123

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Pn-

nlcd irom J°VHNAI- OF Mathematical PsychologyAll RlghtB Reserved by Academic

Press,

New York and London Vol. 5, No.

1,

February 1968Printed in Belgium

5 Explorations with a Discrimination Net Modelfor Paired-Associate Learning 1

Douglas L. Hintzman2

Stanford University,

Stanford,

California 94305

A computer simulation model for paired-associate learning is presented Themodel emphasizes stimulus discnmination learning, and is based on an EPAM-typediscrimination net which grows according to stochastic processes. Group data liresimulated for comparison with human data. Three versions of the model are presentedThe simplest, SAL 1, was farst run in several single-list experiments and evaluated onsuch top.es as: intralist similarity, numberofresponse alternatives,probability learningSAL U, a slightly modified version of the model which allows overlearning was .v„in retroactive interference experiments varying interlist similarity and d_gr s oforiginal and interpolated learning, and is discussed m relation to studies oTpredifferentiation and transfer. Finally, SAL 111, which stores multiple associate wasrun in experiments on recognition vs recall, second and third guesses, v "and modified free recall, retroactive vs proactive

interference,

distributed practiceand response latencies. t__-u_e,

Gibson (J 940), ma now classic paper applying conditioning principles to verballearning emphasized the differentiation among stimuli as an important sub-processin paired-associate (PA) learning. Although this theory provided a long-actingstimulus for research in verbal learning, recent appraisals (Noble, 1961; Underwood1961) have noted that the theory has declined in its usefulness and become somewhatbarren of relevant implications regarding modern problems. Thus modern workersin verbal learning have concentrated increasingly on analysis of response integrationavailability, associative learning, pre-experimental habits, mediation, etc as thesefactors operate in PA learning. And increasingly, stimulus discrimination learninghas come to be relegated to a smaller role.

f _ pu rTT on°n a dlssertation submitted in partial fulfillment of the requirementsof he Ph.D degree at Stanford University. The work was done while the author was a Graduatefellow of the National Science Foundation, and was supported in part by grant HD-00954rT.

_.

. rf". °f C.

Ud HCalth and Human Devel°P—t to Dr. Gordon Bower, NSF grantGB-2791 to Dr. James

Greeno,

and grants to the author from the Stanford Computation CenterIhe author is especially grateful to Dr. Bower for his encouragement and for his assistance inpreparing the manuscript. n2 Now at the University of Texas.

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Without denying the potency of these additional factors in PA learning, the thesisof this paper is that stimulus discrimination concepts may have been bypassed beforetheir explanatory power has been fully explored. This paper reports a simple modelof stimulus discrimination in PA learning which accurately simulates results from adiversity of experiments. These simulated results include several beyond the originalscope of Gibson's theory, as well as some which have been cited as evidence againsther theory. Inaddition, the model proposed here is written as an elementary computerprogram, so that theoretical predictions for learning experiments can be "derived"(by simulated runs) in an unambiguous manner. It is not claimed that PA learningis "nothing but" stimulus discrimination learning, since that is patently false. Theapproach taken here is to explore the range of experimental results which can beexplained by this process acting alone, eliminating in the model those factors relatedto response learning, response generalization, mediation, and so forth. Furtherprocesses are added only when necessary to expand the generality of the theory.

The model, dubbed SAL (for Stimulus and Association Learner), is based on some

simple assumptions about the processes underlying the acquisition, storage, andretrieval of paired associates. The basic memory construct of the model is thediscrimination net, which will be described in detail below. In addition to exploringthe general usefulness of discrimination learning concepts for verbal learning theory,thepresentworkcan be considereda further test of the usefulness of the discriminationnet as a specific model of theprocesses responsible for discrimination learning.

The SAL model is closely related to the EPAM theory of verbal learning developedby Feigenbaum and Simon, which is also based on the discriminationnet. EPAM hasgone through several stages of development and has been applied with considerablesuccess to increasingly complex phenomena in both serial and PA learning(Feigenbaum, 1959, 1963, 1965; Feigenbaum and Simon, 1961, 1962, 1963a, 1963b;Simon and Feigenbaum, 1964). The discrimination net, the central memory constructof bothEPAM and

SAL,

is a system of tests or choice points and branches throughwhich a stimulus item is sorted in order to retrieve the correct response. The learningof a PA list involves the elaboration of the net until it is capable of correctly sorting(discriminating among) all the items of the list.

