a case of syntactical learning and judgment: how ...pal/pdfs/pdfs/dulany84.pdfracy on 2,000 - 821 =...

$: A Case of Syntactical Learning and Judgment: How ...pal/pdfs/pdfs/dulany84.pdfracy on 2,000 - 821 = 1,179 trials would explain only 694 + 589.5 = 1,283.5 of the reported 1,620 correct$
Journal of Experimental Psychology: General1984, Vol. 113, No. 4, 541-555.

Copyright 1984 by theAmerican Psychological Association, Inc.

A Case of Syntactical Learning and Judgment:How Conscious and How Abstract?

Don E. Dulany, Richard A. Carlson, and Gerald I. DeweyUniversity of Illinois at Urbana-Champaign

This study examined two possible bases for grammatical judgments followingsyntactical learning: unconscious representations of a formal grammar, as inReber's (1976) hypothesis of implicit learning, and conscious rules within infor-mal grammars. Experimental subjects inspected strings generated by a finite-stategrammar, viewed either one at a time or all at a time, with implicit or explicitlearning instructions. In a transfer test, experimental and control subjects judgedthe grammatically of grammatical and nongrammatical strings, reporting onevery trial the bases for their judgments. In replication of others' results, experi-mental subjects met the critical test for grammatical abstraction: significantlycorrect classification of novel strings. We found, however, that reported rulespredicted those grammatical judgments without significant residual. Subjectsevidently acquired correlated grammars, personal sets of conscious rules, each oflimited scope and many of imperfect validity. Those rules themselves were shownto embody abstractions, consciously represented novelty that could account forabstraction embodied in judgments. The better explanation of these results, weargue, credits grammatical judgments to conscious rules within informal gram-mars rather than to unconscious representations of a formal grammar.

What is conscious and what unconscious isa central question for current cognitive psy-chology. Indeed, that question has providedsome of our deeper historical issues (Hilgard,1980; Klein, 1977) and more controversialexperimental literatures: subception and per-ceptual defense (Dixon, 1971), learningwithout awareness or attention (Brewer,1974; Dulany, 1968; Kellogg, 1980), and sev-eral varieties of preconscious processing(Broadbent, 1977; Dixon, 1981). But no-where is the claim for unconscious processesstronger, or more Significant if true, thanwhen the hypothetical processes are amongthe most complex of which we are capable—processes such as abstraction, inference, de-

Completion of this study was aided by a research grantfrom the Graduate College of the University of Illinois.

Several readers provided very helpful comments on anearlier draft of this article: William Brewer, Robert Hart,Douglas Medin, and Brian Ross.

We are especially grateful to Arthur Reber for gener-ously providing experimental materials and detailedcomments at the time we planned this study.

Requests for reprints should be sent to Don E. Dulany,University of Illinois, Department of Psychology, 603East Daniel Street, Champaign, Illinois 61820.

cision, and judgment. This is the claim for afully psychological unconscious.

In an important series of articles, Reber(1967,1969,1976) proposed just such a pro-cess, which he called implicit learning, and heand his associates reported a series of experi-ments designed to investigate its behavior(Allen & Reber,.1980; Reber & Allen, 1978;Reber, Kassin, Lewis, & Cantor, 1980; Reber& Lewis, 1977). From many passages we ex-tract what we consider to be the essence of theimplicit process: According to Reber (1976),(a) information may be passively encodedby a "nonconscious abstraction system"(p. 276). (b) What is learned is "tacit knowl-edge" (Reber & Lewis, 1977, p. 355), an un-conscious and abstract representation ofstructure in the information given, (c) Thejudgment that new information does or doesnot satisfy that representation is "implicit inour sense that [subjects] are not consciouslyaware of the aspects of the stimuli which leadthem to their decision" (Reber & Allen,1978, p. 218). (d) The process is evoked, it issaid, when "subjects are not actively trying tobreak the code," "the stimulus environmentexhibits exceedingly complex structure"

541

542 D. DULANY, R. CARLSON, AND G. DEWEY

(Reber, 1976, p. 88), and the structure is notso salient as to evoke an alternative process(Reber et al., 1980). Implicit learning is pro-posed as a mechanism for acquiring a varietyof "complex structures underlying language,socialization, perception, and sophisticatedgames" (Reber et al., 1980, p. 492). Through-out this work, the implicit process is con-trasted with an explicit learning process inwhich one tries to decipher rules by testingconscious hypotheses, leading instead to a setof conscious rules that describe the domainand guide judgment. A similar contrast be-tween types of learning was proposed byBrooks (1978) and by Anderson, Kline, andBeasley(1980).

For their series of studies, Reber and asso-ciates designed unusually interesting experi-mental tasks, with finite-state grammars,realizing the aim of complexity while permit-ting a precise description of the material to belearned. Displayed in Figure 1 is a representa-tive grammar used in Reber and Allen (1978)and also in the present study. With each tran-sition from State / to State j or recursion onState /, the system writes a letter. In this waythe grammar generates a letter string for eachpermissible sequence of transitions and re-cursions from the entrance state to the exitstate (Chomsky, 1963; Miller & Chomsky,1963). Using this and very similar experi-mental tasks, Reber and his associates repli-cated the central finding over a variety oflearning conditions: Given grammaticalstrings and implicit learning instructions,subjects are significantly accurate when theyhave a later opportunity to judge the gram-maticality of novel grammatical and non-grammatical strings. This capability followsmemorization to criterion (Reber, 1967,1976; Reber & Lewis, 1977), paired-associatelearning to criterion (Reber & Allen, 1978),and observation learning of strings presentedsequentially (Reber & Allen, 1978) or simul-taneously (Reber et al., 1980). Althoughsomewhat diminished, the capability was stillpresent 2 years after original learning (Allen& Reber, 1980).

In our view, however, the basic and fre-quently replicated finding does not in itselfprovide strong evidence for (a) unconsciousabstraction, (b) abstract and unconsciousrepresentation, or (c) grammatical judgment

Figure 1. Schematic diagram of finite-state grammar.

based on criteria outside the subjects' aware-ness. That interpretation would require theassumption that (d) the complex task and in-structions to learn passively did in fact evokethe full implicit learning and judgment pro-cess. It is at least as plausible that informationembodying rulelike regularities would evokea strategy of learning and using consciousrules despite instructions merely to learn pas-sively. We need taps into the process.

