Thecircular keys were mounted flush with the wall,10 cm apart. Approximately 0.15 N appliedto the face of a key depressed it sufficiently(about 2.0 mm) to operate one or both of twoseries-connected microswitches. Stimuli wereprojected through the keys by lamps locatedbehind each key. The chamber was constantlyilluminated and the noise of the exhaust fanwas always present. Stimuli were programmedand data were collected by solid-state digitallogic located in an adjacent room.

ProcedureSessions were conducted 4 to 6 days per

week and a session lasted until a monkeystopped key pressing for approximately 5 min.

A

Red Orange Yeow

0DGreen

0DBlue Vket

C)

B Odd Evenc 8 8 c

5 3 S

C

Fig. 2. A. The colors used as stimuli are ordered ac-cording to wavelength. The circled numbers adjacent toeach color name are used in all discussions requiring ref-erence to a specific color or combinations of colors. B. Thecolor combinations used for the conditional discriminationtraining task. Color combinations requiring the Odd re-sponse are on the left and those requiring the Even re-sponse are on the right. Cij indicates the comparison stimuliand S,j indicates the corresponding samples. The arrowsindicate which Cij is the correct selection for each com-bination. In training, the lateral location of the comparisonpairs was randomized for each sample. C. Schematic ofthe stimulus relations established by the conditional dis-criminations in Panel B.

* 1 - 1 and 2 - 2 reflexivity training were conductedso that Colors 1 and 2 would be presented as comparisonstimuli during training and location/order effects wouldnot affect later symmetry testing.

** Only Manley received this training for five sessions.

If fewer than 30 trials were initiated in a ses-sion, the session was often continued later thesame day. The final schedule on which themonkeys were trained was a three-key con-ditional discrimination task using six colorsprojected onto the translucent response keys.The colors were not pure wavelengths, but toa human observer they were clearly discrimi-nable as red, orange, yellow, green, blue, andpale violet. For purposes of description, thecolors are numbered and will be discussed asshown in Panel A of Figure 2.

Discrimination training. A trial was initiatedwhen the center key (the sample) was illu-minated with one of the six colors (see Figure3). The keylight remained illuminated until

4 Wavelength

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KENNETH D. McINTIRE et al.

NAME COMPARISON

Incorrect SELECTION

W COMPARISON PRESENT

Incorrect NAME SAMPLE

* (ij) * SAMPLE PRESENT

4 Sec

* * ITI

START

Fig. 3. Beginning at the bottom with the intertrialinterval (ITI), the sequence of events during a trial isshown schematically. The sample (Sij) is presented and a

response (Rij) is emitted in its presence. An incorrect R,jrestarts the ITI. A correct Rii turns off the Sij and turnson the comparison keys (Cij). An incorrect selection or anincorrect Rij results in an ITI. Correct Ri. and C.- selectionresults in a reinforcer on 65% of the trials and the initiationof the ITI on all trials.

one of two responses was emitted on the samplekey. An "Odd" response was completed whena key was pressed and held continuously for3.5 s. Any break in the continuity of the Oddresponse reinitiated timing of the 3.5-s dura-tion requirement. An "Even" response wascompleted with the eighth key press, that is,the key had to be pressed and released seventimes prior to the eighth press (fixed ratio 8).The Odd response was correct when the odd-numbered colors were present and the Evenresponse was correct for even-numbered colors.If an incorrect response to the sample occurred,the keys were darkened for 4 s. Any key press-ing during this intertrial interval (ITI) delayedthe onset of the next trial until 4 s after press-ing ceased. If a correct response occurred onthe illuminated sample key, the key was dark-ened and the two side keys (comparisons) wereilluminated. One of the comparison keys wasan Odd color and one an Even color. Thelateral arrangement of colors was randomwithin each pair. When a monkey pressedeither comparison key, the other comparisonkey was darkened and became inoperative.Thus, the monkey was forced to complete thetrial on the comparison key that was initiallyselected. The selected comparison key re-