Despite the common assumption of the discriminationnet, SAL differs from EPAMin several respects. First, learning in SAL is a stochastic process, while in EPAM it is

deterministic. If an investigator gives EPAM a list to learn, erases the memory andthen presents the same list again, he will obtain two identical (or nearly identical)protocols. Thus, if one wants to know the predicted shape of a precriterion learningcurve, for example, he must run EPAM on a number of different lists, use differentpresentation rates, or use some other laborious method to obtain "group" data. TheSAL model, in contrast, is governed by stochastic processes, and can generate anynumber of unique protocols for the learning of a given list. The resulting data canthen be submitted to the same types of analysisas data from groups of human subjects,

and direct comparisons can be made. It should be mentioned here that stochasticprocesses are used in SAL only to facilitate the derivation of predictions. They areintended as statements of ignorance, rather than assertions that learning is basicallyprobabilistic.

Second, in SAL all processes which are not necessary in order to do runningsimultations of PA learning have been eliminated. "Macroprocesses," such as thosein EPAM concerned with allocationof processing effort, have been greatly simplified.Also, SAL does not make use of "stimulus images" or of a scanfor differences betweenthe image and the presented stimulus, as does EPAM (cf. Feigenbaum, 1963). It ishoped that, since there are fewer postulated processes in SAL, it will be easier toidentify specific processes or combinations of processes with specific resultingpredictions. Thus, it should be easier to understand why the model makes a corrector incorrect prediction, and to make appropriate changeswhen needed.

Third, SAL uses the discrimination net only for stimulus discrimination learning,while EPAM uses it for both stimulus learning andresponse integration. Accordingly,the "task environment" of SAL consists only of lists of trigram-digit pairs, wheretheresponses are already well known, and only the stimuli are unfamiliar. The purposeof this restriction is simple. It is felt that if stimulus discrimination learning is to beunderstood, it should be isolated from possible confounding processes, such as thoseconcerned with response integration, and so on. Despite these restrictions, SALmakes predictions that can be meaningfully applied to a wider variety of materialsin similar experimental situations. This will become evident in the experiments anddiscussions which follow.

The present paper is divided into three main sections, describing and evaluatingthree versions of the SAL model. SAL I, the simplest version, is first described indetail and applied to several single-list experimental situations. SAL 11, the over-learning model which involves a slight alteration in SAL I, is then presented alongwith some data on retroactive interference. Finally, SAL 111, the "push-down stack"model is described and datafrom severalrelevantexperimental situations arepresented.It should be noted that the three versions of SAL represent progressive steps inelaborationof the same model. The major findings concerning the behavior of SAL Iand II also hold for SAL 111.

SAL

I. THE BASIC MODEL

Sorting

When a stimulus trigram is presented, the model sorts it through the discriminationnet to retrieve a response. The discrimination net can be represented as a "sortingtree"—a hierarchy of binary choice points called test nodes, and descendingbranches.E]ach pathway through the net leads eventually from the initial test node to a terminal

126 127HINTZMAN

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explanation see text.

Learning

node at the base of the net, where a response image may be stored. At each test node,some characteristic of the stimulus is noticed and subjected to a matching test; thebranch chosen at that point depends on the outcome of the test, either positive ornegative. In SAL, test nodes are based on letter units, although this was an arbitrarydecision; phonemic, visual, or possibly semantic features of the stimuli could alsobe used. The sorting process in SAL is essentially the same as that of EPAM II(Feigenbaum, 1963).

and (b) after growing a new test node. ForFig. 1 . A SAL discrimination net (a)

Figure la represents a discrimination net consisting of three test nodes—onefirst-letter test and two second-lettertests—leading to four terminalnodes. A stimulustrigram would be sorted in this net by submitting it to a series of matching tests.Imagine, for example, the sorting of the trigram XBN. Sorting begins at the topmosttest node, which tests the first position for X. The test is positive, leading to anothertest node which tests the second position for F. The trigram fails this test, leadingto a thirdtest node which tests the second positionagain, this time for Q. The negativeoutcome of this test leads to the terminal node containing an image of the response 1,which can now be retrieved and output. The net illustrated in Fig. la would performwithout error on the list: XBN-1, RGP-2, XFM-3, XQL-4.

