AND UNIVERSITYOFNORTHCAROLINA -...

JOURNAL OF THE EXPERIMENTAL ANALYSIS OF BEHAVIOR

STIMULUS EQUIVALENCE AND ARBITRARILYAPPLICABLE RELATIONAL RESPONDING

DAVID STEELE AND STEVEN C. HAYES

UNIVERSITY OF NORTH CAROLINA AT GREENSBORO ANDUNIVERSITY OF NEVADA

Subjects' responses to nonarbitrary stimulus relations of sameness, oppositeness, or difference werebrought under contextual control. In the presence of the SAME context, selecting the same comparisonas the sample was reinforced. In the presence of the OPPOSITE context, selecting a comparison asfar from the sample as possible on the physical dimension defined by the set of comparisons wasreinforced. Given the DIFFERENT context, selecting any comparison other than the sample wasreinforced. Subjects were then exposed to arbitrary matching-to-sample training in the presence ofthese same contextual cues. Some subjects received training using the SAME and OPPOSITE contexts,others received SAME and DIFFERENT, and others received SAME, OPPOSITE, and DIFFER-ENT. The stimulus networks established allowed testing for a wide variety of derived relations. Intwo experiments it was shown that derived performances were consistent with relational respondingbrought to bear by the contextual cues. In contexts relevant to the relation of sameness, stimulusequivalence emerged. Other kinds of relational networks emerged in the other contexts. Arbitrarilyapplicable relational responding may give rise to a very wide variety of derived stimulus relations.The kinds of performances seen in stimulus equivalence do not appear to be unique.Key words: stimulus equivalence, relational responding, relational frames, nonarbitrary stimulus

relations, arbitrary stimulus relations, stimulus control, matching to sample, button press, humans

The basic phenomenon now called stimulusequivalence has had several incarnations inmodern psychology. In 1971 Sidman resur-rected the area by linking it to a powerfulprocedure: matching to sample. Since then, be-havior-analytic research has focused on thelimits of the equivalence phenomenon (e.g.,populations, stimulus modality, stimulus ar-rangements), refinement of its measurement(e.g., Sidman & Tailby, 1982), and descrip-tions of conditions under which it may arise(e.g., Sidman, 1986). Behavior analysts havedevoted little attention, however, to a theoret-ical account of equivalence. At present, stim-ulus equivalence is merely the description ofa behavioral outcome-the process involved isunknown.

Early researchers (e.g., Sidman & Cresson,1973; Spradlin, Cotter, & Baxley, 1973) ten-tatively discussed their work in terms of pos-sible response mediation, much along the linesof stimulus-response learning theory. Re-sponse mediation was later rejected as unnec-

Correspondence and reprint requests may be addressedto Steven C. Hayes, Department of Psychology, Universityof Nevada-Reno, Reno, Nevada 89557-0062.

essary on the grounds that the particular re-sponses (i.e., selecting stimuli) are onlydifferentiated with reference to the stimuli in-volved and thus add little to the explanationof the derived stimulus relations themselves(Sidman, 1986; Sidman, Cresson, & Willson-Morris, 1974; Sidman & Tailby, 1982). Re-cently, response mediation models havereemerged in the form of naming-based inter-pretations (e.g., McIntire, Cleary, & Thomp-son, 1987). The effects of naming, however,also require a theoretical explanation. Theproposed alternatives either do not yet haveexperimental support, as in McIntire et al.'shomogeneous chain model (Hayes, 1989; K.Saunders, 1989), or themselves assume name-object derived relations in order to explain sim-ilar derived relations between samples andcomparisons.A recent account views equivalence as the

result of relational responding arbitrarily ap-plied to the matching-to-sample situation(Hayes, 1991; Hayes & Hayes, 1989). Or-ganisms from insects to primates can learn torespond to nonarbitrary relations among stim-uli (e.g., larger than, darker than; see Reese,1968). These relations can be brought undercontextual control and can generalize to new

519

1991, 56, 519-555 NUMBER 3 (NOVEMBER)

DAVID STEELE and STEVEN C. HAYES

sets of formally related stimuli (Lowenkron,1989). Verbal humans, however, seem also toapply these kinds of relations when there arecontextual cues to do so without significantregard for the form of the items being related.The reader told that A = B > C will be ableto specify the relation between A and C (>)or C and A (<) and so on, but the letters A,B, and C had nothing to do with the particularrelations being applied. Such arbitrarily ap-plicable relations have been termed "relationalframes" (Hayes & Hayes, 1989). Relationalframe theory holds that arbitrarily applicablerelational responding has an extensive history,largely in the context of language training, thatcan be brought into the experimental situationby virtue of contextual cues to do so. In thisview, stimulus equivalence as commonly seenmay be the result of an application of a learnedframe of "coordination" (sameness) to thestimuli in arbitrary matching-to-sample pro-cedures.A wide variety of relational frames are pos-

sible, and the nature of the derived perfor-mances they comprise v1aries widely. For ex-ample, the abstract relation of oppositeness hasthe property that an opposite of an opposite isthe same, an opposite of an opposite of anopposite is an opposite, and so on. Whereasstimulus equivalence may be an outcome of ahistory establishing the frame of sameness orcoordination, frames of opposition or of dis-tinction would give rise to very different kindsof relational networks. Conditional discrimi-nation training could thus give rise to no de-rived performances, derived equivalence, orother derived relations, depending on the na-ture of the relations brought to bear on thesediscriminations via the contextual cues in-volved.The relational frame concept requires a dis-

tinct nomenclature, part of which will be re-viewed because it is necessary to a descriptionof the present experiments and their results.Symmetry, although appropriate for equiva-lence, is not an appropriate general term forall arbitrarily applicable relations becausemany are not strictly symmetrical (Russell,1919, 1937). For example, if A is better thanB, then B is worse than A. Hayes (1991; Hayes& Hayes, 1989) suggested the term mutualentailment, defined as follows:

Crel.{A rel.B I B relyA}.

That is, in a context that brings a particularkind of relational responding to bear (Crel.),the designation of that relation between EventsA and B through direct training entails (en-tailment is symbolized by I) a derived re-lation between B and A (rely) that may or maynot be the same as the designated relation. Inthese terms, symmetry is a special case of mu-tual entailment.

Similarly, transitivity is not applicable to allkinds of arbitrarily applicable relational re-sponding (Russell, 1919, 1937). Hayes andHayes (1989) suggested the term combinatorialentailment, defined as follows:

Crelx and Crel {A relxB and B relyC A.relpC and C relqA}.

That is, given contexts (Crel. and Crely) thatspecify mutual relations (relx and rely) amongthree or more items, relations are entailed (relpand relq) between the stimuli based on thecombinations of these mutual relations. In theseterms, transitivity and the equivalence relationdescribed by Fields, Verhave, and Fath (1984)are special cases of combinatorial entailment.

Reflexivity, in Sidman's sense, can alwaysinvolve recognizing stimuli as themselves basedupon formal properties of the stimuli involved.Identity matching based on form is, by defi-nition, not an arbitrary relation. Relations inthe abstract, however, can either be reflexiveor irreflexive. For example, the arbitrary re-lation of sameness is reflexive, but oppositenessis not (A cannot be the opposite of A). We willuse the term relational reflexivity/irrefiexivityto refer to the relation of a stimulus to itselfin a given relational context. This is viewedas a special case of mutual entailment.The present study sought to establish three

different types of relational responding (same,different, and opposite) and apply them to anarbitrary matching-to-sample context. De-rived performances were then examined to seeif they could be understood as instances ofmutual and combinatorial entailment.

EXPERIMENT 1The strategy in this experiment was to pre-

train arbitrary contextual cues to control same,opposite, or different responding with non-arbitrary stimulus sets. Four subjects were ex-posed to same and opposite pretraining, and3 were exposed to same and different pretrain-

520

ARBITRARILY APPLICABLE RELATIONAL RESPONDING

ing. These pretrained cues were then used inan arbitrary matching-to-sample context, andthe impact of the cues on derived stimulusrelations was examined. Two control subjectswere given arbitrary matching-to-sampletraining, but without pretraining with regardto the contextual cues. Relations among thetraining stimuli were assessed in unreinforcedtesting trials given to both the experimentaland control subjects.The network of relations presented dia-

grammatically in Figure 1 allowed the assess-ment of a variety of derived relations. Con-sider, for example, the relation "opposite." IfAl is the opposite of B2 and Al is the oppositeof C2, B2 and C2 are the same, not opposite.Thus, we wanted to assess whether subjectstrained to pick B2 and C2 (given Al) only inthe presence of a pretrained cue for an "op-posite" relation would now not pick B2 givenC2 in the presence of that cue, but insteadwould do so in the presence of a pretrainedcue for a "same" relation. Similarly, stimulirelated across three stages of the opposite re-lation are opposites: If Al is the opposite ofB2, Al is the opposite of C2, and C2 is theopposite of D1, then B2 and D1 are opposites.Thus, we assessed whether subjects trained topick these stimuli in the presence of a pre-trained cue for an "opposite" relation wouldnow pick B2 given Dl in the presence of thatcue, but not in the presence of pretrained cuefor a "same" relation.

TrainedRelatlons

Bi

C1

S~B2

Al

C20 s

DI D2

Baslc Set of TestedDerivedRelatlons

0

.-------------- B1Bi

0A_, _

Al ------------------------

' i-------C -----------------;-----------------------------

--------------------------------------- Di

s

C2I

*, 0D2

0

Fig. 1. Basic network of relations trained and testedin Experiment 1. Solid arrows indicate trained discrimi-nations, and dashed arrows indicate assessment of relationsby probe items. Letters S or 0 indicate relational stimulusSAME or OPPOSITE. Same/different subjects weretrained in the same fashion but DIFFERENT was usedin place of OPPOSITE. Additional relations were trainedand tested with some subjects (see tables and figures).

METHODSubjects

Nine subjects, 13 to 17 years old, were re-cruited through offers of paid participation.Five were male, and 4 were female. Subjectswere paid at a mutually agreed upon rate basedon their usual rate of compensation for part-time work such as baby-sitting, but receivedno less than $2.00 per hour. All subjects werein college preparatory classes in high school.

ProcedureSessions lasted up to 2 hr and were generally

scheduled on consecutive days for individualsubjects. The following instructions were givenat the start of the first session:

This is an experiment in learning. It is not apsychological test of any kind. We are inter-

ested in aspects of learning common to all peo-ple.When the experiment begins, the screen in

front of you will show some geometric figures.There will be either two or three figures at thebottom of the screen. Your task is to choose oneof these figures by using the joystick. The joy-stick controls the movement of a box on thescreen. Move the joystick until the box is aroundthe figure you want to choose. Then press thebutton on the joystick. Sometimes there will betwo figures in the bottom section of the screen,and at other times there will be three. You makeyour choice the same way in either case.

Sometimes, after you press the button, a mes-sage on the screen will tell you whether or notyou have made the correct choice. We want youto learn to make as many correct responses aspossible. Try to make correct responses on allproblems. At first, the problems may be easy,but they will get harder. You will need to pay

521

Stimuli Used in Experiments

[OPPOSITE (EXP. 1)

DIFFERENT

B2

D2 (EXP. 1)C3 (EXP. 2)

OPPOSITE (EXP. 2)

C1

xi

wT7Ni N2

(stimuli randomly reassigned for Subject 4. See text.)

Fig. 2. Arbitrary visual stimuli used in training and probe items in Experiments 1 and 2.

N3

AlSAME

Bi

Dl (EXP. 1)B3 (EXP.2)

C2

X2

I I

r-i


attention right from the start, because what youlearn at first can be used later to make correctresponses.

If you have any questions, ask them now. Icannot answer any questions after you start.

Subjects were seated at a table in front of acomputer monitor connected to a Radio Shack®Color Computer and a joystick. All experimen-tal tasks were presented and monitored via thecomputer (software, written in CoCoBASIC,is available from the first author). In a giventrial, an arbitrary visual stimulus cueing therelation involved was presented in the centerof the top third of the monitor screen. (Byconvention, we will refer to these second-orderconditional stimuli by the generic name of "re-lational" stimuli; when speaking of a specifictype we will refer to them as the SAME, OP-POSITE, or DIFFERENT stimuli, capital-ized to avoid literal confusion.) After 2 s, thesample stimulus was presented in the centerof the middle third of the screen. After another2 s, the comparison stimuli were presented inrandom positions (left, center, or right) at thebottom of the screen while the relational andsample stimuli remained. All stimuli used inthe experiment are shown in Figure 2.Moving the lever on the joystick from left

to right moved a box on the monitor screen soas to surround one of the available comparisonstimuli. Pressing a button on the joystick case"selected" the stimulus inside the box. In ad-dition to recording the comparison selected, foreach trial latency of response was recordedfrom the complete presentation of the com-parisons to a selection response. No specialinstructions regarding speed of responding weregiven to the subjects (see instructions above).During training and reviews of previouslytrained relations, feedback was given. Whenthe response was correct, two tones soundedand "correct" appeared on the screen. If aresponse was incorrect, a repetitive low-pitchedtone sounded and "wrong" appeared.

Pretraining for same/opposite control. Foursubjects were given same/opposite pretrain-ing. During pretraining, it was possible to re-late the sample and comparison stimuli on thebasis of their physical properties. Eight sets ofstimuli were used, each with three comparisonstimuli varying on a single physical dimension:(a) short to long lines; (b) small to large squares;(c) sets of few to many dots; (d) sets of closelyspaced to distantly spaced lines; (e) a scale witha cursor that is located at the top, bottom, or

middle; (f) a scale with a cursor that is locatedat the left, right, or center; (g) figures drawnwith very thick to thin lines; and (h) tall toshort lines. Each set was presented with thesample drawn from either end of the range ofdifferences, yielding 16 different sets of sampleand comparison stimuli. For example, a shortline might appear as the sample and short,medium, and long lines might appear as com-parisons. In the presence of the SAME stim-ulus, selection of the short line was reinforced.In the presence of the OPPOSITE stimulus,the selection of the longest line was reinforced.