Total trans 40/41 24/26

Total sym 50/51 42145

Total refl 34/36

Total sym x trans 21/24

TOTAL EQUIVALENCE 1451151

22123

12/12100/106

Fig. 4. Stimulus combinations used during equiva-lence testing are listed on the left, adjacent to the name ofthe relationship that is tested by each combination. Intesting, the lateral arrangement of comparison colors wasrandomized for each sample. Results of testing are shownin the right panel, and are presented as the number ofcorrectly completed trials divided by the total number oftrials of each combination presented to each monkey.

mained illuminated until either an Odd or anEven response was completed, regardless ofkey color. The completion of an Odd or Evenresponse darkened all keylights, initiated the4-s ITI, and presented a reinforcer when atrial was completed correctly. A correct trialrequired selecting the Odd comparison whenan Odd sample had been present and emittingthe Odd response in the presence of both Oddcolors. Emission of the Even response in thepresence of the Even sample and correspond-ing Even comparison key was also correct. Allother combinations of stimulus selection andresponse emission resulted in the darkening ofthe keys and the initiation of the ITI. A rein-forced trial may be construed as analogous toa human subject's pointing to the sample andcorrectly naming it, followed by pointing tothe correct comparison and naming it the same.When performance stabilized on this schedule,reinforcers were presented following correcttrials with a probability of .65.A correction procedure was intermittently

RELATIONS RESULTS

Odd RANG MANLEY

F(i(i) TransItivity 19/19 14114

K) ( Smmetry 16117 20/215/5

Reflexivity 17/18 10/11

Sym X Trans 12/12 5/5

Even

G4® Transitivity 21/22 10/12

~ 22/22 22/24M Symmetry

Reflexivity 17/17 12/12

Sym X Trans 9/12 7/7

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CONDITIONAL RELATIONS

Table 1Equivalence responses/trials for each monkey during test sessions.

Test Rang Manleysession Refl Sym Tran T x S Refl Sym Tran T x S

1 2/2 2/2 2/2 2/32 8/8 2/23 3/3 5/54 4/4 2/25 10/10 5/56 15/15 6/77 4/4 1/18 5/6 5/6 7/8 5/59 3/3 3/3 3/3 5/610 1/1 3/3 3/3 4/511 6/6 9/912 6/6 7/713 3/3 4/4 3/3 6/714 5/5 4/4 4/4 9/915 3/3 4/4 3/3 7/716 3/3 9/1017 4/5 7/718 5/5 5/519 5/620 4/5

Total 34/35 50/51 40/41 21/24 22/23 42/45 24/26 12/12

used during training sessions. When the cor-rection procedure was in effect, an incorrecttrial was repeated after the ITI until it wascompleted correctly. The order of presentationof the training combinations was quasi ran-domized on punched paper tape with the re-striction that no trial was repeated unless anerror had occurred.The color combinations used as sample and

comparison stimuli on the final conditionaldiscrimination procedure are shown in PanelB of Figure 2. Additionally, Panel C of Figure2 shows in schematic form the color relationsthat were established by the training combi-nations.

Equivalence testing. After each monkey'sperformance stabilized on the training sched-ule, equivalence test sessions were conductedone to three times per week. During test ses-sions, stimulus combinations were presentedthat had not occurred during training. Thesetest combinations were selected to reveal thepresence of conditional relations not specifi-cally trained. Equivalence testing sessions wereprocedurally the same as training sessions withthe following exceptions: First, errors on acomparison stimulus never caused a trial to berepeated. Second, the probability of reinforce-

ment for correct completion of a trial involvingstimulus combinations that had been used dur-ing training was increased to .80. Third, onein seven stimulus combinations, on average,was a test combination that never had beenpresent during training conditions. Addition-ally, and importantly, test combinations werenever followed by reinforcement. Figure 4shows the color combinations introduced dur-ing equivalence testing sessions.

Correctness during equivalence testing wasevaluated using the same criteria that wereused during training: The proper comparisonmust be selected and the proper response emit-ted in its presence. Testing the symmetry re-lations required placing Colors 5 and 6 on thesample key for the first time. During testing,Samples 5 and 6 were repeated until a correctsample response was emitted. Test sessionswere interspersed among the continuing train-ing sessions.