Discrimination learning consists of the elaboration of the discrimination net byadding new nodes and branches as they are needed. Suppose that the net of Fig. lais confronted by a new pair, LCS-5. The trigram is sortedand theresponse 2 retrieved.The information that an error has been committed triggers the growing of a new testnode and two new terminals.At this point, a theoretical question must be answered:how is the modelto decidewhich letter to incorporate into the new test node ? EPAMbases this decision on a scan for differences between the stimulus and an internalimage. In

SAL,

the answer is simply an unchanging left-right noticing order. If insorting the stimulus the first letter has not been positively identified, then the first

letter will be learned. If the stimulus has already passed a first-letter test but has notbeen identified by a second-letter test, then the second letter will be learned, andsimilarly for the third letter. Thus, since the trigram in our example did not pass afirst-letter test during sorting, the first letter of the stimulus just presented is usedin the new test node. The new (reinforced) response, 5, is stored at the positiveterminal, and the old response, 2, is stored at the negative terminal. The net can nowbe represented by the diagram in Fig. lb. It will perform without error on all fivepairs which it has learned.

Note that if instead of LCS-5 we presented RCS-5 as the fifth pair in the list,one new test node would not be sufficient. For, after constructing a new first-lettertest for R, the model would err on RGP on the next trial, responding with 5 insteadof with 2. Although the response 2 would be present in the net, it would be storedat a negative terminal, and would thereforebe inaccessible when its stimulus,

RGP,

was sorted in the net. The two stimuli beginning with R would interfere with eachother until an appropriate second-letter test was added. This example illustratesthe manner in which a discrimination net produces oscillation and retroactive inter-ference (cf. Feigenbaum, 1963).

If learning were to take place after every error, acquisition would be much too fast.In SAL, therefore, the creation of a new test node is characterizedas an all-or-noneevent which has probability a of occurring after an error. The learning parameter acanbe consideredan unspecified function ofsuch variablesas exposuretime,response-reinforcement interval, motivation, and so on; it is the major determinantof the rateof acquisition of a list.

Stating that discriminationlearning does not always occur following an error raisesan additional question. What should take place when an error is made and (withprobability 1 — a) the appropriate test node is not added to the net ? There are severalpossible alternatives: the new, reinforced response could replace the old one at theterminal node; the old response could be erased leaving an empty terminal; bothresponses could coexist at that terminal, interfering with each other; or the oldresponse could simply remain. In version I of SAL it is assumed that the reinforcedresponsereplaces the old one at the terminalnode with probability b, theold responseremaining with probability 1 — b (a slightly different process is assumed in SAL III).The value of b affects the tendency to perseverate, or to continue giving the sameincorrect response to a stimulus for several trials. However, b affects the acquisitionrate only in transfer situations. The functions of the parameters a and b in learningare summarized in Fig. 2.

In the work done with SAL to date, no attempt has been made to "fit" dataquantitatively. There are two reasons for this: first, no economical methods of param-eter estimation have been developed for SAL. Second, even if such methods wereavailable, themodelstill couldnot be applied quantitatively to therange ofexperimentsreported here, simply because SAL learns only trigram-digit pairs, while actual

(b)(a)

before

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HINTZMAN

Fig. 2. The functions of parameters a and bin SAL I.

experimental materials vary widely. For these reasons, the work reported in thispaper has centered on obtaining good qualitative agreement with human data ina wide variety of experimental tasks; the primary purpose is to demonstrate therange of phenomena consistent with the assumption of a discrimination-netbasedmemory structure.

The performance of SAL I is evaluated in the following section.

APPLICATION OF SAL I TO SINGLE-LIST SITUATIONS

In learning a PA list, SAL typically produces learning curves which are negativelyaccelerated exponential functions. However, the shape of the curve depends partlyon whether presentation order is randomized from trial to trial. If a restriction ismade that items appearingnear the end of one trial cannot appear near thebeginningofthe next, or if items are in the sameorder on every trial, SAL produces an S-shapedlearning curve, with an initial period of positive acceleration lasting two or threetrials.