Training was conducted in blocks of 20 tri-als. Within each block, the number of trialswith the sample drawn from a given end ofthe continuum or using a given relational stim-ulus was balanced. For example, when com-parisons were long to short lines, the OP-POSITE stimulus was presented for 10 trials,five trials with the short line as sample andfive trials with the long line as sample. A sim-ilar procedure was used for the SAME stim-ulus, yielding a total of four specific problemsin each set. Individual trials within a blockwere intermixed in random order.

Subject 2 did not respond correctly to pre-training problems presented concurrently, sothe procedure was modified slightly for thissubject. A given problem was presented overand over until 90% accuracy was achieved ina 20-trial block, and then a different problemwas presented. After accurate responding wasestablished to each of the four problems in aset (presented serially), all four problems inthe set were presented in mixed blocks. Afterthe initial three stimulus sets were learnedusing this procedure, Subject 2 was able tomaster the remaining pretraining tasks withthe general procedure used with all other sub-jects.The first part of pretraining with feedback

was conducted with three sets of stimuli-longto short lines, large to small squares, and tallto short lines. The subjects had to achieve a90% accuracy rate on each set of stimuli beforegoing on to the next set. Once responding onall three sets was at the 90% accuracy level,problems from the three sets were presentedconcurrently in blocks of 32 trials. When a90% accuracy rate within a block was achieved,unreinforced probes were used to test for gen-eralized control by the relational stimuli: Anovel set of stimuli (from the eight above) waspresented for six trials with no feedback (three

523

DA VID STEELE and STEVEN C. HAYES

trials with each kind of relational stimulus).If any errors were made in relational respond-ing to the novel stimuli, responses to this setof stimuli were trained to criterion and anotherset of novel stimuli was presented for six trials.If all responses to a novel set of stimuli werecorrect, additional novel sets were presentedwithout feedback. The criterion for successfulpretraining was errorless performance on alltrials during the presentation of three consec-utive novel sets of stimuli. If a subject madeany incorrect responses with a set of stimuli,responses to those stimuli were trained withfeedback and an additional set of novel stimuliwas presented.

Pretrainingfor same/different control. Threesubjects received same/different pretraining.This was identical to the same/opposite train-ing above except that the DIFFERENT re-lational stimulus was used instead of OP-POSITE and only two comparisons werepresented, one of which was identical to thesample. There was no particular physical di-mension along which the two comparisons dif-fered (e.g., the two comparisons might be arectangle and a circle). In the presence of theSAME stimulus, the selection of the compar-ison that was identical to the sample was re-inforced. In the presence of the DIFFERENTstimulus, selection of the comparison that wasnot identical to the sample was reinforced. Twocomparisons were used with these subjects be-cause if three comparisons were used, therewould be two correct answers in the presenceof the DIFFERENT stimulus. This could havedistracted the subjects from the specific natureof the relation being trained. Training wasconducted in blocks of 20 trials- 10 trials withthe SAME stimulus and 10 with the DIF-FERENT stimulus. Each block used one setof two arbitrary stimuli (e.g., a rectangle anda circle), and each stimulus in the set was usedas the sample an equal number of times.

Arbitrary matching-to-sample training. In thetables and in the text for all experiments, ar-bitrary matching-to-sample problems andprobes are described using the same conven-tions. The relational stimulus is given first,using the letters S, 0, and D to represent theSAME, OPPOSITE, and DIFFERENTstimuli. The next letter/number combinationin brackets is the sample, and the next set ofnumber/letter combinations separated bydashes is the set of comparison stimuli. The

reinforced comparison, or the "correct" one inprobe trials, is italicized. For example, the no-tation O[Al]B1-B2-B3 indicates that in thepresence of the OPPOSITE stimulus, select-ing B3 given Al was reinforced or correct. Attimes there is no need to describe the unrein-forced (or "incorrect") comparisons and onlythe reinforced or predicted comparison is given.

All subjects received arbitrary matching-to-sample training: 4 with SAME and OPPO-SITE relational stimuli, 3 with SAME andDIFFERENT (using the network of relationsshown in Figure 1 except that some subjectshad DIFFERENT instead of OPPOSITE),and 2 control subjects who received no pre-training but were otherwise treated identicallyto the same/opposite subjects. In all trainingblocks each problem was presented for 10 tri-als, randomly intermixed with the other prob-lems. The size of the training block thus de-pended on the number of specific problemsinvolved.The basic training and testing sequences are

presented diagrammatically in Figure 3. Ex-amination of Figure 3 is essential to an un-derstanding of this complex experiment. Thebasic flow of events was as follows. First, A-Band Y-X relations were trained. Y-X trialswere included so that the X stimuli wouldprovide a pool of incorrect comparisons thathave a history of reinforced selection and couldbe used in subsequent probes for mutual en-tailment and combinatorial entailment. Probesthen assessed whether the subjects showed mu-tual entailment (e.g., S[B1]A1-X2) and rela-tional reflexivity/irreflexivity (e.g., O[Al]Al-N2). Note that a novel stimulus, N2, was usedin this test to avoid complicating the relationalnetwork. Then combinatorial entailment (e.g.,O[Bl]B2-X1) of the trained relations was as-sessed. Following each additional training set(A-C and C-D relations) all of the trainedrelations were reviewed concurrently withfeedback given on each trial, and probes as-sessed mutual entailment and combinatorialentailment of the trained relations withoutfeedback. To advance to the next phase of thestudy, a subject had to achieve 90% accuracyfor the block of trials and no lower than 80%accuracy on any given problem. Failure toachieve criterion resulted in a return to thesame training block.The number of different types of training

and testing trials was kept to the minimum

524


PRETRAINING

(an example: see text)0 S

(correct)

EXPERIMENT

Train A-B and Y-X relationsS 0

Probes

Mutual entailment0 SDl D2

Cl C2 C1 C2(correct)

Combinatorial entailment

0 S 0 SDl DI Al Al

Bi B2 B1 B2 Dl D2 Dl D2

SAl Al Yl Yl

B1 B2 B1 B2 Xl X2 Xl X2Fig. 3. (Continued)

Mutual en

0B2

Al X2

Probes

Relatitailment reflexivity/i

S SB1 Al

Al X2 Al NI

Combinatorial entailment0 0Bl B2

Xl B2 X2 Bi

Train A-C relations(and review previously trained relati

0 SAl Al

C1 C2 Cl C2

Probes

Mutual entailment0 SC2 Cl

Al X2 Al X2

Combinatorial entailment0 0C1 C1

B1 B2 C2 X2 BI B2

Train C-D relations(and review previously trained relat

0 S

C2 C2Dl D2 Dl D2

Fig. 3. The basic training and testingExperiment 1. Specific sequences varied for

needed to support or disconfirm the presenceof a derived relational network. A network

ional based on a lean set of examples was experi-rreflexivity mentally advantageous in part because the task

o was quite complex and we did not wish toAl overload the subjects. The primary concern,

Al N2 however, was that derived relations can emergein increasingly complex and difficult-to-pre-dict ways (e.g., through combinations of ex-clusion and equivalence) in complex relationalnetworks of the kind trained in this experi-ment. The results from uncluttered networksare thus more open to the detection of sourcesof control other than those intended. In thetraining and testing sequence as described, it

ions) may not be immediately obvious why specificproblems were constituted as they were (e.g.,why certain comparison stimuli were used),why only a certain subset of tests was done,or why tests were conducted in particular se-quences. The number of considerations in-volved were very numerous and thus expla-nations for every decision are not included inthis report, but the driving consideration wasthe development of a network in which thesources of control over responding went be-yond equivalence and simple forms of exclu-sion, or other sources such as reinforcement

o density or consistent reinforced pairings be-B1 tween relational stimuli and specific compar-

Cl C2 isons. For example, in Experiment 1 testingfor combinatorial entailment dealing solelywith same (Bl-Cl) was delayed or avoided

tions) entirely to reduce the chance that perfor-mances derived through relations of differentor opposite involved simple exclusion via apreviously established equivalence relation.

Testing blocks. Two to four types of probessequence for were presented in the testing trial blocks, ran-some subjects. domly alternating with previously trained

0

SC2

525


Subject 1 (Pretrained Same/Opposite)0 (5- 100%)

° 6 - 96%)

--r------ Bi ------------------------------- B2 --0 (3 100%)

| ,S (1 100%) ""0> (1 - 100%)/r~~~~~~~~e%i 4 fnfonX

AlS'> E(6-96%)lS (4 - 100%) ' . 0(4- 100%)

S but not0 (2 - 100%)-C -- C2------

0 (5-100%) A0 (6-96%) A

0 (5- 100%)0 (6 - 96%)

B1

Tralned:Bi B2

AlWsCl C2

DI D2

B2 0 (8 -100%)0 (10-100%)

,,1Al ------------------------

S (8- 100%) ,,S (10- 100%) ,, E

4

'S (8 - 100%)(10 - 100%)

c2

f%j.y 0/ c

0 (8- 100%) 't,0 (10 - 100%) \

II

I-~i~e,i"7 7c:_7_Dl ?JI''-I°o) OtQ-f°O) D2

0° (9 - 100%) s (9 - 100%)L

Fig. 4. Testing performance of Subject 1 (pretrained with SAME and OPPOSITE). Dashed lines indicate probesthat were above 80% correct, where "correct" is defined as selecting the indicated stimulus. Wavy lines indicate probeswere below 80% on at least one of the testing blocks recorded in that section. The letters S and 0 indicate the relationalstimulus presented. Numbers in parentheses indicate the specific testing block (these same numbers are used in Table1 for cross reference) and the percentage correct. See Table 1 for specific comparison stimuli used and training sequences.

problems, all without feedback. In any givenblock, all types of probes were presented anequal number of times (a minimum of eight),and the total number of probe trials and thenumber of trials over previously trained prob-lems were equal. These constraints dictatedthe total number of trials in a given block. Forexample, if a block was to contain six previ-

ously trained problems presented withoutfeedback and four types of probes, each typeof probe would be presented on nine trials (fora total of 36 probe trials) and each trainedproblem would be presented without feedbackon six trials (for a total of 36 trials). Eachblock of trials was planned for the smallestnumber of trials that would meet these criteria.

526

IL-- I A= -9 F-lr,%13Z IL


Table 1

Percentage of correct responses on training problems and probes for Subject 1 (SAME/OP-POSITE pretrained).

Trained problem or testing probe

Train A-B and Y-X relations (total of 40 trials)1. Probe B-A mutual entailment: O[B2]A1-X2 and S[Bl]A1-X22. Probe relational reflexivity/irreflexivity3. Probe combinatorial entailment: O[Bl ]B2-Xl and O[B2]Bl-X2

Train A-C relations (total of 20 trials)Review A-C, A-B, and Y-X with feedback (24 trials)

4. Probe C-A mutual entailment: O[C2]A1-X2 and S[Cl]A1-X25. Probe combinatorial entailment: S[C2]Bl-B2, O[C1]C2-X2, O[C1]B1-B2, and O[Bl]C1-C2

[Break between sessions]Review A-B, A-C, and Y-X with feedback (24 trials)

6. Probe combinatorial entailment: S[C2]Bl-B2, O[Cl]C2-X2, O[ClIB1-B2, and O[BlJC1-C2Train C-D relations (20 trials)Review A-B, Y-X, A-C, and C-D with feedback (32 trials)

7. Probe D-C mutual entailment: O[Dl]Cl-C2 and S[D2]C1-C28. Probe combinatorial entailment: O[Dl]Bl-B2, S[Dl]B1-B2, O[A1]D1-D2, and S[Al]D1-D2

Review C-D relations (5 trials each, 10 trials total)9. Probe D-C mutual entailment: O[Dl]Cl-C2 and S[D2]Cl-C2

10. Probe combinatorial entailment: O[Dl]B1-B2, S[Dl]Bl-B2, O[Al]Dl-D2, and S[A1]D1-D2

Correct

9310010010095100100100

100961009875100100100100

The criterion for mastery was 90% accuracyfor the block of probes and no lower than 80%accuracy on any given type of probe. Usually,when a subject failed to achieve these accuracyrates, he or she was given a review of all pre-viously trained problems; this was followed bya return to the same block of probes where thedifficulty was encountered. Because repeatedreviews might provide the subject with feed-back about inaccuracy, if three reviews did notproduce accurate responding on a given probeblock, other problems were presented beforereturning to the problematic set of probes.

Use ofexpanded probe sets. Sometimes a sub-ject failed to show correct responding even af-ter reviewing trained relations. Because wehad chosen to use an abbreviated set of allpossible probes, it then was possible to givesubjects additional related probes without pro-viding any feedback about current or previousresponses. Several studies have shown thattesting of relations alters the emergence of otherrelations (e.g., Harrison & Green, 1990; Ken-nedy & Laitinen, 1988). The use of expandedprobe sets contributed to the complexity of theresulting designs for individual subjects. Athorough description of the exact training andtesting sequences actually used in a given caseis more easily understood in the context of theResults section and is presented there.

RESULTSSubjects Who Received Same/OppositePretraining

Pretraining. Pretraining was accomplishedin the following number of training blocks:Subject 1, eight 20-trial blocks; Subject 2, 15blocks; Subject 3, eight blocks; and Subject 4,eight blocks. Subject 2 was the only subject toexperience substantial difficulty with the pre-training process. A special procedure (de-scribed previously) was used in the initial partof the pretraining with Subject 2.

Matching-to-sample training. All of the sub-jects who received same/opposite pretrainingachieved a 90% accuracy rate for A-B relationsin the first block of 40 training trials. Theyalso were better than 90% accurate in the first20-trial block of A-C training. Subjects 1, 3,and 4 achieved accuracy rates of at least 90%in the first 20-trial block of C-D training.(Subject 2 chose to withdraw prior to thisphase.)