RESULTSRang received 2,162 trials and Manley 5,536

trials of shaping prior to exposure to the con-ditional discrimination task. Rang received3,104 trials of conditional discrimination

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KENNETH D. McINTIRE et al.

ODD EVEN

( Rj i) Rj

B

R4-Ri Rj RjFig. 5. A. Schematic of relations established between

stimulus elements and naming responses during discrim-ination training. B. Schematic of proposed relations re-sponsible for the establishment of equivalence classes.

training prior to equivalence testing and Man-ley received 3,073 training trials. In the finalthree training sessions prior to equivalencetesting, Rang performed at 95% accuracy (241/254) and Manley performed at 87% (278/319). Figure 4 shows that both monkeys per-formed as accurately on the test color combi-nations as they did on the color combinationsused during training. Both Rang and Manleydemonstrated conditional discrimination per-formance based on reflexivity (97%, 96%),symmetry (98%, 93%), and transitivity (97%,92%). Additionally, both monkeys demon-strated equivalence with a test pair that re-quired a combination of symmetry and tran-sitivity (87%, 100%). These equivalenceperformances were stable over 18 and 20 test-ing sessions distributed over 5 and 8 weeks forManley and Rang, respectively. Hence, oncethe equivalence classes were established, theemergent relations were robust and stable inthe absence of reinforcement. Table 1 showsthe equivalence performance for each monkeyduring each test session.The difficulty in establishing discriminative

control prior to testing is evident in the rela-tively large number of shaping and trainingtrials required prior to the introduction of thetest combinations. It is probable that stimuluslocation and/or temporal order, in addition towavelength and response topography, weresources of discriminative control. (Evidence for

this was not quantified because of equipmentlimitations.) However, it was clear that manyresponses to the test combinations were of adifferent latency and/or duration than the pre-dictable, steady responding in the presence ofthe training combinations. Additionally, test-ing symmetry relations required placing Colors5 and 6 on the sample key for the first time.Rang apparently generalized to Sample 5(blue) from Sample 4 (green) and emitted sev-eral Even responses in the presence of Sample5 prior to emitting Odd responses. Manley hadan analogous problem with Sample 6 (orange),apparently generalizing to it from 1 (red) or3 (yellow). It is possible that this additionalsource of control affected Rang's accuracy onthe symmetry x transitivity test involvingSample 6.

DISCUSSIONEstablishing differential response patterns

that appear to share properties with a two-word naming system (Odd-Even) resulted inthe establishment of equivalence classes whereprevious procedures had met with limited suc-cess. These findings indicate the potential im-portance of differential response topographyin the ontogeny of equivalence classes and theemergence of reflexivity, symmetry, and tran-sitivity. The use of the language metaphor inour description of the monkeys' performancesis not intended to imply complete similarity tohuman language. A metaphor, like all equiv-alence classes, is conditional. However, an ex-planation for the development of equivalenceclasses in the present study may provide insightinto analogous functions performed by humanlanguage. The conditional discrimination taskused here required the monkeys to respondcorrectly to 12 patterns of training stimuli,combined with two very distinctive patterns ofresponding. If the monkeys had simply learnedconfigurations of colors or stimulus-stimulusassociations, they would not be expected toform equivalence classes. Additionally, learn-ing all possible stimulus-response sequencesis not a very efficient way of performing thistask. A much simpler and more efficient strat-egy would be to relate each element of eachstimulus class (the colors) with the appropriateresponse topography, as shown in Figure 5;that is, name each stimulus as it appears.

Once the responses were clearly differen-tiated and the stimuli were discriminated,

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CONDITIONAL RELATIONS 285

stimulus events related to the emission of thefirst naming response set the occasion for asubsequent naming response of the same type.This process can account for our results andis consistent with previous observations thatsome complex discriminative performance maybe facilitated or mediated by the emission oftopographically distinct "coding" responses (seeCarter & Werner, 1978). It is possible thatthe use of names by humans shares functionalproperties with the differential responses emit-ted by the monkeys in our study. Names maybecome functionally related to sets of otherwisedissimilar stimuli and result in the formationof equivalence classes, that is, conditional re-lations. Consequently, the formation of equiv-alence classes, hence of reflexivity, symmetry,and transitivity, may arise from the use of afunctional naming system.