In order to see whether an implicit processmight elude introspection, Reber and Allen(1978) obtained open-ended verbal reportsafter learning, then left the tape recorder run-ning throughout the test while "subjects wereencouraged to keep up a running commen-tary . . . to provide reasons and justifica-tions for their judgments wherever theycould" (p. 198). "In summary," they re-ported, "our subjects tell us that the observa-tion procedure tends to produce knowledgewhich is abstract in nature but which feelsintuitive" (p. 203). Moreover, "learningoccurs in the absence of explicit code-break-ing strategies; our subjects cannot tell us verymuch about what they know" (p. 204). De-spite this summation, the authors also re-ported the following:

Specific aspects of the letter strings were often cited asimportant in decision-making . . . first and last letters,bi-grams, the occasional tri-grams and recursions werementioned. . . . Instrospections after [observationlearning] abound with references that have abstract rule-like qualities. Subjects refer to what can (and what can-not) be, what feels right (or wrong) and what is coherent(or not), (p. 202)

Nevertheless, they concluded the following:

SYNTACTICAL JUDGMENT 543

subjects emerged with a small but solid body of articu-lated knowledge which they used to make decisionsabout the well-formedness of novel letter strings,. . . [but they] also have a solid but tacit apprehensionof the grammatical structure which serves them on thoseoccasions when they have no conscious criteria, (pp.211-212)

Although these reports provide valuableexploratory data, they seem insufficient toshow whether conscious rules could explainthe grammatical judgments. Subjects re-ported justifications of their judgments on821 of their aggregate 2,000 trials. Of these821,694 were "appropriate" in the sense that"the subjects' reasons for a response were anaccurate reflection of the constraints of thegrammar" (Reber & Allen, 1978, p. 209). Ata glance, the rules would seem to underpre-dict correct judgments. Appropriate justifi-cations on 694 trials with 50% guessing accu-racy on 2,000 - 821 = 1,179 trials wouldexplain only 694 + 589.5 = 1,283.5 of thereported 1,620 correct judgments. The trou-ble is this: As Reber and Allen (1978, p. 210)recognized, an appropriate justification mayyield an incorrect judgment if something elsein the string is nongrammatical; and an "in-appropriate" justification may yield a correctjudgment if the justification itself is in error.A two-valued metric—consistent or incon-sistent with the grammar—does not ade-quately capture what a subject may use toproduce a particular level of correct judg-ments. The problem we see with Reber andLewis's (1977, p. 352) use of reports is vir-tually identical. If we are to determine howwell reported rules could explain judgments,we must know the probability of a correctjudgment given the use of any rule reported.We provide such a validity metric for re-ported rules.

The present study is motivated by twoclosely related questions:

1. Do subjects acquire consciously avail-able rules that could explain their grammati-cal judgments? If so, this would challenge thepostulation of an unconscious and abstractrepresentation that guides their grammaticaljudgments. In fact, we ask whether the rulesacquired might constitute something otherthan the formal grammar that generated thestrings. It is a cornerstone of modern linguis-tic theory that any finite set of strings can be

generated by or classified by an infinite num-ber of grammars (Pinker, 1979), as Reber etal. (1980, p. 500) recognized. Far as the for-mal grammar in Figure 1 is from the con-scious ken of imaginable subjects, the gram-mar each subject acquires may very well be aset of informal and consciously availablerules. Although each of the rules alone maybe limited in scope, and many imperfectlyvalid, they may in aggregate be sufficient toexplain the significant but imperfect levels ofperformance observed. We examine the pos-sibility that subjects acquire corf elated gram-mars, an alternative conception of whatmight be abstracted from the structure of adomain.

2. Do conscious rules themselves embodyabstraction in the sense of novelty? The keyand conventional mark of grammatical ab-straction is the successful classification (orgeneration) of novel strings, strings unen-countered before but nevertheless classifiableby a grammar that generates all and onlygrammatical strings. If subjects' judgmentsmeet this test for abstraction and are also pre-dicted by rules, we ask what it is about thoserules that may permit that significant kind ofabstraction. If conscious rules could be alocus of abstraction, this would enhance thetheoretical utility of any formulation giving aprominent place to those rules.

In short, how conscious and abstract issyntactical learning and judgment, wherehow may be taken to mean both in what senseand in what degree?

MethodDesign

During the acquisition phase, experimental subjectswere arranged within a 2 X 2 design, with between-sub-jects conditions of implicit or explicit learning instruc-tions and strings viewed either one at a time or all at atime. Control subjects did not participate in the acquisi-tion phase. All subjects participated in a test phase inwhich they judged the grammaticality of strings and re-ported rules.

TaskWe selected a finite-state grammar used by Reber and

Allen (1978), the grammar they felt most likely "to keepthese explicit processes at a minimum" (p. 194). It gener-ates relatively short strings, and "the longer a grammati-cal string becomes, the more salient the internal struc-ture is and the more likely it becomes that subjects will


try explicitly to 'crack the code'" (Reber & Allen, 1978,p. 194). Shown in Table 1 are the 20 grammatical stringspresented at acquisition and the 25 grammatical and 25nongiammatical strings presented at the transfer test.With an arbitrary limit of 4 on the number of possiblerecursions at States 2 and 5, the grammar in Figure 1generates exactly the set of 40 strings used, plus 1 otherarbitrarily discarded by Reber and Allen. They con-structed nongrammatical items by introducing thegrammatically impermissible letter substitutions and re-versals underlined in Table 1.

ProcedureAcquisition. All subjects participated in groups of 15

to 18, with a very general introductory instruction call-ing for their attention, care, and cooperation through-out. In all experimental groups, too, the task called forobservation learning only, as in Reber and Allen (1978)and Reber et al. (1980). This is the most passive of thelearning tasks used in this work.