Responses to probes. Testing results for de-rived relations shown by Subject 1 are picturedin Figure 4. Table 1 shows more completeinformation on retraining and testing se-quences and the specific comparisons used.Subject 1 responded correctly on 96% to 100%of all probes following A-B and A-C training.

527

Subject2 (Pretrained Same/Opposite)

B1

Tralned:Bi B2

Al1

CsC1 C2

'AS (1 -60%) AlS (2 - 0%)S (3 - 0%)S (4 - 0%)S (5 - 0%)S (6- 100%) -New comparisons

0 (13 - 0%)0 (14 - 0%)

/'I/N-r

B20 (1 - 40%)0 (2-100%)0 (3- 100%)0 (4-100%)0 (5-100%)

I -a -------------------- --------0 (8 -95%) S(B2-_%)

( v ~~~~~~~~~S(lo - 0%)S (12 - 100%)

s (9 - 100%) Al

) S (1 I - 1 00°%) ,,0tA " (9 - 100%) ,) ~~~~S but not O (7 - 100%)

'O- 0 (10-100%) C2

0(13 -0%) 0-(12--100%) A0 (14 - 0%) / S (1 1 - 100%)

0 (17- 100%)

4A r1-----------____.

----- B2 --

,.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1_

S (16 - 100%)

l- S,S(15C1------------,-,-

Alr 'N

- 1 00%)

S (16- 100%)

> O (15 -100%)

(17-100%)

(17-100%)


((CC

"I.J

\4----------------

-------i-100- C2 t

S (16- 1 00%)

v t


Table 2

Percentage of correct responses on training problems and probes for Subject 2 (SAME/OP-POSITE pretrained).


Train A-B and Y-X relations (40 trials)1. Probe B-A mutual entailment: O[B2]A1-X2

and S[Bl]A1-X2Review A-B and Y-X with feedback (total of 40 trials)

2. Probe B-A mutual entailment: O[B2]A1-X2and S[B1]A1-X2

Review A-B and Y-X with feedback (40 trials)3. Probe B-A mutual entailment: O[B2]A1-X2

and S[Bl]A1-X24. Probe B-A mutual entailment: O[B2]A1-X2

and S[Bl]A1-X2[Break between sessions]

Train A-B and Y-X relations (40 trials)5. Probe B-A mutual entailment: O[B2]A1-X2

and S[B1]A1-X2Review A-B and Y-X relations (40 trials)

6.a Probe B-A mutual entailment: S[Bl]A1-Xl and S[Bl]A1-B27. Probe relational reflexivity/irreflexivity8. Probe combinatorial entailment: O[Bl]X1-B2 and O[B2]B1-X2

Train A-C relations (20 trials)Review A-B, Y-X, and A-C with feedback (24 trials)

9. Probe C-A mutual entailment: O[C2]A1-X2 and S[Cl]A1-X210. Probe combinatorial entailment: S[C2]Bl-B2

O[CI ]C2-X2Review A-B, Y-X, and A-C with feedback

11. Probe combinatorial entailment: a S[B2]C2-C1and mutual entailment: S[C1 ]A 1-X2

12. Probe combinatorial entailment: S[C2]Bl-B2 and O[Cl]C2-X213. Probe combinatorial entailment: O[Cl]B1-B2 and O[Bl]C1-C214. Probe combinatorial entailment: O[Cl]B1-B2 and O[Bl]Cl-C2

[Break in sessions. Program modified at this point]Review A-B, A-C, and Y-X with feedback (40 trials)

15. Probe C-A mutual entailment: O[C2]A1-X2 and S[Cl]A1-X216. Probe combinatorial entailment: S[C2]B1-B2, a S[B2]C1-C2, S[Bl]C1-C2, and S[Cl]B1-B217. Probe combinatorial entailment: O[Cl]C2-Xl, O[C1jB1-B2, and O[Bl]C1-C2

a Change of problems normally used in testing.

After C-D training, Subject 1 responded cor-

rectly to D-C trials only 75% of the time (TestBlock 7 in Figure 4). An error in the computerprogram allowed progress to the next set ofprobes, and Subject 1 responded correctly toD-B probes. After a brief review of C-D train-ing, responses to D-C probes for mutual en-

tailment were 100% accurate. The probes forD-B relations were repeated, and responseswere again 100% accurate.

Thus, responses to a wide variety of com-binations of A, B, and C stimuli were consis-tent with relational control by SAME and OP-POSITE contexts. The relations described inthe introduction to Experiment 1 provide an

example. Subjects had a trained history of se-

lecting B1 given Al only in the presence ofSAME, and of selecting B2 given Al only inthe presence of OPPOSITE. Yet when sub-jects were given the choice of B 1 or B2 givenC2, in the presence of SAME they now choseB2 100% of the time, not Bi.

After initial training of the A-B relations,Subject 2 (see Figure 5 and Table 2) failed toshow mutual entailment in the presence of theSAME stimulus. Even after repeated reviewof the trained A-B relations, mutual entail-ment given SAME was not demonstrated. Atthis point the procedure was altered (alterationof procedure is indicated in the tables with an

asterisk) to provide additional probes for mu-tual entailment of the SAME relations. Orig-

529

Correct

100406096100

0100100

0100

0

93100

01001001009595100100

0100100100100100

00

100100100100


Subject 3 (Pretrained Same/Opposite)

- 10(-------------_ B2 _-

0-O (1-100%)

AlS (4 -100%) --,>-0 (4 -100%)

S but not 0 (2 -100%)"'CO5----- C2 --100%)0 (5.100%) S (5-loo%)

0 (10 -100%)

B1 --------------------------------- B2 -

0 (8-100%)

S(6 - 95%) -0(6-95%)

Al', S (9 - 1 00Yo) 0,A> (9 - 100%)

, -- S but not0 (7 - 90%)------ C1 o-O--- 1C2-0 (10-100%) I

Trained:BI B2

Alss AC1 C2

Dl D2

S (10 - 100%)

0 (10 -100%)

B2 0 (12 - 88%)-M, O (14 - 100%)

Al -----------------------------------------0 (13 - 88%)

-63%)-100%) , S(13-100%) C

' C~~2

\44< 51 ° (1 1 94%) S (11 - 94%) D2DlO(1DtA


B1 --- -----O-(----

S (1 - 100%) '-',

BI

(S (12

) S (14)

530

A


Table 3

Percent of correct responses on training problems and probes for Subject 3 (SAME/OPPOSITEpretrained).

Trained problem or testing probe Correct

Train A-B and Y-X relations (40 trials) 901. Probe B-A mutual entailment: O[B2]A1-X2 and S[Bl]A1-X2 1002. Probe relational reflexivity/irreflexivity 1003. Probe combinatorial entailment: O[Bl]Xl-B2 and O[B2]B1-X2 100

Train A-C relations (20 trials) 95Review A-C, A-B, and Y-X relations (24 trials) 100

4. Probe C-A mutual entailment: O[C2]A1-X2 and S[C1]A1-X2 1005. Probe combinatorial entailment: S[C2]B1-B2 and O[Cl ]C2-X2 100

[Break between sessions]Train A-B and Y-X relations (40 trials) 95

6. Probe B-A mutual entailment: O[B2]A1-X2 and S[B1]A1-X2 957. Probes for relational reflexivity/irreflexivity 908. Probe combinatorial entailment: O[Bl]Xl-B2 and O[B2]X2-B1 100

Train A-C relations (20 trials) 95Review A-C, A-B, and Y-X relations (24 trials) 100

9. Probe C-A mutual entailment: O[C2]A1-X2 and S[C1]A1-X2 10010. Probe combinatorial entailment: S[C2]Bl-B2, O[C1]C2-X2, O[C1]B1-B2 and O[B1]C1-C2 100

Train C-D relations (20 trials) 90Review A-B, Y-X, A-C, and C-D with feedback (32 trials) 100

11. Probe D-C mutual entailment: O[Dl]Cl-C2 and S[D2]Cl-C2 9412. Probe combinatorial entailment: O[Dl]Bl-B2 88

and S[DI]B1-B2 6313. Probe combinatorial entailment: O[A1JD1-D2 88

and S[Al]D1-D2 10014. Probe combinatorial entailment: O[Dl]Bl-B2 and S[Dl]B1-B2 100

inally this probe presented SIBI]Al-X2. Theadditional probes used Xl and B2 as incorrectcomparisons. This procedure resulted in 100%accurate responses to probes for mutual en-tailment. Following the training of A-C re-lations, Subject 2 responded accurately to allprobes for combinatorial entailment, except shedid not relate C2 and B2 in the presence ofSAME. Review of trained relations did notalter this performance. Again, the procedurewas altered to provide for additional unrein-forced probes (see Table 2 and Figure 5 fordetails) for combinatorial entailment of theSAME relation. The subject then showed 100%accurate responding. At this point Subject 2chose to withdraw from the experiment.

Subject 3 (see Figure 6 and Table 3) made90% or more correct responses on all blocks oftraining and probes until the D stimuli wereadded. Subject 3's responses to probes for con-trol by D-B relations were 63% to 88% ac-curate on the first test (12, Figure 6). Afterprobes for the intermediate A-D relations, D-Brelations were 100% accurate.

The roles of specific arbitrary visual stimuli(Figure 2) were randomly reassigned for Sub-ject 4's training and probes (e.g., the stimulusthat functioned as Al for earlier subjects mightnow be the B2 stimulus). This was done tomake sure that some incidental feature of thestimuli had not produced the pattern of controlobserved with the first 3 subjects. Subject 4mastered the trained A-B relations quickly andthen demonstrated B-A mutual entailment andcombinatorial entailment (see Figure 7 andTable 4). After A-C training, Subject 4 failedto pick B2 in probe S[C2]Bl-B2 (Test 5 inFigure 7). A scheduled session break occurredat that point, so in the next experimental ses-sion previously trained relations were re-viewed. Subject 4 responded correctly to allprobes for mutual entailment and combina-torial entailment of the A, B, and C stimuli.Following C-D training, Subject 4 respondedincorrectly to probes for D-B relations (Test12 in Figure 7). After probes for the inter-mediate A-D relations, his D-B performancesrose to 88% correct, and after another test of

531

Subject 4 (Pretrained Same/Opposite)

B1 o------------------------------ B2 Taieed:0 (3-100%)BI B

S (1 - 100%) -- - 0 (1 -100%) j

Al S(5-0%) Al

S(4-100%) -- 4 0 (4-100%)

I A1 s (10- 83%%)

butnot0 (2 -C%) C2Cl - ~~~0(5-92%) 0C

DI D2

0 (10-92%)

i 0 (8 -100%) -S(6- 100%) 0 (6-100%)

Al S (10 -83%)

S(9-100%) ~ '~ 9100%)S but ot 0 (7-100%)

------Cl ----------------- ----- --------------C2--------0 (10-100%)0 (10-100%)

0 (12 - 13%)

Bl B2 ~~~~~0(15-88%)Bi ~~<80% on any~Bes 0 (17 100%)

S (12-0%) S (13-75%) 0 (13 -100%)S (15-88%) S (14-100%) 0 (14-100%)

S(17100%) S(D1 0(11-100%) 0(11-100%) D2DI 0 110 S0I-10) D



A-D relations, D-B relations were 100% ac-curate.

Latency of responding. Reaction-time data(Wulfert & Hayes, 1988) have supported theidea that problems increase in difficulty as thenumber of stimulus relations involved in-creases (Fields et al., 1984; Sidman, Kirk, &Willson-Morris, 1985; Sidman & Tailby,1982). In the present study, the fact that twotypes of relational responding were potentiallyestablished complicates the issue. Difficulty ofthe problems may have been increased in thoseprobes in which the subjects had to apply therelational frames of both same and opposite inarriving at a choice. Reaction-time data, or-ganized by the number of trained and derivedstimulus relations and the number of types ofrelations involved, were examined. For ex-ample the probe S[Al]D1-D2 involves rela-tions between A-C and C-D. Dl was broughtinto the network by training O[C2]D 1-D2, andAl was related to C2 by training O[Al]Cl-C2. So two types of relations (the two trainedopposite relations and the derived same rela-tion) and two specific trained relations (A-Cand C-D) were required to respond correctlyto this probe.

Probes were divided into the following fourtypes: (a) those with one specific stimulus re-lation and one type of relation (e.g., probes formutual entailment and probes for relationalreflexivity/irreflexivity), (b) those with twotrained stimulus relations and two types ofrelations (e.g., O[Bl]B2-X1), (c) those withone trained and one derived relation and twotypes of relations (e.g., O[Cl]B1-B2), and (d)those involving two derived and one trainedrelation and two types of relations (e.g.,O[D1 ]B1-B2). Latency data were analyzed forall trials in the four types of probes for subjectswith complete training histories (1, 3, and 4).The mean response time increased as probes

increased in complexity: 1.8 s, 2.4 s, 3.4 s, and4.1 s for probe Types (a) through (d) above,respectively. These response latencies were an-alyzed with a single-factor (type of probe)analysis of variance, and a statistically signif-icant effect was found, F(3, 830) = 10.83, p< .0001. Differences between groups were ex-amined using Tukey's studentized range(HSD) test. Type (a) probes had significantly(p < .05) shorter response times compared toTypes (c) and (d). Type (b) probes differedsignificantly from Type (d).

Table 4

Percentage of correct responses on training problems andprobes for Subject 4 (SAME/OPPOSITE pretrained).