Although the above interpretation requiresdirect testing, there are some relevant resultsfrom early work on mediated association. Birge(1941) showed that naming can be an effectivemediator for children who learned the namesof four boxes with distinctive designs on thetop. Two boxes shared one name and two boxesshared another. After the child learned thenames of the boxes, one pair with contrastingnames was repeatedly presented with candyunder one of them. The child was then pre-sented with the other pair of boxes and toldto guess which one had candy under it. Underthese conditions, performance was essentiallyat the chance level. However, when the childwas required to name the boxes as they werebeing selected, there was substantial facilita-tion of correct selections. This procedure, al-though not a conditional discrimination task,is in several respects similar to the procedureused in the present experiment.Of course, a simple homogeneous naming

chain such as that used here is not the onlyinteraction possible between verbal operantsand the formation of stimulus classes. Indeed,the complexities of children's verbal behaviorduring discrimination training (Lazar et al.,1984) indicate the rapidity with which het-erogeneous verbal sequences may develop.However, the simple homogeneous responsechains used here may constitute a relativelysimple mechanism upon which complex re-lations are established. For example, use ofOdd-Even and Even-Odd response chainsmight have facilitated Rang's and Manley'sperformances as effectively as the Odd-Odd

and Even-Even chains used in the presentstudy.

It is questionable whether any set of trainingprocedures will greatly increase Rang's orManley's equivalence sets or the number ofequivalence sets they demonstrate. However,pongids, which are capable of emitting a largenumber of different manual signs (Gardner &Gardner, 1975; Patterson, 1981), would beexpected to be relatively adept at formingequivalence classes. In the wake of the ape-language controversy, it may be profitable toreaddress the issues of comparative develop-ment from the beginning, including naming(Terrace, 1985) and stimulus equivalence.

REFERENCESBirge, J. S. (1941). The role of verbal response in transfer.

Unpublished doctoral dissertation, Yale University.Carter, D. E., & Werner, T. J. (1978). Complex learn-

ing and information processing by pigeons: A criticalanalysis. Journal of the Experimental Analysis of Behav-ior, 29, 565-601.

D'Amato, M. R., Salmon, D. P., Loukas, E., & Tomie,A. (1985). Symmetry and transitivity of conditionalrelations in monkeys (Cebus apella) and pigeons (Co-lumba livia). Journal of the Experimental Analysis of Be-havior, 44, 35-47.

Gardner, R. A., & Gardner, B. T. (1975). Early signsof language in child and chimpanzee. Science, 187,752-753.

Kant, I. (1929). Critique of pure reason (N. K. Smith,Trans.). London: Macmillan. (Original work pub-lished 1781)

Lazar, R. M., Davis-Lang, D., & Sanchez, L. (1984).The formation of visual stimulus equivalences in chil-dren. journa! nf the Experimental Analysis of Behavior,41, 251-266.

Patterson, F. G. (1981). Ape language. Science, 211, 86-87.

Sidman, M. (1971). Reading and auditory-visual equiv-alences. Journal ofSpeech and Hearing Research, 14, 5-13.

Sidman, M., & Cresson, O., Jr. (1973). Reading andcrossmodal transfer of stimulus equivalences in severeretardation. American Journal ofMental Deficiency, 77,515-523.

Sidman, M., Kirk, B., & Willson-Morris, M. (1985).Six-member stimulus classes generated by conditional-discrimination procedures. Journal of the ExperimentalAnalysis of Behavior, 43, 21-42.

Sidman, M., Rauzin, R., Lazar, R., Cunningham, S.,Tailby, W., & Carrigan, P. (1982). A search forsymmetry in the conditional discriminations of rhesusmonkeys, baboons, and children. Journal of the Exper-imental Analysis of Behavior, 37, 23-44.

Terrace, H. S. (1985). In the beginning was the "name."American Psychologist, 40, 1011-1028.

Received July 21, 1986Final acceptance January 5, 1987