Critical features of the explicit and implicit learninginstructions were taken verbatim from Reber (1976),with minor rephrasing elsewhere to accommodate thepresent learning task. In the implicit learning conditions,subjects were read the following:

Table 1Strings Presented During Acquisitionand Test Periods

•> AcquisitionGrammatical

MTTTTVMTTVTMTVMTVRXMTVRXMMVRXMVRXRRMVRXTVMVRXVMVRXVT"VXMVXRRVXRRM ,VXRRRRVXTTVTVXTVRXVXTVTVXVRX"VXVRXVVXVT"

Grammatical

VXTTTVMTTTVMTTVRXMVRXVT"MTVRXVMTVRXRMVRXMVXVRXRMTTTVTVXRMMVT ,MTVTMTTVMVRXRVXRRRVXTVVXRVXVT"MTV"VXRRRMVXTTVVXVVXVRX'VXVRXVMVRXRM

Test

Nongrammaticalb

VXRRTVXXVXRVMXVRXRRXTTTTVMTVVMMVRXMVRTRMTRVRXTTVTMTTVTRTVTTXVRVTMXVTVRRRMXRVXVVVXRMVXRTMTRVVXMRXVMTMTXRRMMX.VRXMMTVRTRRRRXV

" Items in both acquisition and test periods.b Strings areunderlined at point of grammatical violation.

This is a simple memory experiment. You will seeitems made of the letters M, R, T, V, and X. The itemswill run from three to six letters in length. You will seea set of 20 items. Your task is to learn and remember asmuch as possible about all 20 items.

Subjects in the explicit learning conditions heard thoseinstructions with the following addition:

The order of letters in each item of the set you areabout, to see is determined by a rather complex set ofrules. The rules allow only certain letters to followother letters. Since the task involves memorization ofa large number of complex strings of letters, it will beto your advantage if you can figure out what the rulesare, which letters may follow other letters, and whichones may not. Such knowledge will certainly help youin learning and remembering the items.

In the sequential conditions, modeled closely onReber and Allen (1978), each grammatical string wasprojected onto a screen for 10 s, and the set of 20 items,was presented 3 times in a different order each time. Inthe all conditions, modeled closely on Reber et al.(1980), the entire set of 20 grammatical items was pre-sented on a single slide for 10 min, resulting in a totalpresentation time equal to that in the sequential condi-tions. In both conditions, the order of presentation ofthe strings was randomized, with randomization con-strained to avoid introducing structure that would makethe grammar especially salient. Before starting, subjectswere told how long they would view each string or allstrings.

Test. The test phase immediately followed the ac-quisition phase in experimental conditions and immedi-ately followed the introductory instructions in the con-trol condition. Given a paper-and-pencil test, subjectsjudged the grammatically of 100 strings, reporting ineach instance the rule by which they judged the string tobe grammatical or nongrammatical. The 50 unique teststrings, consisting of 25 grammatical and 25 nongram-matical items, were repeated once.

Control subjects were given the preliminary informa-tion that, "another group of subjects saw items made upof the letters M, R, T, V, and X. We can't tell you whatthey were, but the items ran from three to six letters inlength." All subjects were then instructed as follows(with the variant for controls in parentheses):

The order of letters in each item of the set you (they)saw was determined by a rather complex set of rules.The rules allow only certain letters to follow otherletters. Half of the strings of letters on your answer

, sheets are well-formed according to the rules that gen-erated the letter strings you (they) studied, and half ofthe strings violate those rules. When you look at youranswer sheets, for each item (1) Look at the item anddecide whether it is well-formed or violates the rules.(2) If you think the item is well-formed, underline thatpart of the item that makes it right. (3) If you think theitem violates the rules, cross out that part of the itemyou think violates the rules.

For emphasis and understanding, those three pointswere repeated twice, in sequence and in close para-phrase; subjects were reminded to "be as careful as possi-ble in marking each item."


In response to this instruction, subjects reported boththeir judgments of grammaticality and rules implyinggrammaticality. For example, they might view VXTTTVand underline VXT, or they might view VXRRT and crossout T. In doing so, they would report a string to be gram-matical by underlining and nongrammatical by crossingout. In doing so, too, they would report a conscious rule,a rule in which the feature marked is asserted to implythe grammatical status of the string. For any feature, inthe sense of a letter or sequence of letters, subjects re-ported a rule of the form, "Feature;' in the string impliesthat the string is grammatical" or "Feature i in the stringimplies that the string is nongrammatical." The rule is astate of prepositional awareness, with feature as the sub-ject and asserted gramrhaticality as the predicate. Be-cause they could convey a judgment of grammaticalityby the form of a mark and a feature in the rule by whatwas marked, this procedure minimizes intrusiveness ofassessments and eliminates lag between assessments. Inan effort to solicit care in responding, we also requiredsubjects to mark confidence in each trial's response on a7-point scale ranging from complete uncertainty'to com-plete certainty.

The experimenter paced the test phase by asking thesubjects to move to the next item every 30 s for the firstfive items, then every 15s thereafter. To prevent lookingback at earlier responses, possibly increasing the consist-ency of answers, subjects were instructed to slide theiranswer sheets into folders as each item was completed.

SubjectsSubjects were 65 undergraduates, participating as. a

requirement in an introductory psychology course. Thedata from an additional 7 subjects were discarded be-cause of their failure to follow instructions, either bymarking all test items grammatical or all nongrammati-cal, or by marking single items both grammatical andnongrammatical. This resulted in two groups with 13subjects, the explicit - all and explicit - sequential condi-tions; two groups with 12 subjects, the implicit-all andimplicit-sequential conditions; and a control groupwith 15 subjects.

Results and DiscussionJudgments and Conditions

A preliminary check for string-type bias orresponse bias showed that proportions cor-rect were closely equivalent when judginggrammatical and nongrammatical strings(M= .635 and .630, N= 65) and also whenjudging strings to be grammatical and non-grammatical (M= .632 and .632, N = 65).Subjects judged the strings grammatical on.503 trials and nongrammatical on .497trials. We therefore compared subjects withrespect to proportion correct as the depen-dent variable.

Did subjects learn in the sense that theirgrammatical judgments benefited from in-specting grammatical strings? In all four ex-

perimental groups, the mean proportion cor-rect exceeded the control subjects' mean of.555; M = .644, t(26) - 2.74, p = .011, forthe explicit-all group; Af=.645, ?(26) =3.38, p = .002, for the explicit-sequentialgroup; M= .695, f(25) = 5.95, p< .001, forthe implicit-all group; and Af=.630,f(25) = 2.85, p = .009, for the implicit-sequential group. Evidently, a substantialnumber of individual subjects learned; 46%of the experimental subjects exceeded all but1 control subject. Although Reber and Allen(1978) reported .81 and .80 correct judg-ments using "ten specially selected advancedundergraduates and graduate students" (p.194), our range of .63 to .70 mean correctjudgments closely replicates the .62 and .66correct in Reber et al. (1980, Experiment I,Random Display, and Experiment II, Im-plicit Instructions). This is the precedingwork with the most comparable proceduresand subjects: observation learning and stu-dents from an introductory psychologycourse.