Train A-B and Y-X relations (40 trials)1. Probe B-A mutual entailment:

O[B2]A1-X2 and S[Bl]A1-X22. Probe relational reflexivity/irreflexivity3. Probe combinatorial entailment:

O[Bl]Xl-B2 and O[B2]B1-X2Train A-C relations (20 trials)Review A-C, A-B, and Y-X relations

(24 trials)4. Probe C-A mutual entailment:

O[C2]A1-X2 and S[Cl]A1-X25. Probe combinatorial entailment:

S[C2]Bl-B2and O[Cl]C2-X2

[Break between sessions]Review A-B and Y-X relations with

feedback (40 trials)6. Probe B-A mutual entailment:

O[B2]A1-X2 and S[Bl]A1-X27. Probes for reflexivity/irreflexivity8. Probe combinatorial entailment:

O[Bl]Xl-B2 and O[B2]B1-X2Train A-C relations (20 trials)Review A-C, A-B, and Y-X relations

(24 trials)9. Probe C-A mutual entailment:

O[C2]A1-X2 and S[Cl]A1-X210. Probe combinatorial entailment:

S[C2]Bl -B2and O[Cl]C2-X2and O[Cl]Bl-B2and O[Bl]Cl-C2

Train C-D relations (20 trials)Review A-B, Y-X, A-C, and C-D rela-

tions with feedback1 1. Probe D-C mutual entailment:

O[Dl]C1-C2 and S[D2]Cl-C212. Probes for combinatorial entailment:

O[Dl]Bl-B2and S[Dl]B1-B2

13. a Probe combinatorial entailment:O[A1 JD1-D2and S[Al]D1-D2

Review A-B, Y-X, A-C, and C-D rela-tions with feedback (32 trials)

14. Probe A-D combinatorial entailment:O[Al]Dl-D2 and S[AlJD1-D2

15. Probe D-B combinatorial entailment:O[Dl]Bl-B2 and S[Dl]B1-B2

16. Probe combinatorial entailment:O[Al]Dl-D2 and S[Al]D1-D2

17. Probe combinatorial entailment:O[Dl]Bl-B2 and S[Dl]B1-B2

95

10095

100100

100

100

092

92

100100

100100

93

100

831009210095

100

100

130

10075

96

100

88

100

100a Change of problems normally used in testing.

533


Table 5

Percentage of correct responses on training problems and probes for Subject 5 (no pretraining).


Train A-B and Y-X relations (40 trials) 63Train A-B and Y-X relations (40 trials) 58Train A-B and Y-X relations (40 trials) 60Train A-B and Y-X relations (40 trials) 50a Train A-B relations only (40 trials) 83a Train A-B relations only (40 trials) 100a Train Y-X relations only (40 trials) 93Train A-B and Y-X relations (24 trials) 63Train A-B and Y-X relations (24 trials) 100

1. Probe B-A mutual entailment: O[B2]A1-X2 and S[B1]A1-X2 1002. Probe reflexivity/irreflexivity 55

Review A-B and Y-X relations with feedback (24 trials) 1003. Probe reflexivity/irreflexivity 50

Review A-B and Y-x relations with feedback (24 trials) 1004. Probe reflexivity/irreflexivity 50

[Break between sessions]Review A-B and Y-X relations with feedback (24 trials) 100

5. Probe B-A mutual entailment: O[B2]A1-X2 and S[Bl]A1-X2 1006. Probe reflexivity/irreflexivity 50

Review A-B and Y-X relations with feedback (24 trials) 1007. Probe combinatorial entailment: O[Bl]Xl-B2 and O[B2]X2-B1 50


Review A-B and Y-X relations with feedback (24 trials) 1009. Probe combinatorial entailment: O[Bl]Xl-B2 and O[B2]X2-B1 50

Train A-C relations (20 trials) 95Review A-B, Y-X, and A-C relations 100

10. Probe C-A mutual entailment: O[C2]A1-X2 67and S[C1]A1-X2 100

Review A-B, A-C, and Y-X relations (24 trials) 10011. Probe C-A mutual entailment: O[C2]A1-X2 46

and S[Cl]A1-X2 92Train A-C relations (20 trials) 95

12. Probe C-A mutual entailment: O[C2]A1-X2 0and S[C1]A 1-X2 100

[Program modified to provide different wrong comparison]13. Probe C-A mutual entailment: a O[C2]A1-X1 and S[C1]A1-X2 10014. Probe combinatorial entailment: S[C2]Bl-B2 0

and O[C1]C2-X2, O[Cl]Bl-B2, O[Bl]Cl-C2 100[Break between sessions]

Train A-B and Y-X relations (24 trials) 10015. Probe B-A mutual entailment: O[B2]A1-X2 60

and S[B1]A1-X2 100Review A-B and Y-X relations with feedback (24 trials) 100

16. Probe B-A mutual entailment: O[B2]A1-X2 70and S[Bl]A1-X2 100

Review A-B and Y-X relations with feedback 9617. Probe B-A mutual entailment: O[B2]A1-X2 and S[Bl]A1-X2 100

Train A-C relations (20 trials) 10018. Probe C-A mutual entailment: a O[C2]A1-X1, O[C2]A1-X2 and S[C1]A1-X2 100

a S[Cl]A1-Xl 100a Train S[Al]B1-B2, S[Al]C1-C2, and S[Y1]X1-X2 (30 trials) 100

19. Probe mutual entailment: S[Bl]A1-X2 100and S[C1]A1-X2 88and a S[Bl]A1-Xl 100and a S[Cl]A1-X1 88

20. a Probe combinatorial entailment: S[B1]C1-C2 and S[Cl]Bl-B2 100a Train O[AI]B1-B2, O[AI]C1-C2, and O[Yl]Xl-X2 (30 trials) 100


Table 5

(Continued)


21. a Probe mutual entailment: O[B2]A1-X2and O[C2]A1-X2and O[B2]A1-Xl

22. a Probe mutual entailment: O[C2]A 1-X1a Train O[Al]Bl-B2, O[A1]C1-C2, and O[Yl]X1-X2 (30 trials)

23. Probe B-A mutual entailment: O[B2]A1-X2, O[C2]A1-X2, O[B2]A1-X1, O[C2]A1-Xl24. Probe for combinatorial entailment versus conditional equivalence: a O[C2]Bl-(B2)b and O[B2]C1-

(C2)b25. Probe combinatorial entailment: O[Bl]B2-X1

and O[B2]B1-X226. Probe combinatorial entailment: S[C2]Bl-B2

and O[C1]C2-X2, O[C1]B1-B2, and O[BJ]Cl-C227. Probe reflexivity: S[Al]A 1-Ni

and irreflexivity: O[A1]A1-N228. Probe combinatorial entailment: O[Bl]B2-Xl

O[B2]B1-X229. Probe combinatorial entailment: S[C2]B1-B2

O[Cl]C2-X2, O[C1]B1-B2, and O[Bl]C1-C2

88758810096100

0100

00

1000

100100

00

100a Change of problems normally used in training or testing.b Stimulus in parentheses indicates performance expected on Test 24 if conditional equivalence classes had formed.

These items were selected 100% of the time.

Subjects Who Received No PretrainingTrained relations. Subject 5 (see Table 5)

had difficulty mastering the initial training ofA-B and Y-X training. After four 40-trialblocks, he was responding at chance levels. Atthat point the procedure was modified so thatonly A-B relations were trained until a cri-terion level of mastery was reached. Then Y-Xtraining was conducted, followed by a reviewof A-B and Y-X problems presented concur-rently. It took 328 trials to demonstrate mas-tery of these trained discriminations.To avoid Subject 5's problems in mastering

the initial A-B and Y-X discriminations, thetraining procedure was modified for Subject 6(see Table 6). A-B relations were trained first,followed by Y-X relations and concurrent pre-sentation of both sets of problems. Subject 6made accurate responses on more than 90% ofall trials.

Probes for reflexivity and irreflexivity. Fol-lowing A-B training, both Subjects 5 and 6showed mutual entailment (see Figures 8 and9). On the probes for reflexivity and irreflex-ivity, Subject 5 selected the novel stimulus in-stead of the comparison that was identical tothe sample given both SAME and OPPO-

SITE. Subject 6 did so given SAME. Reviewof the trained relations did not produce a changein response pattern for either subject.When pretrained subjects did not show cor-

rect responding, they were given an expandedset of relevant probes. This same tactic wastried with Subject 6. She was given two probesfor reflexivity (S[Al ]A 1-Nl and S[Al ]A 1-N2)and two similar probes for irreflexivity(O[Al]Al-N1 and O[Al]Al-N2). Subject 6developed a consistent pattern of respondingthat resulted in making four different re-sponses to the four probes. This pattern is asfollows (with Subject 6's choice of comparisonin parentheses): S[Al ]Al-(Nl), O[Al ]Al-(N2), S[Al](Al)-N2, O[Al](Al)-Nl.

Probes for mutual entailment. Subject 6 re-sponded correctly to all mutual entailmentprobes. Subject 5 initially showed mutual en-tailment with B-A but not C-A probes. Anexpanded set of probes resulted in C-A mutualentailment (see Table 5).

Combinatorial entailment within sets of com-parisons. Pretrained subjects learned that Blis the same as Al, and B2 is the opposite ofAl. They then responded consistently to theprobe O[Bl]Xl-B2. Subject 5 initially failedto show this pattern of control for Bl and B2,

535


Sublect 5 - No Pretraining ofRelatlonal StUmull0 (7-50%)0 (9- 50%)

m 4 -.O N- N IA M_ Mn

S8(1 -100%) >S (5-100%)

8(10- - 1 00%)

S (11 -921%)S (12 -100%) C1S (13 - 100%) S but no

Al,

' 0 (1-100% )O (5- 100%)

t 0 (2 - 50%)S bt n 0 (3_- 50%)S but not 0 (3 - 50%)S but not 0 (4 - 50%)S but not 0 (6 - 50%)S but not O (8 - 50%)

0 (10-67%)0o (11-46%)

C2 0(12-0%)0 (13-100%) -New comparisons

<80% on any test

0(14-100%)--------------B1 B2S (is - 100%j " >' D

S(16-100%) (15 -60%) qS(16-100 0(16-70%)S(19-100%)Al 0(17-100%)

S (18-100%A)V-' _O (18-100%)S (i19 - 88%1,- s

t-~~~~~------------t1 ------------------=----2I

O (14- 100%)

0 (14 -100%)

S (14 -0%)

Trained:B1 52

AlsC C

C1 C2

00- %046

1


Table 6

Percentage of correct responses on training problems andprobes for Subject 6 (no pretraining).


Train S[Al]B1-B2 and O[Al]Bl-B2 (20trials)

Train S[Yl]X1-X2 and O[Yl]X1-X2(20 trials)

Train all A-B and Y-X relations (40 tri-als)

1. Probe B-A mutual entailment:O[B2]A1-X2 and S[Bl]A1-X2

2. Probe reflexivity: S[Al]A 1-NIand irreflexivity: O[Al ]A1-N2

Review A-B and Y-X relations withfeedback (24 trials)

3. Probe combinatorial entailment:O[B1]Xl-B2 and O[B2]B1-X2

4. Probe B-A mutual entailment:O[B2]A1-X2 and S[Bl]A1-X2

5. Probe reflexivity: S[Al]A 1-Nland irreflexivity: O[Al]AI-N2

Train A-C relations (20 trials)Review A-B, Y-X, and A-C with feed-

back6. Probe B-A mutual entailment:

O[B2]A1-X2 and S[B1]A1-X27. Probe combinatorial entailment:

S[C2]Bl-B2and O[C1]C2-X2

8. Probe combinatorial entailment:O[C1JB1-B2 and O[Bl]Cl-C2

Review A-B, Y-X, and A-C with feed-back (24 trials)

9. Probe combinatorial entailment:O[C1]B1-B2 and O[B1]Cl-C2

[Break between sessions]Review A-B and Y-X relations with

feedback (24 trials)10. Probe B-A mutual entailment:

O[B2]A1-X2 and S[B1]A1-X211. Probe reflexivity: S[A1]A1-Nl

and irreflexivity: O[Al]Al-N2a Probe reflexivity: S[Al ]A 1-N2and a irreflexivity: O[Al ]Al-N1

Review A-B and Y-X relations withfeedback

12. Probe combinatorial entailment:O[Bl]Xl-B2and O[B2]X2-B1

Review A-B and Y-X relations withfeedback (24 trials)

95

95

100

1000

100

100

95

1000

100100

100

100

0

537

Table 6

(Continued)


13. Probe combinatorial entailment:O[Bl]Xl-B2 100and O[B2]X2-B1 0

Train A-C relations (20 trials) 95Review A-B, Y-X, and A-C relations

(24 trials) 10014. Probe C-A mutual entailment:

O[C2]A1-X2 and S[Cl]A1-X2 10015. Probe combinatorial entailment:

S[C2]B1-B2 0and a S[C1]B1-B2, a S[B1]C1-C2 100and a S[B2]Cl-C2 0

Review A-B, Y-X, and A-B relations(24 trials) 100

16. Probe combinatorial entailment:S[C2]Bl-B2 0and O[Cl]C2-X2, O[Cl]Bl-B2 100and O[B1]C1-C2 0

17. Probe combinatorial entailment:S[C2]Bl-B2 0and O[C 1 ]C2-X2 100

18. Probe combinatorial entailment:O[Cl]Bl-B2 and O[B1]C1-C2 100


100 but this pattern of responding was observed in

100 later sessions. Subject 6 responded to theseprobes similarly to the pretrained subjects.

100 Combinatorial entailment across stimulus sets.Following A-C training, subjects were given

100 three probes (S[C2]Cl-B2, O[Cl]Bl-B2, andO[B1 ]C 1 -C2) that tested for combinatorial en-

100 tailment. The control subjects answered cor-

rectly on the two OPPOSITE problems but100 even though trained relations were repeatedly

0 reviewed and expanded probe sets were given,100 they consistently responded to the probe00 S[C2]C1-B2 by selecting the comparison Cl.

