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ED 091 043 PS 006 721

AUTHOR Trabasso, Tom; Riley, Christine A.TITLE An Information Processing Analysis of Transitive

Inferences.PUB DATE May 73NOTE 13p.; Paper presented at the Meeting of the Eastern

Psychological Association (Washington, D.C., May1973)

EDRS PRICE MF-$0.75 HC-$1.50 PLUS POSTAGEDESCRIPTORS Adults; Behavioral Science Research; Cognitive

Development; *Cognitive Processes; Early Childhood;*Logical Thinking; *Memory; *Problem Solving; *TaskAnalysis

IDENTIFIERS *Information Processing (Psychological); TransitiveInferences

ABSTRACTThis discussion of transitive inferences (if A

greater than B & B greater than Co then A greater thean C) emphasizesan information processing analysis of logical thought. The two basicfactors considered in such an analysis are (1) the task environment,including its structure, demands, decisions required, and informationgiven; and (2) the individual as an information processor (hisknowledge, limitations, etc.). In order to make transitive inferencesa person must make several critical operations. He must know that thescale of comparison is transitive and must code task information.Research concerned with childrents coding strategies is discussed toillustrate the importance of this operation. Young children(4-6years) can make the inferences if they are forced to code incertain ways (if their attention is directed to the comparativerelations among key elements of the problem). A second basicoperation is memory storage. Two possible models of storage areidentified: (1) a coordinate model in which each ordered pair ofitems is stored, and (2) a spatial integration model in whichinformation is integrated as it accumulates into one representationwhich is stored for subsequent inferential' thought. Experimental workwith adult subjects indicating that spatial representations areconstructed in transitivity tasks is described. (DP)

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An Informatiln Procesqing Ailalysis of

TCADSitiVP IP(OttInCOS

lom TrAbasso ani Chriotinp A. Miley

Princeton University

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it14.-P4pC`r r, :?al at Yastrn PoychoIoqical hssociationf Aashington,n. c. nay 1-ri, 1973 is part of a Symposia: Lo,jic ithy do we

t4:)study it and what are we doing?

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The central question before us is: why do we studylogic in a psychological context? One answer is that logicpervades human intellectual activity and to study itsoperation is a fundamental investigation of cognition. Cntnis !ie probably all agree.

One could view certain forms of logic as a kind ofcompetence model and use it' as a norm against which todiagnose the presence or absence of logical abilities,Assuming that the adult possesses the highest form ofcompetence, then one could investigate the development cfintelligence as a series of approximations to this higherform. According to this view, the central concern iswhether. or not the child possesses a given logical abilityor structure, The order in which these sttuctures manifestthemselves is of interest.

An alternative approach is to study how people performlogical tasks in order to discaper what they do when forcedto behave within the constraints imposed by the task. Thefocus is on what the person does, not on his success cvfailure. If one knows the cognitive processes that aredetermined by the requirements of the task environment, onecould predict success or failure as well as diagnose it.

The latter position is the one we have developed in ourstudy of reasoning. Our belief is that logical problemsstress our information processing system and reveal muchabout the properties of this system: its structural andcontrol processes. Our attitude is one of discovery ratherthan confirmation, induction rather than deduction.

In this paper, we hope to illustrate the value of aninformation processing analysis of a logical task. We havechosen the transtivie inference problem because it islogically simple but psychologically complex, and becausothis problem has received considerable attention since Burtfirst used it in an inteligence test back in 1919. It is awell known task in Pi.agetian research. rt has receivedconsiderable study, in adults in what are known as"three-term series" problems. Recently, it has become atepic in psycholinguistic research which focuses oninferences male accross sentences in text or connected.discourse.

In formal terms, what is a transitive inference?- Atranstivie inference is a logical operation of the force:- ifA is greater than 8 (A>8) and if B is greatet than C (8>C),then A is greater than C (A>C). We shall consider first thePiagetian view. Here, the failure of a child to forminferences before the stage of concrete operations (at aboutseven to eight years) is attributed to the lan of thelogical grouping structure of addition of asytmetrical

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relations. in other terms, the child is unahle tocoordinate the information about the two relations A>8 and9>C. In order to combine these relations with a commontore, the chili must simultaneously conceive therelationship of the elements in the pair AD in terms of thedirect (A >fl) and the inverse (B

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information.Given that. A is longer than Li is the input, one might

code the information:1. A (is imiortant)2. A is long.3. A is long; B is not long.4. A is long; B is short.