It is important for a test of learning to com-pare experimental subjects with controlsbecause the mean proportion correct forcontrols, .555, significantly exceeded the ex-pected value of .5, t( 14) = 4.03, p= .001.There was no evidence, however, that controlsubjects learned within the test series. Themean proportions correct were .561 at thefirst presentation of the strings and .549 at thesecond, t(l4) = .55.

Implicitly instructed subjects did not learnmore than did explicitly instructed subjects.The mean values for accuracy of judgmentwere .653 and .645, respectively, F(l, 46) =0.818, MSe = 0.005. Reber (1976) foundthat implicit instructions were more effectivethan explicit instructions when subjects weretested after learning strings to a criterion. Ourresults, however, replicate those of Millward(1980) and Reber et al. (1980, Experiments Iand II), where learning procedures were morecomparable to ours. Neither type of presenta-'tion nor its interaction with instructions pro-duced a significant effect (M = .668 and.638, for the all and sequential groups, re-spectively), F( 1,46) = 2.33 and 2.65, p = . 13and.11.

Was there an error consistency effect, suchthat only the explicitly instructed showed aninflated consistency of error? For the two


presentations of each string, the mean pro-portions of judgments that were cor-rect-correct, error-error, error-correct,correct-error, and the average of the twomixed cases are displayed in Table 2. Ac-cording to Reber et al. (1980):If subjects' knowledge of the grammatical structure isveridical but incomplete, . . . these three values [EE,EC, and CE] should all be the same. On the other hand, ifsubjects are systematically using nonrepresentative rulesto make their decisions, an inflated value of EE willemerge, (p. 496)

On their view, syntactic judgments are im-perfectly accurate for either of two reasons:implicit learning has yielded a structure ofrules, veridical but incomplete or explicitlearning has yielded a set of rules, some repre-sentative but some nonrepresentative. Thus,only explicitly instructed subjects shouldshow an inflated consistency of error. Takingproportions of designated error pairs as thedependent variable, an analysis of variance(ANOVA) examined the effects of type of in-struction, conditions of presentation, andtypes of error pair (error-error vs. average ofmixed cases). The mean proportion of error-error pairs was .20, reliably greater than theaverage proportion of the mixed cases at. 15,F(\, 46) =16.27, p<.00l, MSe = 0.004.The explicitly instructed groups were notalone, however, in their inflated consistencyof error, as shown by the lack of a Type ofError Pair X Type of Instruction interaction,F(l, 46) = 0.549.'All other effects were alsononsignificant (ps > .140).

Reber (1976) did find an inflated error-error rate with explicit instructions but notwith implicit instructions. The two parts ofthe effect appear to come and go with condi-tions, however. Explicitly instructed subjectshave sometimes shown an inflated error -error rate (Reber et al., 1980, Experiment I,Random Display, and Experiment II), butsometimes they have not (Reber et al., 1980,Experiment I, Structured Display). Implic-itly instructed subjects have sometimesshown no inflated consistency of error(Reber, 1967; Reber & Allen, 1978, Observa-tion Learning), but sometimes they have(Allen & Reber, 1980, Paired-AssociateLearning; Reber & Allen, 1978; Reber et al.,1980, Experiment II). Nevertheless, weclosely replicate the findings in previouswork with task and subjects most like ours:

Table 2Consistency of Judgments on Pairs ofOccurrence of Strings

Instructions

Explicit Implicit

Judgment

Correct-correctError-errorError-correctCorrect-errorAverage mixed

.490

.205

.134

.171

.153

.512

.217

.125

.146

.136

.563

.160

.133

.144

.139

.467

.212

.138

.183

.161

Note. A = all, S = sequential; both refer to conditions ofpresentation of the strings.

Reber et al. (1980, Experiment I, RandomDisplay, and Experiment II, Implicit Instruc-tions). With explicit instructions, their valuesfor proportions of consistent and mixederrors were .25 and .14, and ours were .211and .143; both cases were reliably different.With implicit instructions, their correspond-ing values were .19 and .15, not reliably dif-ferent by a low-power /2(1) but virtuallyidentical to our reliably different values of.186 and.149.

Although the effect, when found, mightsuggest interesting patterns of rules related toinstructions, we would emphasize that thepresence or absence of the effect is nondiag-nostic for the basic question we raise: Are thecontrolling rules—whatever error patternthey generate—conscious or unconscious?

Rules and Judgments

Each of the subjects' reports is a rule in thesense that (a) it names a feature that couldappear in a set of strings and (b) it predicates agrammatical status of the string containingthat feature. In order to see how well con-scious rules may explain these grammaticaljudgments, we need a metric for the variety ofessentially qualitative rules that subjects re-port. A very general scale is provided by theP(Event is in the correct category|Feature i isin the event). In the categorization literature,we know this scale more concretely as thevalidity of a feature: for example, the validityof wings or feathers for predicting member-ship in the category birds. It is also the scaleon which subjects of propositional rules are


.90 .

.80 .

.70 .

.60 .

.50 .

.40

R = .83SLOPE • .99INTERCEPT = .01

.40 .50 .BO .70

MERN RULE VRLIDITT

I.80 .SO 1.00

Figure 2. Scatter plot of the proportion correct and the mean validity of rules computed over trials withineach subject.

arrayed in the theory of propositional controldescribed earlier by Dulany (1968).

In the present task, the correct category is(a) the set of grammatical strings when a ruleasserts that a feature makes the string gram-matical or (b) the set of nongrammaticalstrings when a rule asserts that a featuremakes the string nongrammatical. In thistask, too, a feature is a letter or sequence ofletters that subjects underline or cross out inreporting a rule.

In this way, a validity metric for our rules isgiven by the following two expressions:

1. When the subject reports a rule assert-ing that "Feature i implies that String; isgrammatical (G),"

Validity =

Validity =

2. When the subject reports a rule assert-ing that "Feature i implies that String j isnongrammatical (NG),"

Validity = P(Sj

Validitymauy

Simply put, the validity of any rule is theprobability that it correctly categorizes a

string, given the presence of the feature it rep-resents. If a subject acted on and validly re-ported a conscious rule .on all 100 trials, theproportion of correct judgments shouldclosely approximate the mean validity ofthose 100 rules. This relation should be re-duced only by a small degree of "sampling"error, the degree to which the trials on whichfeatures are reported are a biased selection ofthe trials on which they occur.