This overall pattern makes sense because each100 of these performances in the presence ofSAME

and OPPOSITE could have been established100 in the experimental subjects (with pretraining)0 via relations in the other context. For example,

100 the sameness between B2 and C2 may havebeen established in the experimental subjects

Fig. 8. Testing performance of Subject 5 (no pretraining on relational stimuli). Dashed lines indicate probes thatwere above 80% correct, where "correct" is defined as selecting the indicated stimulus. Wavy lines indicate probeswere below 80% on at least one of the testing blocks recorded in that section. The letters S and 0 indicate the relationalstimulus presented. Numbers in parentheses indicate the specific testing block (these same numbers are used in Table5 for cross reference) and the percentage correct. See Table 5 for specific comparison stimuli used and training sequences.


Subject 6- No Pretralning ofRelational Stimull

0 (3 - 95%) ___B1 _------------------------- 52 _-S(6-100%) Al 0(-'100%

I~~~~~~~~~~~~~~~~~~~S (4 - I100%) - O. (4-I100%)

S (6 - 100%) * A1 O (6 - 1 00%)(

<80% on any test

0 (8-100%)0 (9- 100%)

--------- B1

C2 S (7 - 0%)S (2 -0%)0 (2-100%)S (5 - 0%)0 (5-100%)

0 13-0%)0 12-0%)

0 (12 -100%)0 (I 3 - I100%) -

S (10-100%) 0(10-100%)Al

S (1 4 - 1 00%),,--v* 0w (1 4-1 00%)

C1 C2

S(11-0%)0 (11-100%)

S (1 1 - 100%) See Table 60 (11 - 0%) See Table 6

0 (7-100%)

S(15-100%)S (15 - 0%)S (16 - 0%)S (17 -0%)

i ----------------- _~0 (16-100%)

0 (17-100%)

Fig. 9. Testing performance of Subject 6 (no pretraining on relational stimuli). Dashed lines indicate probes thatwere above 80% correct, where "correct" is defined as selecting the indicated stimulus. Wavy lines indicate probeswere below 80% on at least one of the testing blocks recorded in that section. The letters S and 0 indicate the relationalstimulus presented. Numbers in parentheses indicate the specific testing block (these same numbers are used in Table6 for cross reference) and the percentage correct. See Table 6 for specific comparison stimuli used and training sequences.

Tralned:BI B2

Alsy AC1 C2

i0 (8-100%)0° (9- 100%)

B2

i----


via a combination oftwo relations of opposition(O[A1]Bl-B2 and O[A1]Cl-C2). For the con-trol subjects, OPPOSITE and SAME weresimply arbitrary stimuli and presumably didnot bring distinct kinds of relational respond-ing to bear on the situation. Thus, the subjectsseemed simply to pick a comparison that hadbeen reinforced in the given context. For ex-ample, the control subjects never had a historyof reinforcement for selecting C2 in the pres-ence of the SAME stimulus but did for Cl(S[Al ]C1-C2).

Subjects Who Received Same/DifferentPretraining

Same/different subjects received the samearbitrary matching-to-sample training as isshown in Figure 2, except that DIFFERENTwas pretrained and used in the place of OP-POSITE. It was not clear whether subjectsgiven same/different pretraining would per-form like the same/opposite subjects. On theone hand, the combinatorial entailment of adifference relation seems distinct from that ofan opposition relation. If B is different fromA and C is different from A, the relation be-tween B and C seems unspecified except thatboth are different from A. In a two-choicematching-to-sample format, it was not clearwhat subjects would do. Given a choice suchas D[C2]Bl-B2, the difference relation mightyield the same performances as the oppositerelation (namely, the selection of B2) via ex-clusion. Essentially, the DIFFERENT pre-trained subjects might show responding likethat seen with OPPOSITE if subjects treat thedifference relation like the "not" relation offormal logic, commonly symbolized by the tilde,. The "logical not" relation has these prop-

erties: 1. a = -a; 2. if a = -b, then b = -a;3. if a = - b, and b = ' c, then a = c. Oppositionhas a similar quality when arbitrarily applied.In lay language, words are opposites if theyrefer to conditions equidistant on either sideof an arbitrarily defined midpoint of a quan-titative continuum for a specific quality (e.g.,"warm" and "cool" are often relative to thetemperature of a human as the midpoint).When stripped of any qualitative or quanti-tative information, opposition has no midpointand collapses into the "logical not" relation.

Pretraining. The subjects who receivedsame/different pretraining required the fol-lowing number of 40-trial blocks to reach the

criterion level of performance: Subject 7, 1 1;Subject 8, 9; and Subject 9, 8. Because theperformance of Subject 7 was unlike the other2, he will be considered separately.A-B training and testing, Subjects 8 and 9.

Both Subject 8 (see Table 7 and Figure 10)and Subject 9 (see Table 8 and Figure 11)showed rapid mastery of A-B training. Onprobes for mutual entailment, relational re-flexivity/irreflexivity, and combinatorial en-tailment, both subjects demonstrated criterion-level performance on the initial block of trials.A-C training and testing, Subjects 8 and 9.

Subjects 8 and 9 showed rapid mastery of A-Ctraining and C-A mutual entailment. Subject9 responded 100% correctly to all of the probesfor combinatorial entailment. Subject 8 failedto show the derived relations, so he was givenan expanded set of probes (see Table 7) andquickly responded correctly. These subjectswere not exposed to C-D training or debriefedat this point; instead they returned to beginExperiment 2 in their next session.

Subject 7. The performance of Subject 7 wasunlike that of any other subject (see Table 9and Figure 12). Following pretraining, the ini-tial A-B and Y-X training was accomplishedin two blocks of trials, and probes for B-Amutual entailment were at the criterion level.On the first probe for relational reflexivity/irreflexivity, Subject 7 failed to show controlby the relational stimuli for the same and dif-ferent relations. Reviewing the same/differentpretraining and reviewing the initial A-Btraining failed to produce consistent respond-ing on these probes. Finally, the problemsS[A1 ]A 1-N2 and D[A1 ]Al-N2 were explicitlytrained using feedback. Even after reflexiveand irreflexive choices were made reliably,Subject 7 failed to show control by any of thederived relations. He should have been able torespond correctly to the probes D[Bl]Bl-B2and D[B2]B1-B2 if the relational stimuli hadcome to control making same and differentchoices. A-C training was begun because al-ternative training and testing options had beenexhausted. Subject 7 mastered A-C relationsin one block of trials, reviewed all trained re-lations, and then showed C-A mutual entail-ment. Even with reviews of trained relationsand expanded probe sets, however, Subject 7failed to show combinatorial entailment.

During debriefing, Subject 7 described anelaborate system he had used to remember the

539


Subject 8 (Pretrained Same/Different)

ralned: Bi1 ----------------- B231a/ned:B1 D(3 -100%)41B2 > D

/ ~S (1 -100%) ', -'D (1 -100%)Al

S (4 - 100%) ,- ,A" v*-, D (4 - 100%)S(4-100%)-S but not D (2-95%)

C1 D (5 -100%)

SAl/D

C1 C2S (5 - 83%)

D (6 - 8%)D (7 - 92%)D (9 - 70%)D (10 - 90%)

/- /r f-

Bi

S (8-83%) S (8-100%)

D (9 - 100%)D_(10 - 100°%lci _ _ __ _

B2 _--

S (8- 100%)( )

S (8 - 83%)

I-/ \/ J vD (6 - 8%)D (7 - 67%)D (9- 100%)D (10- 100%)

Fig. 10. Testing performance of Subject 8 (pretrained with SAME and DIFFERENT). Dashed lines indicateprobes that were above 80% correct, where "correct" is defined as selecting the indicated stimulus. Wavy lines indicateprobes were below 80% on at least one of the testing blocks recorded in that section. The letters S and D indicate therelational stimulus presented. Numbers in parentheses indicate the specific testing block (these same numbers are usedin Table 7 for cross reference) and the percentage correct. See Table 7 for specific comparison stimuli used and trainingsequences.

trained relations. It involved finding some de-tail of the stimuli that could be related to eachother. In the presence of one relational stim-ulus, one detail of the sample and comparisonstimuli was used; with the other relational

stimulus, a different detail was used. He ex-plained that theSAME stimulus meant "choosethe same one," whereas the DIFFERENTstimulus meant "choose the other one"-re-ferring to the same or different formal details.

I

540

-lbo- C2 --------;'* -------


Table 7Percentage of correct responses on training problems andprobes for Subject 8, Experiment 1 (SAME/DIFFER-ENT pretraining).


Train A-B and Y-X relations (40 trials) 88Train A-B and Y-X relations (40 trials) 98

1. Probe B-A mutual entailment:D[B2]A1-X2 and S[Bl]A1-X2 100

2. Probe reflexivity/irreflexivity 953. Probe combinatorial entailment:

D[Bl]Xl-B2 and D[B2]B1-X2 100Train A-C relations (20 trials) 90Review A-B, Y-X, and A-C relations

with feedback (24 trials) 1004. Probe C-A mutual entailment:

D[C2]A1-X2 and S[Cl]A1-X2 1005. Probe combinatorial entailment:

S[C2]Bl-B2 83and D[Cl]C2-X2 100

6. Probe combinatorial entailment:D[C1I]B1-B2, D[Bl]Cl-C2 8

Review A-B, Y-X, and A-C relationswith feedback (24 trials) 100

7. Probe combinatorial entailment:D[C1]B1-B2 67and D[BI]C1-C2 92

Review A-B, Y-X, and A-C relationswith feedback (24 trials) 100

8. Probe combinatorial entailment:S[C2]Bl-B2 and a S[Bl]C1-C2 100and a S[B2]Cl-C2 and a S[C1]B1-B2 84

9. Probe combinatorial entailment:D[Bl]Cl-C2 70and D[ClIC2-X2 and D[C1]B1-B2 100

10. Probe combinatorial entailment:D[Bl]Cl-C2 90and D[C1]C2-X2 and D[C1]BI-B2 100


The relational stimuli apparently exerted con-textual control-but over formal selection cri-teria, not over arbitrary matching.

DISCUSSIONThe performance of Subjects 5 and 6 (the

subjects without pretraining establishing dis-tinct relational histories for SAME and OP-POSITE) showed patterns much like those inthe equivalence literature. It is well knownthat conditional equivalence classes can emergethat arrange subsets of stimuli into classes givensecond-order conditional stimuli (e.g., Bush,Sidman, & de Rose, 1989; Wulfert & Hayes,1988). For Subjects 5 and 6, Al, BI, and Clentered into an equivalence class in the pres-

Table 8Percentage of correct responses on training problems andprobes for Subject 9, Experiment 1 (SAME/DIFFER-ENT pretraining).


Train A-B and Y-X relations (40 trials) 1001. Probe B-A mutual entailment:

D[B2]A1-X2 and S[Bl]A1-X2 982. Probe reflexivity/irreflexivity 1003. Probe combinatorial entailment:

D[Bl]Xl-B2 and D[B2]B1-X2 100Train A-C relations (20 trials) 100Review A-B, Y-X, and A-C relationswith feedback 100

4. Probe C-A mutual entailment:D[C2]A1-X2 and S[Cl]A1-X2 100

5. Probe combinatorial entailment:S[C2]Bl-B2 and D[Cl]C2-X2 100

6. Probe combinatorial entailment:D[CI]Bl-B2, D[Bl]Cl-C2 100

ence of SAME, showing B-A and C-A mutualentailment and B-C combinatorial entailment.Al, B2, and C2 also entered into an equiva-lence class, but in the presence of OPPOSITE.For example, given O[C2]B1-B2, these sub-jects chose B2. They had learned to pick bothB2 and C2 given Al in the presence of OP-POSITE, and thus B2 and C2 were in anequivalence class given OPPOSITE.

All of the pretrained subjects except Subject7 showed patterns of responding that go be-yond equivalence or conditional equivalence.Probes for mutual entailment showed bidirec-tional stimulus functions, as with the controlsubjects but tests for combinatorial entailmentshowed different results. Subject 1, for ex-ample, selected an opposite of an opposite onlyin the presence ofSAME and not OPPOSITE(the C2-B2 relation-Test 5 in Figure 4); anopposite of an opposite of an opposite wasselected only given OPPOSITE and not SAME(the D1-B2 relation-Tests 8 and 10 in Figure4). An opposite of an opposite of a same wasselected only given SAME (the Di-Bl rela-tion-Tests 8 and 10 in Figure 4).Some of the subjects required retraining or

special patterns of testing, but the final pat-terns were quite similar across subjects. Ofcourse, networks such as these give rise to alarge number of possible alternative interpre-tations of the results-a topic that will be ad-dressed later. Of more immediate interest are

541


EXPERIMENT 1 Subject 9 (Pretrained Same/Different)

r--r---- BI --D (3 - I A00nO

S (1 - 98%) *

---_B2 4--

, D (1 - 98%)Al S (5- 100%)

IS (4 - 100%) D (4 - 100%)S butnotD(2-100%)

--C2--------D (5 -100%)4

-P----------------D (6_- 1OO6OZ) T

D (6- 100%)D (10 - 100%)D (11 - 1 00%)

EXPERIMENT 2 Subject 9 (PretrainedSame/Different/Opposite)

V * O 1-100%ysT O 2-100%)

L-Bl B2 B3

S (6- 100%)S (10 - 100%)S (11 - 100%)

+

U

s (1 - 100%)I S (2 - 100%)

0O(-100%) ,,-O(2-100%) --'

S (4- 100%) Al S (5- 100%)S (8 - 100%) * S (9- 100%)

v , S (3- 100%) 0 (3- 100%)Y- XS(S (7- 100%) 0 (7 -100%)> T

---,_ C1 C30 (3-100%)

'"' £ 0 (7-100%)

,, 0 (5-100%)! o~~~~~~~~(9 - 100%) s (1 2 -1I 00%)0 (6 - 100%) (via comparison with Bi and B2. See text.)0 (10 -100%)0 (11 -100%) o 12 - 100%) -

0 (4- 100%)0 (8- 100%)

Tralned:Bi B2 B3

Al

S##D^OCl C2 C3

Fig. 11. Testing performance of Subject 9 (pretrained with SAME and DIFFERENT) in Experiment 1 (tophalf) and her performance in Experiment 2 after being pretrained with SAME, DIFFERENT, and OPPOSITE(bottom half). Dashed lines indicate probes that were above 80% correct, where "correct" is defined as selecting the

Trmined.-Bi B2

Alsl C

C1 C2

542

D (6 - 100%)F-------------------------------------------------------

._IW

a


the similar results between subjects who re-ceived same/different and same/opposite pre-training. On the basis of the subjects' historieswith the relational stimuli, they may simplyhave learned that in the context of one rela-tional stimulus responding on the basis ofequivalence was reinforced, whereas in thecontext of the other relational stimulus re-sponding on the basis of nonequivalence wasreinforced. This would show conditional con-trol over equivalence per se (not to be confusedwith conditional equivalence classes), but itdoes not necessitate an appeal to relationalframes. If equivalence is a basic behavioralprocess, only conditional control over that pro-cess is needed as an explanation.