.5. A is longer than B and P is shorter than A.

Only (5) leads to .the ordered set (A,B), Codes (1), (2),(1) and (4) would lead to success or failure depending uponthe task. We (Riley and Trahasso, 1973) have found that

do not code anything at all about length relationswhen another, simpler code works. That is, we hadfouryear-old children initially learn a series of fourcomparisons A>E, C0 and .FXD where they had tc choosethe element named by the relation leo. choose A when asked',which is longer?',. The children were smarter than we, theylearned a simple rule that A, C and E aro winners and e andD are losers. This corresponds to code (1) above (i.e. A isimportant) .

to another task, when we asked only one cemnar ai .iVoterm iiiroughout: A>13, B>C, C>D and D>3, they couldn't learnthe pairs much less draw inferences. Code (3) or (4) wasused and lead to contradictions of the form identified byPiaget, namely labelling B both not long and long lor shortand long) .

It was only when we used both comparative terms ifilbilla pair, i.e. asking the child Which is longer, A or P7 andWhich is shorter, A cr B? that they succeeded in bothlearning the ordered relation (A,B) and making inferencessuch as B>D (cf. Bryant and Trahasso, 1971; Lutkus andTrabasso, 1973).

A second critical operation is, given that the chillhas coded the relations, he must store it in Memory. How itis stored or represented is a critical question because theoperations upon this stored representation are what lead tocorrect answers in the test.

The nature of the representation in memory is critical\since it- determines tetemines the mental operations tha will be

Potformed on it. In the transitivity task, we can identifyat lease two possible representations, in memory. -, in one,the -person. stores each,ordered pair inmemory. Then, whenquestioned: Which-is longer? (shorter?) he retrieves thecritical pairs and coordinates then via middle terms,consistent with Piagetis analysis. We will call this thecoordinate model.

An alternative representation could arise where theperson integrates the information as it accrues into a

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single representation and stores that in memory forsubsequent inference making, That is, the person begins byfinding the end pairs and uses them as "anchors ". He thenadds elements tc the array as they occur until all eleaestsate so ordered. When questioned, he isolates the criticalelements, notes their order and answers the question. Wewill call this the spatial integration model.

'These models lead to a simple experimental test in thetransitivity task. Look at Table 1 in the Handout. Supposethere are six sticks of different lengths where 1 is theshortest and 6 is the longest. Following a procedure wehave used extensively in showing a child's memory for theinitial information is critical in making transitiveinferences (Bryant and Trabasso, 1971; Lutkus and Trabasso,1973; Riley and Trabasso, 1973), we first train subjects tomake choices among deljegent pairs of sticks. The stices arecolor coded and the subject can use only the colors topredict the length relation. On a given training trial, thesubject is asked one of two questions: either "Which stickis longer ?" or "Which stick is shorter ?", and then is showna pair of sticks of the same length but of different. colors.The subject selects a color by pressing a panel in front ofthe stick. After he makes his choice, he receives feedbackon its correctness. We record the time it takes him to makethe choice,

After training each asjacent pair in a random order, wetest the subject on all possible pairs without feedback.The matrix in Table 1 tells us three pieces of information:

1. The main diagonal (squares) gives us the speed ofretrieving information on the adjecent training pairs.

2. The first row and last column entries (lines) tellUs whether of not there are anchor effects, since these.involve endpoint sticks.

3. The critical, off-diagonal entries are the inferencetests (circles) ,and they involve inference steps of 1 or 2units,

If subjects store only the diagonal (adjacent pair)information and coordinate it to answer questions onoff-diagonal pairs, then we predict that those pairs withmore inferential steps would take longer, tf, on the otherhand, subjects integrate the infoemation into a epatialarray and access this sinle memory representation duringtesting, then we predict that the greater the distancebetween the sticks, the faster the time.

We tested these predictions on adult subjects byrunning three conditions. In one condition, subjectsreceived both visual and verbal feedback after taking achoice in training. That is, they were shown, the sticks and

heard the relation stetee (e.g. Red is longer than blue),In a second (verbal) condition, they were told the relationafter a choice in training. No feedback' of any sort vasgiven during testing in the above condition'. In order totest whether the representation was indeed satill, we ran athird group. Instead of training on pairs, we simply showedthem the entire array of sticks,ordered 1 - 6, The subjectswere tested with the sticks in full view via the same meansas in the visual-plus-verbal and the verbal conditions. Inall cases, we measured the reaction time in answeringquestion.