How strong was that relation? For subjectsin the experimental groups, displayed in Fig-ure 2 is the scatter plot of the proportion ofcorrect judgments and mean validity of rules,showing r = .83, with a slope of .99 and anintercept of .01. Rules asserting grammatical-ity and rules asserting nongrammaticalitywere closely equivalent in their mean validi-ties (.665 and .649, respectively). The valueof r is .87 for all 65 experimental and controlsubjects taken together.

Do rules predict grammatical judgmentswithout significant residual? For each subjectwe computed the signed difference betweenthe mean validity of rules and the proportionof correct judgments. It is shown in Figure 3that this signed error of prediction scattersaround zero, with 49 of 50 subjects within the.05 sampling limits of a hypothetical zero bythe binomial test. If grammatical judgmentsare controlled independently of those rules,


12

10 .

8 .

6 .

4 .

2 .

SIBNEO DIFFERENCE SCORE

Figure 3. Distribution over subjects of signed error of prediction: difference between the proportioncorrect and the mean validity of rules within each subject.

the proportion correct should significantlyexceed the value that their mean validitiespredict. This was true of only 1 of 50 subjects.Because this is a 1-subject finding unrepli-cated in 49 opportunities, it is most plausiblyexplained by statistical or procedural devia-tion.

If control by conscious rules is a processwith generality, we should also expect theerror of prediction to be relatively stable overconditions. Within an ANOVA, absolute dif-ference between the proportion of correctjudgments and the mean rule validity did notvary with instructions, type of presentation,or their interaction, F(l, 46)= 1.29, 0.40,and 0.47; MS; = 0.0008. The overall grandmean for error of prediction was .029.

Rules and Conditions

Did subjects acquire correlated grammars?Consider the set of rules each subject re-ported to be a grammar in the general sense ofa set of rules that will classify a set of stringsinto grammatical and nongrammatical sub-sets. The mean validity of those rules is sim-ply the proportion of trials on which thatgrammar and the finite-state grammar makethe same classification, both grammatical orboth nongrammatical, which is to say the dergree to which that set of rules is a correlated

grammar. If those grammars reflected learn-ing, their mean validities should be greaterfor experimental subjects than for controlsubjects. The mean rule validity, over sub-jects' means over trials, was j648 for experi-mental subjects, reliably greater than .564 forcontrols, t(63) = 4.86, p < .001. To a signifi-cant degree, subjects did acquire correlatedgrammars from inspecting grammaticalstrings. Moreover, with rule validities as withproportion correct, neither type of instruc-tion, conditions of presentation, nor their in-teraction was a significant factor in thatlearning, Fs(l, 46) = 0.620, 0.020, and 2.65;all ps>.l 1, MSe = 0.004.

Not only were most rules imperfectlyvalid, but each was also limited in scope. Re-member that the denominator of the validityindex is the number of strings that containthe feature named in the rule, It is the num-ber of strings for which that rule could beused. Over all experimental-group subjects,that mean scope of rules was 4.17 out of 100strings, significantly below the; mean scope of4.7 for control subjects, r(63) = 2.73, p =.008. Through learning, subjects acquired alarger set of rules, each with more limitedscope, than were available to control subjectsby guessing.

As a further profile of these rules, the meannumber of letters as a function of the number


6 .

S .

4 .

2 .

1 .

NHOLE STRING•—"CONTROL, -6'«—» CONTROL. *N&'•—•EXPEfUMENTRL, '6»—'EXPERIMENTRL.

4 S

STRING LENGTH

Figure 4. Mean number of features mentioned in rule statements, for G (grammatical) and NG (nongram-matical) judgments, for the experimental and control groups. (Whole string length is plotted for compari-son.)

of letters in the string is plotted in Figure 4.Although on a general conception of a rule, asubject may report all features, yielding a rulewith scope of one (two with repetitions)—and on 20% of trials subjects did—it is clearthat mean rule size was substantially less thanstring length (see Figure 4). It is also shown inFigure 4 that rule length did increase withstring length, F(3, 192) = 153.04, p < .001,MSt = 0.166, and was greater with grammat-ical than with nongrammatical judgments,F(l, 64) =173.20, /><.001, MS.-1.66.On these dimensions, experimental and con-trol subjects were indistinguishable, showingsome commonality in the effects of guessingand making use of prior learning. Learning,as we have shown, was reflected in the keydifference to be expected: greater validity ofthe rules that experimental subjects reported.

AbstractionDoes the observed learning reveal itself in

an ability to classify novel strings correctly?Or do subjects merely recognize old stringswhen encountered a'gain at test, and suffi-ciently so to explain the overall effect? On the5 old strings alone (10 with repetition), exper-imental subjects were substantially superiorto control subjects, M correct = .73 and .543,

2.91, p < .005. Excluding these old

strings, we reanalyzed over the remaining 40novel grammatical and 50 novel nongram-matical strings. The mean proportions ofcorrect judgments computed over novelstrings were comparable to those computedover all strings. Values for the experimentalgroups differed reliably from the value of.566 for control subjects in three of four com-parisons, M= .634, t(26) - 2.97, p = .006,for the explicit-all group; M= .641,t(26) = 2.61, £ = .015, for the explicit-sequential group; M-.697, f(25) = 5.75,£<.001, for the implicit-all group; butM=.612, *(25)=1.64, £ = .13, for theimplicit-sequential group. Abstraction was ,a little more common when strings had beenpresented all at a time rather than sequen-tially, M = .666 and .627, F(l, 46) - 4.50,p-= .039, although neither type of instruc-tion nor its interaction with condition of pre-sentation was a significant factor (M = .655and .638, for the implicit and explicit groups,respectively), F(l, 46) = 0.645 and 3.485,MSt

= 0.005. In this most conventional typeof test, subjects' judgments revealed a signifi-cant degree of syntactical abstraction.