Data from groups of simulated subjects show a great deal of variability inperformance, even though parameters are the same for each subject. For example,a simulated group of size 20 learned a 9-pair list of mixed stimulus similarity, withparameters a = .40 and b = .50. Total errors per subject from trial 2 until masterywas used as the measureof learning. The number of errors ranged from 3 to 35, witha meanof 15.0 and SD of 6.62. Similarly, there is considerable variabilityin acquisitionrate for different pairs in a list. Part of this variability can be attributed to actualdifferences in interference produced by intralist stimulus similarity, and part is dueto the stochastic processes involved in learning. A sample SAL protocol from the

group of 20 describedabove is presented in Table 1. Several phenomena characteristicof human subjects can be seen here, including stimulus confusions or generalization(especially between ZXK and ZHJ), perseverative errors (e.g., repetition of theresponse 8 to stimulus ZHJ), and oscillation (e.g., the alternation of correct andincorrect responses to ZXK). These phenomena are also found in EPAM protocols(Feigenbaum, 1963). There are no failures to respond because SAL I does not dealwith response latencies, and therefore assumes there is always enough time for theresponse to occur.

Generally, SAL protocols look much like human protocols, though somediscrepancies can be detected. One discrepancy is that while human subjects willoften reach a criterion of one errorless trial only to follow this with one or moreerrors, SAL I never does. One perfect trial means perfect mastery of the list, andhence perfect subsequent performance. Another discrepancy can be traced to SAL'sfixed and rigid noticing order. Human subjects have difficulty learning to discriminatepairs of trigrams such as LQF and QFL, since the same letters are used in both.

SAL,

on the other hand, would not confuse these two trigrams very frequentlybecause its letter-matching tests are all position specific.

TABLE 1

A SAMPLE SAL PROTOCOL

Trial

2 34 5 6 7 8 9 10Pair

ZHJ-6 4 4 8 8 8 18MBW-3 4

GQK-1

4

Total errors 8 3 2 12 12 0 0

Experiment 1. Intralist Stimulus Similarity

It is well known that the higher the degree of similarity among stimuli of a PAlist, the more difficult the list is to learn (e.g., Restle, 1964; Underwood, 1953a).As SAL learns discriminations by sorting on the basis of distinctive letters, the

GXJ-7 2 2 + + + + + 4- +ZXK-8 4 6 6 + 6 + 6 + +GXK-4 2 + + + + + 4- 4 1-

LQF-5

9 + + + 4- 4- + + +GXF-2 1 + + + + + + + +LXJ-9 + 4- 4- 4- + + + + +

4 -|- + + + + + + -|-

4 + + + + 4- + + +

130 discrimination net model

131

HINTZMAN

amount of overlap among stimuli should affect list difficulty (this is true of EPAM;cf. Simon and Feigenbaum, 1964). The following experiment was done to determinethe effects of intralist similarity on various measures of the model's performance.

Three 8-pair lists varying in intralist stimulus similarity were constructed, eachpairing 8 trigrams with thefirst 8 digits. The stimuli for condition Hi were generatedfrom 6 different letters, 2 alternatives for each position. There was zero redundancyin this set, perfect performance requiring letter tests for all three positions. Stimulifor condition Mcd were generated from a set of 4 possible letters at each position;those for conditionLo used 8 different lettersat each position. In the latter condition,learning is possible on the basis of first (or second or third) letter position alone.Condition Lo is of special theoretical interest because all stimuli are completelydistinctive, representing the ideal situation for comparing SAL with the one-elementmodel (Atkinson, Bower, and Crothers, 1965; Bower, 1961, 1962). Twenty subjectswere simulated in each of the three conditions; a = .40, b = .50.

TOTAI ERRORS PER SUBJECT - ITEM

Fig. 3. Distributions of total errors per subject-item sequence, Experiment 1. Inset:Bower—Levine data, from Restle, 1964.

Stimulus similarity had the expected effect on learning rate. Mean number of trialsper subject to mastery were: Lo, 4.60; Mcd, 5.50; Hi, 6.75. Further evidence of theeffect of similarity is shown in Fig. 3. Here, the total number of errors (from trial 2

until mastery) was determined for each subject-item sequence, and the relativefrequency of each count plotted. It can be seen that the entire curve flattens andshifts toward moreerrors as similarity increases. These distributions comparefavorablywith similar data from human subjects reported by Restle (1964).