In Experiment 1, however, only two rela-tional stimuli and two comparisons were used.This causes analytic ambiguities in certain keyareas. Consider the probe for combinatorialentailment S[B2]Cl-C2. If B2 is the oppositeof Al and C2 is the opposite of Al, then B2and C2 are the same. Subjects given same/opposite pretraining would be expected to se-lect C2, which they did. The subjects whoreceived same/different pretraining had beentrained to select B2 and C2 as being differentfrom Al. In the abstract, this leaves the re-lationship between B2 and C2 undefined; theyare both different from Al, but they could beeither the same as or different from one an-other. The fact that there were only two com-parisons made available another source of con-trol, however, in the actual matching-to-sampletask. Cl, Al, and Bl had entered into anequivalence class in the presence of SAME forthe SAME/DIFFERENT subjects (see Fig-ures 10 and 1 1). B2 was not in that class, andthus given B2 as a sample in the presence ofSAME, subjects could merely exclude Cl andselect C2. These kinds of problems with two-choice procedures in equivalence research havebeen previously noted (Sidman, 1987).To address this analytic ambiguity, a second

experiment was conducted in which three re-lational stimuli were trained: SAME, OP-POSITE, and DIFFERENT. Distinct and

predictable patterns of responding among threeseparate relations cannot as readily be ex-plained on the basis of only two principles:equivalence and nonequivalence. The use ofthese three relations also allowed for the dis-tinction between mere difference and oppo-siteness.

EXPERIMENT 2The intent of Experiment 2 was to bring

three relations-same, opposite, and differ-ent-under stimulus control. Both opposite anddifferent are irreflexive relations, but have dif-ferent implications for a network of relations.

METHODSubjects, Apparatus, and StimuliThe subjects for this experiment were Sub-

ject 8 and Subject 9 who had received SAME/DIFFERENT pretraining in Experiment 1.The apparatus and stimuli were the same asin Experiment 1 except that provision was nowmade to present three different relational stim-uli and two or three comparisons, dependingon the specific problem. Three comparisonswere needed in certain types of probes to re-duce the applicability of simple forms of ex-clusion. Two comparisons were used in sometraining and probe items to distinguish thedifferent and opposite relations.

ProcedureThe general network of trained and tested

relations is shown in Figure 13. The plan forthe training and probes is given in Figure 14.Subject 8 and Subject 9 were first given pre-training with SAME and OPPOSITE iden-tical to that used with other subjects in Ex-periment l. Subjects had already learnedS[Al]B 1, D[Al]B2, S[Al]C1, and D[Al]C2 inExperiment l. They were now given the sametraining as the same/opposite subjects in Ex-periment I except that the B2 and C2 stimuliin Experiment I (what will be called B3 andC3, respectively, in this experiment) were re-

indicated stimulus. Wavy lines indicate probes were below 80% on at least one of the testing blocks recorded in thatsection. The letters S, D, and 0 indicate the particular relational stimulus presented. Numbers in parentheses indicatethe specific testing block (these same numbers are used in Tables 8 and 11 for cross reference) and the percentagecorrect. See Tables 8 and 11 (for Experiments 1 and 2, respectively) for specific comparison stimuli used and trainingsequences.

543

544 DAVID STEELE and STEVEN C. HAYES

Table 9Percentage of correct responses on training problems and probes for Subject 7 (SAME/DIF-FERENT pretraining).


Train A-B and Y-X relations (40 trials) 80Train A-B and Y-X relations (40 trials) 100

1. Probe B-A mutual entailment: D[B2]A1-X2 and S[Bl]A1-X2 75Review A-B and Y-X relations with feedback (24 trials) 100

2. Probe B-A mutual entailment: D[B2]A1-X2 and S[Bl]A1-X2 953. Probe reflexivity/irreflexivity 0

a Review pretraining block for same/different control 954. Probe reflexivity/irreflexivity 0


a Review pretraining block for same/different control 83a Review a pretraining block for same/different control 100

6. a Probe reflexivity/irreflexivity 100Train A-B and Y-X relations (40 trials) 95

7. Probe B-A mutual entailment: D[B2]A1-X2 and S[B1l]A1-X2 958. Probe reflexivity/irreflexivity 0

a Review a pretraining block for same/different control 969. Probe reflexivity/irreflexivity 0

a Review a pretraining block for same/different control 9610. Probe reflexivity/irreflexivity 0

a Review pretraining block for same/different control 9611. Probe reflexivity/irreflexivity 0

a Explicitly train reflexive/irreflexive choices using the experimental stimuli 9612. Probe B-A mutual entailment: D[B2JA1-X2 and S[Bl]A1-X2 10013. Probe reflexivity/irreflexivity 0

a Train reflexivity/irreflexivity with experimental stimuli 7014. Probe reflexivity/irreflexivity 8515. Probe combinatorial entailment: D[Bl]Xl-B2 and D[B2JX2-B1 0

Review A-B and Y-X relations with feedback 10016. Probe combinatorial entailment: D[B1]Xl-B2 and D[B21X2-B1 0

a Train reflexivity/irreflexivity with experimental stimuli 92a Train reflexivity/irreflexivity with experimental stimuli 100

17. Probe reflexivity/irreflexivity 10018. Probe combinatorial entailment: D[B ]Xl-B2 and D[B2]X2-B1 0

Train A-C relations 100Review A-B, Y-X, and A-C relations with feedback (24 trials) 100

19. Probe C-A mutual entailment: D[C2]A1-X2 and S[Cl]A1-X2 10020. Probe combinatorial entailment: S[C2]Bl-B2 0

and D[C1]C2-X2 8Review A-B, Y-X, and A-C relations with feedback (24 trials) 100

21. Probe combinatorial entailment: S[C2JB1-B2, D[Cl]B2-X2 022. Probe combinatorial entailment: S[C2]B1-B2 17

and S[B2]Cl-C2 0and S[B1]C1-C2 50and S[Cl ]B1-B2 0

Review A-B, Y-X, and A-C relations with feedback (24 trials) 10023. Probe combinatorial entailment: S[C2]B1-B2, a S[B2]C1-C2, a S[B1]C1-C2, and S[C1]B1-B2 0

a Change of problems normally used in training or testing.

placed with new figures because the old ones also given a review of the same/different train-had already been related as different from Al ing that they had received in Experiment 1.for these subjects (in the problems D[Al ]B2 As in Experiment 1, probe blocks consistedand D[Al ]C2). This essentially added the fol- of equal numbers of probe items and previ-lowing relations to those trained in Experi- ously trained problems presented without re-ment 1: O[A1 ]B3 and O[A1 ]C3. Subjects were inforcement. Order of the probes was random-


Sub/ect 7 (Pretralned Same/Different)

S (1 - 75%)S (2 - 95%)S (7 - 95%)S (12- 100%)

Txivned:.BI B2

A,Cs

C1 C2

D (15 - 0%)D (16 - 0%)D (18 - 0%)

B1

Al

S but not D (3 - 0%)S but not D (4 - 0%) 3S but not D (5 - 0%) 2S but not D (6 -1 00%)S but not D (8 - 0%)S but not D (9 - 0%)S but not D (10 - 0%)

D (21 - 0%)

D (1 - 75%)D (2 - 95%)D (7 - 95%)D (12- 100%)

<80% on any test

S but not D (11 - 0%)S but not D (13 - 0%)S but not D (14 - 85%)S but not D (17- 100%)

B1S (22 -0%)A{ S (22 - 50%)S (23 - 0%)T%:, S (23 - 0%)

t) ; <Cl - 1C1(1

B2

'Al

Boo- C2^n o/ % I

S (20 - 0%)S (21 - 0%)S (22 - 17%)S (23 - 0%)

u (ZU- w*)

S (22 - 0%)

S (23 - 0%)

Fig. 12. Testing performance of Subject 7 (pretrained with SAME and DIFFERENT). Dashed lines indicateprobes that were above 80% correct, where "correct" is defined as selecting the indicated stimulus. Wavy lines indicateprobes were below 80% on at least one of the testing blocks recorded in that section. The letters S and D indicate therelational stimulus presented. Numbers in parentheses indicate the specific testing block (these same numbers are usedin Table 9 for cross reference) and the percentage correct. See Table 9 for specific comparison stimuli used and trainingsequences.

ized with one exception noted below. On eachtrial the placement of comparisons (left, center,or right) was randomly determined. A-B train-ing was given in blocks of 27 trials (nine foreach problem). The probes for mutual entail-ment and the probe for combinatorial entail-ment (Probes K, L, and M in Figure 14) were

presented in blocks of 27 probes combined with

27 trials in which the trained A-B problemswere presented in extinction. A-C training wasconducted in blocks of 27 trials, and then A-Band A-C training was reviewed with eachproblem presented three times. Probes N, 0,and P, Probes Q and R, and Probes S and T(see Figure 14) were each presented sequen-tially as blocks.

)

545

f,-on %-,

,%1#


EXPERIMENT 2

B2

tDB3

0+zAl

C1 C2

(Also Trained in Experiment 1)

Basic Set of Tested DerivedRelatlons

---51 B2 B3

D S Al sO0::S --- 0"°

j_Cl C2 C3 -

0--

,_----_____--_____-----_ -----_--------_-----________________--____----------_-_-_-___-___ _ -____

Train: (E)S

(F) (G)0 D

Al Al AlBl B2 B3 Bl B2 B3 Bi B2

Probe for mutual entailment

(K)S

B1

(L)0

B3A 1 B2 B3 Al B2

Train: (H)S

Probe forcombinatorialentailment

(M)0B3

Bi B2

(I) U)0 D

Al Al AlCl C2 C3 Cl C2 C3 Cl C2

Probe for mutual entailment.0

(N)S

C1

(0)0

C3

A 1 C2 C3 Al C2

Probe forcombinatorialentailment

(P)0

C3Cl C2

Probe for combinatorial entailment

Fig. 13. Basic network of relations trained and testedin Experiment 2. Solid lines indicate trained discrimina-tions, and dashed lines indicate assessment of relations byprobe items. Letters S, D, and 0 indicate relational stimuliSAME, DIFFERENT, and OPPOSITE. Training andtesting differed for some subjects.

(Q)S

(R) (S) (T)0 S 0

Bl B1 B3 B3

Cl C2 C3 Cl C2C3 ClC2 C3 Cl C2 C3

Probe for combinatorial entailment

Some of the first 10 types of probes (ProbesK through M and N through T in Figure 14)provide additional evidence over the results ofExperiment 1, primarily because they assesswhether both 0 and D worked in Experiment1 via exclusion. In Probe R, for example, sub-jects could exclude C1 (because C1 and B1 arein an equivalence class given S but not 0), butthat would not demand that subjects pick C3instead of C2. Similarly, in Probe T (O[B3]C1-C2-C3) subjects could avoid C3 on the basisof "B3 not Al not C3," but on that basis therewould be no reason to select Cl over C2 (re-sponding to neither had been reinforced given0).The most important evidence came from

Probes U, V, and W. The subject was pre-

(U)S

Cl

B1 B2 N3

(V)DCl

B1 B2 N3

(W)0

Cl

Bl B2 N3

Probes for combinatorial entailment(Subject 9 only)

(X)0

N3Cl C2 C3

(Y)S

N3Cl C2 C3

Fig. 14. The basic training and testing sequence forExperiment 2. Specific sequences varied for specific sub-jects. Letters in parentheses indicate probes.

546

Trained RelatlonsB1

S\

C3


sented with two familiar comparisons (BI andB2) and a novel stimulus (N3) as a compar-ison. Selecting Bi in S[Cl]B1-B2-N3 (ProbeU) can be derived from combinatorial entail-ment of the same relation. In the probe,D[C1 ]B1-B2-N3 (Probe V), picking B2 comesfrom combinatorial entailment of the relationssame and different. Subjects were trained thatB2 is different from Al, and Cl is the sameas Al. Thus B2 is different from Cl. Re-sponding in the last probe, O[Cl]Bl-B2-N3(Probe W), assessed whether OPPOSITEcontrols the same kind of responding as DIF-FERENT. If not, and if responding is basedon combinatorial entailment of the relationssame and opposite, then neither Bi nor B2can be a correct choice. B1 and C1 are thesame as Al and B2 is different from Al, butnot opposite of Al, and thus not of Cl. Theonly choice left is the novel stimulus. If OP-POSITE merely controls nonequivalence, theneither B2 or N3 is a possibility. The predictedpattern of responding to Probe W (O[Cl]Bl-B2-N3) depends on control by the extendednetwork of relations. The subject can select thenovel stimulus (N3) by eliminating the othercomparisons as incorrect. Thus, for Probes U,V, and W, the order of presentation was notrandomized; subjects responded to Probes Uand V at least three times each before beingexposed to Probe W.