We have already shown that rules couldhave a part in explaining that kind of abstrac-tion. They predict correct judgments onnovel as well as on old strings. But do those


rules themselves embody abstractions? Whatwe have asked about the classification ofnovel strings can also be asked about the as-serted classification by rules naming novelfeatures. Does correctness benefit from in-specting grammatical strings at acquisition?The conventional test for abstraction at thelevel of strings is simply extended analo-gously to the level of rules.

Among the 20 novel grammatical strings,13 contained novel features in the sense of apositionally indexed letter or sequence of let-ters that did not occur in strings at acquisi-tion. Those 27 novel features, consisting of13 whole strings and 14 parts of those strings,appear in Table 3. Within each of 25 non-grammatical strings, the appropriate novelfeature is the grammatical violation intro-duced by Reber and Allen (1978), which assuch cannot have appeared in the exclusivelygrammatical acquisition strings. Both setsare previously unencountered features thatcould be used to guide a correct grammaticaljudgment. We therefore examined /"(correctassertion] novel feature in rule) over those 76strings [(25 NG + 13 G) X 2], where NG =nongrammatical and G = grammatical. Weconsidered a novel feature to be in the rule ifexactly that feature and nothing else wasmarked. In all experimental groups, themean value of this conditional probabilityreliably exceeded the mean value of .501 forcontrol subjects; M= .674, t(26) = 2.52,p=.008, for the explicit-all group; M —.692, t(26) = 3.26, p = .003, for the explicit-sequential group; M=.740, ?(25) = 4.07,/?<.001, for the implicit-all group; andM=.652, ?(25) = 2.10, £ = .046, for theimplicit-sequential group. The last group isthe same one that failed to show abstractionat the level of judgments on novel strings.Although this appears to be the most appro-priate index of rule abstraction, note that allexperimental-group subjects exceeded con-trol subjects in /"(Correct assertion and novelfeature in rule), M = .289 and .185, t(63) =3.08, p = .003. Furthermore, experimentaland control subjects were essentially alike inboth /'(Correct assertion | old feature in rule)and /"(Correct assertion\and old feature inrule), Af=.603 and .576, .350 and .368;/(63), ns. As a consequence of learning, rulescould guide judgments more correctly justbecause they represent novel features and

Table 3Novel Features: Features in Novel GrammaticalStrings and Not in Acquisition Strings

Whole strings Parts of strings

1. MTTTVT2. MTTTV3. MTTVRX4. MTVRXR5. MTVT6. MVT7. MVRXM8. MVRXRM9. VXRM

10. VXRRRM11. VXTTTV12. VXVRXR13. MTVRXV

1. MTTTV_TTTVf"

3. MTTVRTTVRX

4. JTVRXR8. VRXRM9. ~XRM

10. ~XRRRMRRRM

11. VXTTT_XTTTV_XTTT

12. _XVRX~R13. TVRXV

Note. Among the 20 novel grammatical strings, 13 con-tained novel features in the sense of a positionally indexedletter or sequence of letters that did not occur in stringsat acquisition.

prescribe judgments more correctly. In thisway, abstraction embodied in rules couldprovide a natural account of abstraction em-bodied in judgments.

Features and Grammars

As a check on our construal of the reportedfeatures, we ran a set of supplementary analy-ses. When subjects marked a feature, theymarked a letter or a sequence of letters in anexact position, counted from the front andback of the string. Is this what they meant ordid they mean something less restrictive? Aletter or a sequence counted; only from thefront? Or could they simply have meant thatletter or sequence of letters in any position?Whether we can construe features as reportedor whether we must assume something lessrestrictive would make for somewhat differ-ent validity computations, because the de-nominator of the validity fraction is some-what different for each conception. Noweach of these three conceptions of a featureentails a conception of grammar describingthe set of each subject's reported rules. Tocheck our construal of a feature, we exam-ined the comparative fit of these grammars tothe rules subjects reported. As shown inTable 4, the grammar designated G3, con-struing features as subjects reported them,consistently provided the best fit by two pairs


Table 4Indexes of Prediction and Acquisition for ThreeGrammars (Gt, GI, G3) Based on ThreeConstruals of a Feature

Index G3* > G,1

Prediction of P correctfrom M rulevalidity

Correlation1 - |Pred. - Obs.|

Relation of rulevalidity toexperimentalgroup vs. controlgroup

M differenceStudent's t

.866

.971

.0844.83

.816

.965

.0794.44

.571

.905

.0303.02

Note. P correct = proportion correct. Pred. = predictedjudgment. Obs. = observed judgment.* A feature is a letter or sequence of letters (a) irrespectiveof position in string, on G,; (b) in a given position countedfrom first letter, on G2; or (c) in a given position countedfrom first and last letter, on G3.

of indexes: (a) That grammar (G3) is the bestpredictor of grammatical judgments. This istrue for the correlation of the mean validityof the rules with the proportion of correctjudgments and also for the mean of 1 —absolute error of prediction, (b) On thatgrammar, too, rules respond most strongly toacquisition. This holds for the mean differ-ence between experimental and controlgroups in the validity of rules and for Stu-dent's t of that difference (properly a measureof relation). Because G3 was the grammar onwhich validities were computed for data inFigures 2 and 3, these findings support the.basic analyses.

Confidence and Conditions

Although assessment of confidence wasdesigned to enlist care in responding, its non-specific form allowed subjects to report con-fidence in judgments or in rules or in both,and they might have done so variously. Wenote incidentally, however, that experimen-tal subjects were more confident of their re-sponses than were control subjects, M = 6.69and 5.38, f(63) - 2.87, p = .006. Further-more, neither type of instruction, conditionof presentation, nor their interaction affectedconfidence, Fs(l, 46) = 0.013, 1.187, and

0.069, respectively, MSe = 2.309. Evidently,learning was manifested in greater confi-dence in responding, and the lack of differ-ences in confidence over groups is consistentwith the lack of differences in learning overgroups.

General Discussion

Judgments, Conscious Rules, and Grammars

On this evidence, it would seem that sub-jects' conscious rules could indeed be centralto a process explaining their grammaticaljudgments. Not only do the validities of re-ported rules strongly predict correct judg-ments, but they do so without significant re-sidual. This is our most basic finding. Itchallenges the hypothesis of implicit learningand judgment, in particular Principles b andc, on which subjects are said to be uncon-scious of their grammatical representationand unconscious of aspects of strings guidingtheir judgment. (Refer to the beginning ofthis article for Principles a-d.) The findingseems strong. It is multiply replicated overindividuals. We have provided the suggestedconditions (the complex task and implicit in-structions), which should, based on Principled, evoke the implicit process. Furthermore,other aspects of these results closely replicatefindings in the literature.