There were 12 college students as subjects in eachcondition and there were four tests per pair.

Table 2 in the Handout gives the raw OT data on eachguesti2n for each of the three conditions. Cf particularimportance are the underlined R7s for steps of 1 or 2.

In five cut of six tables, you will note that thetwo-step RT is raster than the one-step RTs.

In order to see the relations more clearly, we scaledthese data, finding a tvc- dimensional representation of allinter-pair distances. In this analysis, distance equals thereciprocal of RT GO that faster times give longer distances.

Slide 1 shows the distances for the question longer?Note first of all how similar these distance plots are forall three conditions. The longest stick (numbe 6) isclearly further from the other five; the remainieg fivesticks are ordered 1,2,3,4,5 in distance.

Slide 2 shows the scaling results for the questionshorter? Now we find the shortest stick (number 1)separated from the rest. The remaining sticks are generallyordered 2,3,4,5,6 with 6 separated slightly further away.

In our next analysis, we removed the longest stick(number 6) data and the shortest stick ( number 1) data fromthe matrices with matching questions. we then collapsedstatistically equivalent data points for distances of 0(adjacent pairs), 1, 2, or 3 inferential steps. The meanRTs as a function of these distances are shown in Slide 3for each condition. The data are remarkably similar accrossconditions. The adjacent pair or 0 step RTs are the longestdespite the fact that these were the ones upon which thesubjects were trained. ST decreases linearly as a functienof step size, perfectly consistent with the spatialintegration model. The visual and verbal feedbaCk data arevirtually idEntical with that obtained when subjects havethe display in front of, them, suggesting that HAWrepresentations are constructed. The verbal RTs are longerand subjects indicated-that they had trouble end-anchoringin training when the feedback was only verbal. Clearly, the

coordination model finds Di! SUrpOtt 16 AJtA.Thus, adults who aro st4pesed to ba in the fotedl

operations stage Jo nct perform such operations intransitivity tests. Rather they use their knowledge thatlength is transitive, isolate the extreme ends of the scale,order each pair and add single elements to a spatial arraywhich is stored in memory for later.. use in answeringoltransitivityp questions. The integration of separatepieces of information into one unit conserves space andenables one to efficiently answer a wide variety ofinferential questions.

We are currently carrying out these 'Same experiments oneight to nine-year-old children. The results on the displayand visual and verbal feedback groups are in and look verysuch like our adult data.

rn overview then, our inquiry into transitive reasoninghas lead us to' discover a number of things. We have foundthat very young children (four to six years of age) can maketransitive inferences if one assures that they are askedquestions which direct their attention to the comparativerelations among the elements. They may fail if the codingis inadequate, as determined by the task demands, or if theyforget the original, ordered codes.

Our adult latency studies (and subsequent studies onconcrete operational children) show that coorlinaion orititagration occurs spontanously during training as subjectsintegrate ordiu.ed patr inrormation into spatial arrays.This integratien is an efi*icient representatic,n for veaoryand inference ta!:0g, a procQss not of all envtnioncd bylogical oplatior.al lualysis, These studies couvinccdus of the valuz of vit.-.1:11g the tiv1)an eA an inforationprocessor Iv is hasicAy a good problem using hislimited cap,Icitks an,!. traordinary proce:i,;es to operate ona variety of task environments. Logical processes are onlyone sv.all part of these skills.

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References

Bruner, J.S., Giver, R.B. And Greenfield, P.M. §tudig§ inCnnitive gg2wtt. New York: John Viley and Sons, Inc.,1966.

Bryant, P. E. and Trabasso, T. Transitive inferences andmemory in young children. NAture, 1971, 212, 4t6-45e.

Flavell, J.H. 2119 P.91142RDWA1 in2b212U/ 2t 42a12 Litaa.New York: Van Nostrand Reinhold Company, 1963.

Lutkus, A.D. and Trabasso, T. Transitive inferences in"preoperational" retardates. Unpublished paper,Princeton University, 1973.

Riley, C.A. and Trabasso, T. Logical structure versusinformation processing in making inferences. Paperpresented to the society for Research in Child--Development, March, 1973.

Simon, Cn th development IA the proceseicr, inParnhe,A-Diggory, S. (Ed.) L1'P:SIVAii211 kl:221frniva iOgitAldr%n. New 'fork: Academic Press Inc. 1972.

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