Additional probes for Subject 9. If subjectsdid pick N3 in Probe W, then N3 might enterinto the network of relations as the oppositeof Cl and therefore the same as C3. Subject9 was given an additional probe for mutualentailment (O[N3]C1-C2-C3) and a probe forcombinatorial entailment (S[N3]C1-C2-C3)to see if N3 had entered into the network ofrelations via testing alone.

RESULTS AND DISCUSSIONSubject 8

After same/opposite pretraining and a re-view of same/different pretraining, Subject 8(see Table 10) mastered the A-B relations inone block of 27 trials. There are some initialproblems with probes for mutual entailmentand combinatorial entailment, but after fourblocks of probes responding was at criterionlevels (see Figure 15a).

Training A-C relations required only oneblock of 27 trials, but Subject 8 failed to showcombinatorial entailment of responding with

Probe R (O[B 1 ]C 1 -C2-C3). Review of trainedrelations and further probe trials failed to alterthe pattern. On Probes U, V, and W, Subject8 responded at criterion levels on the secondpresentation (see Figure 15b). On the fourthpresentation of these probes, he sometimes se-lected comparison N3 when given Probe V(D[C1]B1-B2-N3). It should be noted that interms of control by arbitrary relations, this isnot an incorrect response. If the previous ex-posure to N3 established it as the opposite ofCl, then N3 is also different from Cl (this isone reason that exposure to Probe W was re-served until after Probes U and V). On threefurther exposures to this set of probes, Subject8's responses followed the predicted pattern on100% of the trials. Finally, the experimenternoticed a clue to Subject 8's failure to respondcorrectly on Probe R. When the previouslytrained relations were presented in extinction,Subject 8 sometimes made erroneous responsesto the previously trained problem O[AI]C1-C2-C3. A set of probes that included O[A1 ]C1-C2-C3, S[Bl ]A 1-B2-B3, and O[Bl ]C1-C2-C3were added. Immediate increase in correct re-sponding to Probe R was observed, to 100%after two blocks of these probes.

Subject 9Subject 9's performance was characterized

by extremely accurate responding (see Table11). Her data are displayed side by side withExperiment 1 data (see Figure 11) to enablea fuller grasp of her total performance. Aftersame/opposite pretraining and a review of thesame/different pretraining, A-B training wasaccomplished with only one wrong response.A-C training was also accomplished with onlyone wrong response. Responses to all probeswere 100% correct. Probes U, V, and W weregiven Subject 9 three times even though shewas 100% accurate on the first presentation inorder to assess her consistency of responding.Subject 9 was given the two additional probesto see if N3 entered into the network of re-lations, and again all responses were consistentwith the predicted pattern.

GENERAL DISCUSSIONPrevious work has shown that nonarbitrary

stimulus relations can be brought under con-textual control and applied to novel sets offormally related stimuli (Lowenkron, 1989).

547


Table 10Percentage of correct responses to training and probe trials for Subject 8, Experiment 2 (SAME/DIFFERENT/OPPOSITE pretraining).


Train A-B relations (with same, different, and opposite conditional stimuli for 27 trials) 971. Probe B-A mutual entailment: S[Bl]A1-B2-B3 100

and combinatorial entailment: O[B3]B1-B2 33Review A-B relations with feedback (18 trials) 100

2. Probe B-A mutual entailment: S[B1]A1-B2-B3 100and combinatorial entailment: O[B3]B1-B2 0

Review A-B relations with feedback (18 trials) 1003. Probe B-A mutual entailment: S[Bl]A1-B2-B3 100

and 0 [B3] A1-B2 78and combinatorial entailment: O[B3]B1-B2 100

Review A-B relations with feedback (18 trials) 1004. Probe B-A mutual entailment: S[B1]A1-B2-B3 and O[B3]A1-B2 100

and combinatorial entailment: O[B3]B1-B2 100Train A-C relations (27 trials) 97Review A-B and A-C relations with feedback (24 trials) 100

5. Probe C-A mutual entailment: S[Cl]A1-C2-C3 and O[C3]A1-C2 1006. Probe combinatorial entailment: O[C3]C1-C2, S[Bl ]C1-C2-C3 100

and O[B1]Cl-C2-C3 11Review A-B and A-C relations with feedback (24 trials) 100

7. Probe C-A mutual entailment: S[C1JA1-C2-C3 and O[C3]A1-C2 100and combinatorial entailment: O[C3]C1-C2 100

8. Probe combinatorial entailment: S[Bl]C1-C2-C3 100and O[B1]C1-C2-C3 0

[Break between sessions]Review pretraining for same, different, and opposite conditional stimuli 100Train A-B relations (27 trials) 100

9. Probe B-A mutual entailment: S[B1 ]A 1-B2-B3 100and O[B3]A1-B2 89and combinatorial entailment: O[B3]B1-B2 100

Train A-C relations (27 trials) 100Review A-B and A-C relations with feedback (24 trials) 100

10. Probe C-A mutual entailment: S[Cl]A1-C2-C3 and O[C3]A1-C2 100and combinatorial entailment: O[C3]C1-C2 100

11. Probe combinatorial entailment: S[Bl]C1-C2-C3 89and O[B1]Cl-C2-C3 0

Review A-B and A-C relations with feedback (24 trials) 10012. Probe combinatorial entailment: S[Bl]C1-C2-C3 89

and O[B1]Cl-C2-C3 013. Probe combinatorial entailment: S[B3]C1-C2-C3 89

and O[B3]C1-C2-C3 44Review A-B and A-C relations with feedback 100

14. Probe combinatorial entailment: S[B3]C1-C2-C3, O[B3]C1-C2-C3 8915. Probe combinatorial entailment: S[B3]C1-C2-C3 89

and O[B3]C1-C2-C3 10016. Probe combinatorial entailment: S[Cl]B1-B2-N3 88

and D[Cl]Bl-B2-B3 75and O[Cl]Bl-B2-N3 88

Review A-B and A-C relations with feedback 10017. Probe combinatorial entailment: S[C1 ]B1-B2-N3 100

and D[C1]Bl-B2-B3 88and O[Cl]B1-B2-N3 100

18. Probe combinatorial entailment: S[Bl]Cl-C2-C3 100and O[B1]C1-C2-C3 11

Review A-B relations with feedback (24 trials) 10019. Probe B-A mutual entailment: S[Bl]A1-B2-B3 and O[B3]A1-B2 100

and combinatorial entailment: O[B3]B1-B2 100Train A-C relations (27 trials) 100


Table 10(Continued)


20. Probe C-A mutual entailment: S[Cl]A1-C2-C3 and O[C3]A1-C2 100and combinatorial entailment: O[C3]C1-C2 100

21. Probe combinatorial entailment: O[C3JC1-C2, S[BI]C1-C2-C3 100and combinatorial entailment: O[B1 ]Cl-C2-C3 0

22. Probe combinatorial entailment: S[B3]C1-C2-C3, O[B3]C1-C2-C3 10023. Probe combinatorial entailment: S[Cl]B1-B2-N3 100

and D[Cl]Bl-B2-B3 50and O[Cl]Bl-B2-N3 100

Review A-B and A-C relations with feedback 10024. Probe combinatorial entailment: S[Cl]Bl-B2-N3, D[CI]Bl-B2-N3, O[Cl]Bl-B2-N3 10025. Probe B-A mutual entailment: S[Bl]A1-B2-B3 and O[B3]A1-B2 100

and combinatorial entailment: O[B3]B1-B2 10026. Probe C-A mutual entailment: S[C1]A1-C2-C3 88

and O[C3]A1-C2 100and combinatorial entailment: O[C3]C1-C2 100

27. Probe combinatorial entailment: O[C3]C1-C2, S[B1]C1-C2-C3 100and combinatorial entailment: O[lB1]Cl-C2-C3 0

28. Probe combinatorial entailment: O[C3]C1-C2, S[Bl ]C1-C2-C3 100and O[Bl]C1-C2-C3 0

29. Probe combinatorial entailment: S[B3]Cl-C2-C3 100and O[B3]C1-C2-C3 89

30. Probe combinatorial entailment: S[Cl ]B1-B2-N3, D[C1 ]B1-B2-B3, O[C1 ]B1-B2-N3 10031. Probe B-A mutual entailment: S[Bl]A1-B2-B3 and O[B3]A1-B2 100

and combinatorial entailment: O[B3]B1-B2 10032. a Probe previously trained relation: O[Al]C1-C2-C3 100

and mutual entailment: S[BI IA 1-B2-B3 100and combinatorial entailment: O[Bl ]C1-C2-C3 89

33. Probe combinatorial entailment: O[C3]Cl-C2, S[B1]C1-C2-C3, O[Bl]Cl-C2-C3 10034. Probe combinatorial entailment: S[B3]Cl-C2-C3 100

and O[B3]C1-C2-C3 8935. Probe combinatorial entailment: S[Cl]B1-B2-N3, D[Cl]Bl-B2-B3 100

and O[Cl]Bl-B2-N3 89a Change of problems normally used in testing.

This finding was essentially replicated in thepretraining phases of both experiments. Thepresent study seems to be the first to show thatsuch contextual control over relational re-sponding can extend to stimuli not related byvirtue of their formal properties. Subjectsshowed patterns of performance that were con-sistent with control by the relations of same,opposite, and different in an arbitrary match-ing-to-sample context. These performances in-stantiate "arbitrarily applicable relational re-sponding" in the sense that the relationalresponses involved were brought to bear onitems by virtue of contextual cues to do so (inthe present case, SAME, OPPOSITE, andDIFFERENT). In short, the present resultsdemonstrate the existence of relational frames.A wide number of alternative explanationscould be provided, however.

Alternative AccountsEven in simplified relational networks such

as the ones used here, the complexity of pos-sible derived relations and unintended sourcesof control is very great. For any given set ofprobes it is relatively easy to identify a sourceof control that could explain these results with-out an appeal to arbitrarily applicable rela-tional responding. We will briefly consider twoalternative accounts.

Direct S+ and S- control by the relationalstimuli. Performance on many specific probescould be explained on the basis of S+ and S-control by the relational stimuli. Consider, forexample, Probe W in Experiment 2 (see Fig-ure 14). Subjects were confronted withO[Cl]Bl-B2-N3. B1 and B2 had been S-stimuli in the presence of 0, and selection of

549


Subject 8 (Pretrained Same/Opposite/Different)

I S (1 - 100%)

" S(2-1009'I S(3-1

S

:S (6-100%)S (8 -100%)

\_ %._ N_./ \

0 (1 -33%)0 (2-0%)0(3-100%) B3

YO) O (4-100%)100%) 0 (3-78%)(4-100%) 0(4-100%)

Al 0 (6-11%)0 (8-0%)"""V

0 (5-100%)0 (7-100%)

0 (6-100%)0 (7- 100%)

0 (9 - 100%)

0 (13-44%)0 (14-89%)0 (15 - 100%)

LEJ1">s S (9 -100%)

S (11 - 89%)S (12 - 89%) Al

0 (9-89%),, '-

1,I

S 13 - 89%)S 14- 89%

N>p~ S 15- 89%),

O(lo0-1I00%) ""> t

B3 J (q

0 (10 -100%)

Fig. 15a. Testing performance of Subject 8 (pretrained with SAME, DIFFERENT, and OPPOSITE) in Ex-periment 2. Dashed lines indicate probes that were above 80% correct, where "correct" is defined as selecting theindicated stimulus. Wavy lines indicate probes were below 80% on at least one of the testing blocks recorded in thatsection. The letters S, 0, and D indicate the particular relational stimulus presented. Numbers in parentheses indicatethe specific testing block (these same numbers are used in Table 10 for cross reference) and the percentage correct.See Table 10 for specific comparison stimuli used and training sequences.

Tralned:Bi B2 B3

Al

C1 C2 C3

51

,-' S (5 - I100%)S (7 - 100%)Cl C3 -

)

0 (11 - 0%)0 (12 - 0%)

Fig. 15b. Continuation of testing performance of Subject 8 (pretrained with SAME, DIFFERENT, and OP-POSITE) in Experiment 2. Dashed lines indicate probes that were above 80% correct, where "correct" is defined asselecting the indicated stimulus. Wavy lines indicate probes were below 80% on at least one of the testing blocksrecorded in that section. The letters S, 0, and D indicate the particular relational stimulus presented. Numbers in

550

r% gm

IIVKI

I,- S(10-100%)


Subject 8 Testing (continued)

D (16-75%)D (17 - 88%)D (23 - 50%) BID (24- 100%)

AS (16 - 88%): ISS (17-100%): sS (23-100%)I isS (24-100%) :s

I,

0(19-100%)0 (25 - 1 00%)

B2S (19-100%)" S (25- 100%)

;(18 - 100%j)"(21 - 100%)(27 -100%) 1(28 - 100%) 'r

S (20-100%)S (26 - 88%)

0(19-100%) ,,0 (25- 100%),,,-'

A1U S (22- 104

0 (20-1 00%)js0 (26-100%) -

C3--A 0 (20-100%) 0 (21-100%)* O(26- 100%) O (27- 100%) O (28- 100%)!

0 (16 - 88%) via comparison with Bi and B2. See text.0 (17-100%)0 (23-100%) O 024 - 100%)

---------------------------------------------------________D (30-100%)-D (35-100%) --,

I

AS (30- 100%)S (34- 100%)

B2S (31 - 100%)

>^S(32- 100%)

"IAS (33 - 100%) Al

I---v--C C1Lo.