To the degree subjects learned, they couldbe said to have acquired correlated gram-mars. For each subject, the grammar can besimply characterized as the union of twosets of rules defined on features, strings,and grammatical classifications, (Ft G Sj) —»(Sj G G) or (F| £ Sj) -»(Sj G NG), where afeature, F, refers to a positionally indexed let-ter or sequence of letters. It is a personalgrammar; every subject may have, and doeshave, a different set of rules. It is a correlatedgrammar to the degree that the subject's rulesand the finite-state grammar make the samegrammatical classifications. Moreover, weknow the grammars reflected learning, atleast to a degree, because the validities ofthose rules benefited when subjects had in-spected grammatical strings.

But could these sets of rules be more rea-sonably characterized as parts of the finite-state grammar rather than as separate andcorrelated grammars? We think not, at least


not in the relevant sense of that part of afinite-state grammar that generates judg-ments. A finite-state grammar consists of aset of nonterminal symbols (the states in Fig-ure 1), a set of terminal symbols (the letterslabeling the arcs in that figure), and a set ofproductions for the letter-writing transitionsamong those states. With the grammar real-ized as a finite automaton, it classifies a stringas grammatical if it can generate that string,and it classifies a string as nongrammatical ifit cannot (Chomsky, 1963; Hunt, 1975).When we construed features in rules as lettersor as letter sequences, we described consciousstates representing terminal symbols but notnonterminal symbols. Furthermore, rulesdeclaring nongrammaticality as well as gram-maticality are integral to the grammar; theyare alike in form and in predictiveness. Hav-ing said as much, we acknowledge that wehave brazenly Characterized as "grammars"what might not seem to be proper grammarsat all. To us, however, the more interestingpoint is this: Sets of rules that are intuitivelybut unconventionally grammars predictedwithout significant residual to the conven-tional index of grammatical abstraction—classification of novel strings. And those rulesappeared in consciousness. They consciouslyrepresent novel arrangements of terminalsymbols, thereby gaining functions analo-gous to the nonterminal symbols in conven-tional grammars: a key role in'generatingnovel judgments. Simply put, some judg-ments may go beyond the information givenbecause consciousness goes beyond the in-formation given.

Abstraction

How abstract are the rules subjects report?In one sense, not very. On the average, eachrule had dominion over only four strings, thenumber containing the feature on which thatrule could prescribe a classification. With aminimal scope of one (two with repetitions),the rule completely described a single stringand became equivalent to the very concreteexemplar representation in Brooks (1978) asa special case. Learning, in fact, moved rulestoward greater concreteness in this sense; therules that control subjects reported hadgreater scope than those of experimental sub-jects.

In another sense, however, these rules em-body abstractions that could have a signifi-cant place in explaining the key and conven-tional index of grammatical abstraction,success in classifying novel strings. By anindex analogous to the conventional index,subjects used novel features in rules to implycorrect classification of novel strings—andsignificantly so in reflection of their experi-ence with grammatical strings during acqui-sition. Within our data, this appears to hap-pen in two ways, both evidently asabstractions from what is remembered andobserved to what is reported. One way couldbe called combinatorial abstraction. Whencorrectly classifying novel grammaticalstrings, the novel feature implying grammati-cality is in fact a combination of old featuresalready seen in two or more grammaticalstrings at acquisition. (This simply followsfrom our definition of a novel feature: If anyletter or sequence of letters within a novelfeature had not appeared during acquisition,our algorithm would have identified that let-ter or sequence as still another novel feature.)Following observations of features in sepa-rate grammatical strings, observations oftheir joint occurrence may suggest that thestring is grammatical. Another way could becalled substitutive abstraction. When cor-rectly classifying novel nongrammaticalstrings, the novel features substituted for oldfeatures that would have left the string gram-matical. Following observation of one fea-ture in a grammatical string, observation ofits replacement may suggest that the teststring is, nongrammatical. Of course, too,subjects exhibited .selective abstraction—anolder sense of abstraction (Lashley, 1929)—when they used old features to classify oldstrings as grammatical.

When abstraction yielded rules for noveljudgments, the process evidently operated oninformation from both the earlier acquisitionstrings and the current test strings, a possibil-ity that contrasts interestingly with the viewthat grammars must be completely formedby prior learning alone. In this study, how-ever, we directly examined only what reflectsabstraction and predicts judgments, not theearlier abstractive process itself. A fuller ex-planation would, of course, call for a detaileddescription of the processes that yield thoseconscious rules embodying abstraction.


Conscious or Unconscious Control

For this experiment, the one clear predic-tion of a theory of unconscious control—more correct judgments than predicted byconscious rules—was clearly discontinued.But are there suitable auxiliary assumptionsthat would enable a theory of unconsciouscontrol to predict these results? Subjectscould entertain rules and act on them—oract and entertain rules, either independentlyof, or in justification of, that action. Our pro-cedures are not so constraining that subjectscould behave in only one way, and the datashould in some degree reflect selectively onthose possibilities.

We should first recognize that these datawould not be explained by mechanisms ofunconscious control of judgments and inde-pendent guessing of rules. Notice in Table 1that every string of one grammatical classcontains letters and sequences of letters ap-pearing in strings of the other grammaticalclass. On any subset of trials, random guess-ing should select many features appearing inboth grammatical classes. When grammati-cal judgments are incorrect, the rules wouldhave a mean validity greater than zero andwould overpredict correct judgments. Whengrammatical judgments are correct, the ruleswould have a mean validity less than one andwould underpredict correct judgments. Itfollows, therefore, that as the proportion ofcorrect judgments increases beyond .5, ran-dom guessing would produce rules withmean validities that progressively underpre-dict. We know from Figure 2, however, thatthe proportion correct was related to themean validity of rules by essentially unitslope (.99).1