0 (31 -100%)

B30 (31 -100%), -

S (29 -1 00S (34- 10093 C6)

C3_I0 (33-100%)

J((C

)

))

0 (18-11%)0 (21 -0%)0 (27 - 0%)0 (28 - 0%)

parentheses indicate the specific testing block (these same numbers are used in Table 10 for cross reference) and thepercentage correct. See Table 10 for specific comparison stimuli used and training sequences. See also Figure 15a.

C(C(

0 (22-100%)

Tralned:BI B2 B3

stSAl

Cl C2C3

O (32 - 89%)0 (33 - 100%)

0 (30 - 100%) (via comparison with Bi and B2. See text.)0 (35-89%)----------------------------------------------------------------l N3

0 (29 - 89%)0(34-89%)

551

0%):I

r

1)

:1

----------


Table 1 1

Percentage of correct responses on training and probes for Subject 9, Experiment 2 (SAME/DIFFERENT/OPPOSITE pretraining).


Train A-B relations (with same, different, and opposite conditional stimuli for 27 trials)1. Probe B-A mutual entailment: S[Bl]A1-B2-B3 and O[B3]A1-B2

and combinatorial entailment: O[B3]B1-B2Train A-C relations (27 trials)Review A-B and A-C relations with feedback

[Break between sessions]Review same/different pretraining for 24 trialsReview same/opposite pretraining for 24 trialsReview A-B relations (with same, different, and opposite conditional stimuli)

2. Probe B-A mutual entailment: S[Bl]A1-B2-B3 and O[B3]A1-B2and combinatorial entailment: O[B3]B1-B2

Train A-C relations (20 trials)Review A-B and A-C relations with feedback

3. Probe C-A mutual entailment: S[Cl]A1-C2-C3 and O[C3]A1-C2and combinatorial entailment: O[C3]C1-C2

4. Probe combinatorial entailment: S[B1]C1-C2-C3, O[Bl]C1-C2-C35. Probe combinatorial entailment: S[B3]Cl-C2-C3, O[B3]C1-C2-C36. Probe combinatorial entailment: S[C1 ]B1-B2-N3, D[Cl ]Bl-B2-N3, O[Cl ]B1-B2-N37. Probe C-A mutual entailment: S[Cl]A1-C2-C3 and O[C3]A1-C2

and combinatorial entailment: O[C3]C1-C28. Probe combinatorial entailment: S[Bl]C1-C2-C3, O[Bl]C1-C2-C39. Probe combinatorial entailment: S[B3]Cl-C2-C3, O[B3]C1-C2-C3

10. Probe combinatorial entailment: S[C1]B1-B2-N3, D[C1]B1-B2-N3, O[Cl]B1-B2-N311. Probe combinatorial entailment: S[C1]B1-B2-N3, D[Cl]Bl-B2-N3, O[Cl]Bl-B2-N312. a Probe combinatorial entailment: S[N3]C1-C2-C3, O[N3]C1-C2-C3


N3 could thus be explained on that basis. Butif such an explanation is adopted, performanceon Probe M (Figure 14) would have to beexplained, because subjects selected B1 givenO[B3]Bl-B2. Many of the other probes wouldalso predict different performances than thoseactually seen if mere S+ and S- control werethe issue. An account in terms of S+ and S-control does not fit with all of the testing resultsand is inadequate on these grounds.

Equivalence and exclusion. Many of the probeperformances can be explained on the basis ofequivalence and exclusion. Explaining Ex-periment 2 strictly in these terms is difficultbecause three distinct patterns of performancewere shown. This seems at least to require an

appeal to higher order forms of exclusion, inwhich stimuli selected by virtue of exclusionin the presence of DIFFERENT were them-selves excluded in the presence of OPPOSITE.Such an analysis would be complicated but issurely not impossible.

Consider the wide variety of qualitative re-

lations that can be modeled with digital com-

puters. At the level of circuitry, all can bereduced to combinations of "on" and "off."Equivalence and exclusion have this same on/off quality and presumably could be used bybehavioral theorists to model a wide variety ofcomplex cognitive relations, including oppositeand different. In computer modeling of com-

plex relations, however, very many combina-tions of on and off can be necessary, and thesame may be true for models of complex re-

lations based on equivalence and exclusionalone.

Conversely, arbitrarily applicable relationalresponding may itself be taken to be the basicunit. In that case, both exclusion and equiv-alence would be viewed as examples of a

broader behavioral process. The results of thepresent experiments fit with this idea, but theydo not eliminate the alternatives. Selectingamong these and other alternatives will re-

Correct

9710010097100

100100100100100100100100100100100100100100100100100

552


quire better behavior-analytic methods, andthe present study may be of some use in thisarea.

Implications for EquivalenceThe present studies have several implica-

tions for the study of equivalence.Compound stimuli. In their study of condi-

tional equivalence classes, Bush et al. (1989)pointed out that apparent second-order con-ditional stimuli may have entered into a com-pound with the sample and thereby exertedcontrol over conditional discriminations. Theprocedure in the present study rules out controlof responding by a compound stimulus andgives unequivocal evidence for second-orderconditional control. Consider the probeS[C2]B1-B2. Pretrained subjects in Experi-ment 1 reliably selected the comparison B2, aspredicted by a relational response account.There were no training items that used C2 asa sample, and all previous probes with C2 asa sample had been presented with the OP-POSITE stimulus as the relational stimulus.Further, there were no training items in whichB2 was the reinforced comparison selectionwhen the SAME stimulus was presented asthe relational stimulus. The relational stim-ulus and the sample must have functioned in-dependently to produce the pattern of respond-ing observed in the present study. This providessupport for Sidman's development of the four-and five-term contingency nomenclature (Sid-man, 1986), but only if these terms are avail-able to control distinct responses. For example,although the SAME, OPPOSITE, and DIF-FERENT stimuli can be thought of as fifthterms in contingencies, their effects were dis-tinct.

Contextual control over equivalence and non-equivalence. For pretrained subjects, one re-lational stimulus reliably resulted in the choiceof reflexive or equivalent sample-comparisonselections. The other relational stimuli re-sulted in irreflexive or nonequivalent choices.At the least, this shows that forming equiva-lence itself can be brought under contextualcontrol. In the presence of one relational stim-ulus, a given comparison would enter into anequivalence relationship with a sample. In thepresence of the other relational stimulus, thesame comparison would be excluded from theclass of stimuli equivalent to that same sample.

This finding is distinct from demonstrations ofconditional equivalence classes (e.g., Wulfert& Hayes, 1988) that involve the compositionof equivalence classes, not the presence or ab-sence of equivalence.To the extent that these data strengthen the

plausibility of the relational frame account,there are other implications for issues of con-textual control of equivalence. Arbitrarily ap-plicable relational responding must be able tobe brought to bear by the context, not solelyby formal properties of the items being related.What contextual factors might be involved inequivalence research?

Probably the most fundamental languageprocess is that of naming. Of importance tothe present argument is the development ofcoordination between the productive and re-ceptive aspects of naming. For example, chil-dren are taught to name an object and also toorient toward a named object. Each discrim-ination may be trained unidirectionally at first,but the overall performance occurs in consis-tent contexts in which the bidirectional rela-tion is applicable. (Parenthetically, coordi-nated name-object and object-name relationsare not strictly symmetrical because the re-sponses involved differ. This may be resolvedif the child has a generalized imitative rep-ertoire that enables the repetition of soundsthat are heard. Thus, the symmetrical versionof productive naming is: hear name-orienttoward object [given A then B]; when orientedtoward object-hear name [then say the nameheard] [given B then A produce A].)

If a child with an extensive naming historyis taught "This is your boat," contextual cues(such as the word "is," or the naming contextmore generally) reliably predict that if this isa boat, a boat is this. Thus, the child may noworient toward the boat when asked "Where isyour boat?" without direct training to do sobecause contextual cues brought a frame ofcoordination to bear on the trained relation.The naming situation is similar to the

matching-to-sample preparation usually usedin experimental studies of equivalence. In nat-ural language circumstances children are oftenasked, for example, which item of several "iscalled" a sample name-essentially a match-ing-to-sample situation. Thus, the matching-to-sample procedure itself may serve as a con-textual cue for responding in terms of sameness

553


because of the formal properties of the trainingand testing situation in combination with thechild's history with a variety of relational taskssuch as naming. Note that we are not ap-pealing to naming as a mediational process.From the point of view of relational frametheory, a history of relational responding wouldexplain the derived relations seen both in nam-ing and in equivalence. Such a history in onearea may affect responding in another, how-ever, through the development and instantia-tion of a common behavioral process.To assess the kinds of contexts in which

equivalence will emerge, more research shouldbe done on the ease with which equivalence isshown in a variety of tasks and experimentalpreparations other than matching to sample,especially with very young children. Workneeds to be done on ways of breaking up andpreventing the formation of equivalence rela-tions because this may assess whether thereare contexts in which equivalence is unlikely.To assess the role of history in equivalence,longitudinal studies need to be conducted onthe development of equivalence in infantsyounger than 2 years (because children alreadyshow equivalence by then; Devany, Hayes, &Nelson, 1986).The experimental procedure used in many

studies of equivalence could also have encour-aged its formation. Some studies (e.g., Lazar,Davis-Lang, & Sanchez, 1984; R. Saunders,Wachter, & Spradlin, 1988; Sidman et al.,1985; Sidman & Tailby, 1982) exposed sub-jects to identity matching (though often in un-reinforced trials) before beginning the trainingwith the arbitrary stimuli. This may have cuedthe application of the relation of sameness inthe arbitrary matching-to-sample task that fol-lowed, much as SAME did in the present stud-ies. In other studies (Devany et al., 1986; Gatch& Osborne, 1989; Spradlin et al., 1973; Weth-erby, Karlan, & Spradlin, 1983), subjects wereinstructed to choose the comparison that "wentwith" the sample, perhaps cuing a frame ofcoordination.

Rather than view such factors as problemsto be avoided, the present concept suggests thatthey are important variables to be studied.Verbal humans appear to have a wide varietyof relational responses under contextual con-trol, and, in the present study, pretrainingprobably only actualized already learned be-havior. If pretraining had been omitted and

the words "same," "different," and "opposite"were used as relational stimuli, the results couldwell have been similar. The study of contex-tual control (including verbal control) over re-lational responding may provide a fruitful av-enue of research for the study of equivalence,exclusion, and other types of relations.

Increasingly, behavior analysts are viewingstimulus equivalence and similar phenomenaas important preparations for the investigationof human language and cognition. The presentstudy provides a method for the study of amuch wider range of stimulus relations thatcan be brought to bear on arbitrary stimuli.As such, it may be useful for behavior-analyticinvestigations of complex cognitive and verbalphenomena.

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

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

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

Fields, L., Verhave, T., & Fath, S. (1984). Stimulusequivalence and transitive associations: A methodolog-ical analysis. Journal of the Experimental Analysis ofBehavior, 42, 143-157.

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

Harrison, R. J., & Green, G. (1990). Development ofconditional and equivalence relations without differ-ential consequences. Journal of the Experimental Anal-ysis of Behavior, 54, 225-237.

Hayes, S. C. (1989). Nonhumans have not yet shownstimulus equivalence. Journal of the Experimental Anal-ysis of Behavior, 51, 385-392.

Hayes, S. C. (1991). A relational control theory of stim-ulus equivalence. In L. J. Hayes & P. N. Chase (Eds.),Dialogues on verbal behavior (pp. 17-40). Reno, NV:Context Press.

Hayes, S. C., & Hayes, L. J. (1989). The verbal actionof the listener as a basis for rule governance. In S. C.Hayes (Ed.), Rule-governed behavior: Cognition, contin-gencies, and instructional control (pp. 153-190). NewYork: Plenum Press.

Kennedy, C. H., & Laitinen, R. (1988). Second-orderconditional control of symmetric and transitive rela-tions: The influence of order effects. Psychological Rec-ord, 38, 437-446.

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

Lowenkron, B. (1989). Instructional control of gener-alized relational matching to sample in children. Jour-

ARBITRARILY APPLICABLE RELATIONAL RESPONDING 555

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McIntire, K. D., Cleary, J., & Thompson, T. (1987).Conditional relations by monkeys: Reflexivity, sym-metry, and transitivity. Journal of the ExperimentalAnalysis of Behavior, 47, 279-285.

Reese, H. W. (1968). The perception ofstimulus relations:Discrimination learning and transposition. New York:Academic Press.

Russell, B. (1919). Introduction to mathematical philos-ophy. London: Allen & Unwin.

Russell, B. (1937). The principles of mathematics (2nded.). London: Allen & Unwin.

Saunders, K. J. (1989). Naming in conditional discrim-ination and stimulus equivalence. Journal of the Ex-perimental Analysis of Behavior, 51, 379-384.

Saunders, R. R., Wachter, J., & Spradlin, J. E. (1988).Establishing auditory control over an eight-memberequivalence class via conditional discrimination pro-cedures. Journal ofthe Experimental Analysis ofBehavior,49, 95-115.

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

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

Sidman, M. (1987). Two choices are not enough. Be-havior Analysis, 22, 11-18.

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crossmodal transfer of stimulus equivalences in severeretardation. American Journal of Mental Deficiency, 77,515-523.

Sidman, M., Cresson, O., Jr., & Willson-Morris, M.(1974). Acquisition of matching to sample via medi-ated transfer. Journal of the Experimental Analysis ofBehavior, 22, 261-273.

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.

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Spradlin, J. E., Cotter, V. W., & Baxley, N. (1973).Establishing a conditional discrimination without di-rect training: A study of transfer with retarded ado-lescents. American Journal ofMental Deficiency, 77, 556-566.

Wetherby, B., Karlan, G. R., & Spradlin, J. E. (1983).The development of derived stimulus relations throughtraining in arbitrary-matching sequences. Journal oftheExperimental Analysis of Behavior, 40, 69-78.

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Received May 15, 1990Final acceptance April 30, 1991

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