Is there some more systematic way thatrules might come to track judgments withoutcontrolling them? In fact, two possibilitiescome fairly readily to mind. On both possi-bilities, subjects unconsciously abstractedvarying portions of the finite-state grammar,or some other abstract but correlated gram-mar, and then carried over its unconsciousrepresentation and judged grammaticalitywhile still unaware of anything in the stringsguiding their judgments. On one possibility,the reported rules are learned in parallel withthe unconscious grammar and then are re-called as cued by the string at hand. On the

other possibility, each rule emerges only afterits accompanying judgment, as a consciousreconstruction of some aspect of the uncon-scious grammar. In either case, the consciousrules are said to be merely noncontrollingjustifications of an unconsciously controlledjudgment.2 We see two kinds of problems,however, with this pair of accounts:

1, For neither account do we find linkingassumptions, which is to say a description ofa process that would strongly relate assumedamounts of unconscious grammatical learn-ing to the observed mean validities of reports.Consider the first account: On what addi-tional assumptions would subjects who learnjust enough of the unconscious grammar tocontrol P correct judgments, also learn justthe set of conscious rules whose validitiespredict P correct judgments without signifi-cant residual? The problem for the secondaccount is analogous: On what additional as-sumptions would subjects who learn justenough of that grammar to control P correctjudgments find themselves able to use thatgrammar—which is, after all, said to beunconscious—to reconstruct just the set ofconscious rules with validities that predictP correct judgments without significant re-sidual?

2. At this stage of inquiry, too, the hypoth-eses of conscious and unconscious control

1 On A. S. Reber's (personal communication, Febru-ary 25,1984) convincing us that we should further exam-ine the question, we simulated rule guessing on the com-puter with a program that randomly selected a featuralrule for each judgment of each subject, simulating our 50experimental subjects 100 times. The mean rule valid-ity over 100 simulations did progressively underpredictas the proportion correct increased (slope =1.65,intercept = —.38). Furthermore, all 100 simulations ofthe 50 subjects showed both progressive and overall un-derprediction of correct judgments from the mean valid-ity of guessed rules. Our experimental subjects had abest-fitting function and an essentially zero (.004) meanerror of prediction that stood clearly apart from the gen-erated sampling spaces for guessing. A full description ofthe simulations will be submitted for publication.

2 In interesting ways this question parallels an earlierquestion about learning without awareness (Dulany,1968; Brewer, 1974). These are the same "parallelist"and "emergentist" assumptions that behaviorists used todefend the theory of unconscious reinforcement fromexperimental challenge. Furthermore, forming corre-lated grammars parallels forming correlated hypotheses,an alternative to the process of learning by the automaticaction of reinforcement.


have different statuses on an important con-sideration: the identification of postulatedprocesses. For one kind of explanation, thecontrolling states are conscious and assessed.For the other, one postulates an unconsciousand unassessed process that convenientlydoes all the work. The two problems are ob-viously connected: Without some constrain-ing identification of the processes, the uncon-scious grammar can be asserted to takewhatever values are needed, namely, to bepresent in each subject in just that degree co-ordinate with the correctness of judgmentsand the validities of rules. Every parameter isfreely adjustable after the fact.

The difficulty for the augmented formula-tion is that it does not in fact predict theseresults—and could not, we think, in the ab-sence of independent indexes of an uncon-scious grammar and still further process as-sumptions that would link that grammar tothe validities of reported rules. It is also achallenge, Of course, that may eventually bemet in further work, perhaps aided by for-mulating the problem in this way. In view of •this difficulty, however, we think the moretenable account of these data would simplysay that reported rules predicted grammaticaljudgments because subjects were consciousof rules controlling their judgments. Further-more, the explanation gains utility in cover-ing rules that may generate novelty by repre-senting novelty in consciousness.

Possible ExtensionsWe confronted the question of implicit

learning where it was raised, focusing on afinite-state grammar that lacked a semanticinterpretation. Generalization to natural lan-guage is obviously limited because naturallanguage embodies a semantic componentand a higher order grammar with hierarchi-cal structures. The results may not, however,be irrelevant tp learning and judgment withnatural language material. Although seman-tic interpretation may aid the learning of anartificial grammar (Moeser & Bregman,1972; Morgan & Newport, 1981), Morganand Newport (1981) found that it was notessential to learning and that semantic repre-sentation of dependencies was of no addi-tional benefit. Furthermore, English submitsto a finite-state description within hierarchi-cally organized constituents. Our results at

least raise an interesting and researchablequestion: What, if any, may be the role ofcorrelated grammars, with conscious rules oflimited scope, when learning a semanticallyinterpreted and hierarchically organized arti-ficial language—and by further extension, anatural language? Much the same could besaid and asked of structured domains of playand social ritual.

The generality of these results also seems tobe challenged by very strong intuitions'fromwithin structured domains of the real world.We often intuitively judge the grammatical-ity of a sentence or the legality of a move orthe propriety of an act without conscious ac-cess to the formal syntax of the domain. Butlet us turn the tables somewhat. It is an inter-esting possibility that each of those intuitionsis one of a set of informal rules of limitedscope and perhaps imperfect validity. The in-tuitions seem quite conscious. We knowsomething that seems right or wrong, evenwhen we don't think of or know the properrule from a formal system. With intuitionreclaimed for consciousness, we would notdisagree with Allen and Reber (1980, p. 178)that "decisions about the well-formedness oftest strings are made largely on an intuitivebasis."

Because the average amounts of learningin this study and in earlier studies were rela-tively small, we should also ask how well thisparadigm models syntactical learning andjudgment at large. Even as individualsachieved up to 83% correct judgments, how-ever, our results were the same: no significanterror of prediction from conscious rules. Fur-thermore, the syntaxes of games, rituals, andsecond languages are often imperfectly mas-tered, and all late learning is preceded byearly learning, with consequences interestingin their own right. What happens with au-tomatization in very advanced stages oflearning does indeed raise new questions, butthey are questions with significant ties to thequestions examined here. On one very com-mon view, rules that were once consciousmay continue to control but at an uncon-scious level. Consequently, if entirely auto-matic judgments do occur, we can askwhether they express the internalized syntaxformalists have in mind or the automatizedresidue of informal rules the learner once hadvery consciously in mind. If the common


View is correct, these findings would suggestthat unconsciously controlling rules may bemore informal than has commonly beenthought. But is this what really happens or iscontrol passed to still other informal andconscious rules, perhaps at some higher levelof syntactic or conceptual organization? Anumber of interesting questions are only sug-gested but not answered by the present exper-iment.

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Received October 18, 1983Revision received May 21, 1984 •

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