We next turn to precriterion curves. The precriterion phase in the learning of asubject-item sequence is definedas those responses from trial2 up to, but not including,the last error in that sequence. All precriterion responses can be averaged togetherto obtain the precriterion proportion correct for each trial, plotted as a precriterioncurve. These curves for conditions Hi, Mcd, and Lo are presented in Fig. 4.

TRIAL NUMBER

Fig. 4. Precriterioncurves from the three similarity conditions ofExperiment 1

All three precriterion curves rise as trial number increases. Curves for conditionsHi and Mcd appear to be negatively accelerated, asymptoting below .50. The Locurve appears to be positively accelerated, although the small number of observationsmakes it quite variable beyond trial 3. These precriterion predictions can be directlycontrasted with those of the one-element model, which predicts a horizontal curve,stationary at the value 1/(number of responses), in this case, .125 (Suppes andGinsberg, 1963). SAL does not exhibit stationarity because its increased ability todiscriminate is accompanied by a restriction in the range of possible responses itwill make to a given stimulus. That is to say, the moretest nodes a stimulus has beensorted through, the more likely it is that the correct response image is stored at the

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132 HINTZMAN

133DISCRIMINATION

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terminal node. That this should also be true of the condition Lo precriterion curvemay at first seem paradoxical, as the stimuli in this list bear no formal similarity toone another. Nonetheless, some stimuli are "confused" because they are as yetunlearned; SAL has not yet constructed first-letter tests appropriate to them, andconsequently is sorting several stimuli to the same negative terminal node. Thenumber of "unlearned" items sorted to negative terminals decreases as learningprogresses, thus increasing the probability of a correct precriterion response.

Another interesting feature of the precriterion curves of Fig. 4 is that, comparedto the ease of learning, there is a curious reversal of performance among the threeconditions. Condition Hi has the highest precriterion proportion correct, conditionLo the lowest. The reason for this can readily be seen if one considers the effect ineach condition of building one test node. In condition Hi, this test node sorts thestimuli into two groups of equal size—in effect, doubling theprobability of a correctresponse. In condition Lo, the test node isolates one stimulus from the others. Thispair no longer contributes to the precriterion curve, since it is now learned. At thesame time, the number of unlearned items has been decreased by one. This increasesthe probability of a correct precriterion response, but the increase is small comparedto that in condition Hi. Thus, one added test node increases precriterion performancemore in condition Hi than in conditionLo; condition Mcd falls between.

Experiment 2. Number of Response Alternatives

An easily testable prediction of the one-element model is that of precriterionstationarity (Atkinson et al., 1965; Bower, 1961, 1962, 1967; Estes, 1964a; Suppesand Ginsberg, 1963). It was seen in Experiment 1 thatSAL didnot exhibitprecriterionstationarity on any of the three lists learned. Bower (1967), in reviewing the evidencefor the one-element model, has suggested that the critical variable for producingstationarity maybe thenumber of response items in thePA list. If there are onlytwo(well-integrated) responses, the precriterion curve is usually stationary. If there aremore than two, it rises as learning progresses. Clearly, the results of Experiment 1do not contradict this analysis, as 9 different responses were used in each list SALlearned. On theother hand, it seems reasonable to expect SAL to exhibit stationarityon a 2-response list, since the subprocesses (building test nodes) involved are all-or-none events. The following experiment was run to determine the effects of thenumberof unique responses on SAL's performance.

One condition (9-R) consisted of 20 simulated subjects learning the list shown inTable I—the1—thecritical factor herebeing that the 9-stimulus trigrams of mixed similaritywere paired with 9 unique responses. The other condition (2-R)randomly paired thesame 9 trigrams with the digits 1 and 2, four stimuli to one response and five to theother. All simulated subjects were run to mastery, with the parameters a = .40,b = .50.

TRIAL NUMBER

Fig. 5. Learning and precriterion curves from the 9-response and 2-response conditions ofExperiment 2. Insets from Hintzman, 1967.

Learning and precriterion curves are plotted in Fig. 5. Comparing the learningcurves of the two conditions, it can be seen that, while the 2-R condition started withhigher performance because ofthe higher initial guessingprobability,9-R performancewas actually slightly better by trial 6. Obviously, the 9-R list was learned morequickly than the 2-R list. These differential learning rates resulted from the factthat the model learns—that is, builds a new test node—only after committing anerror. In the9-R condition, errors have a higher precriterion probability than in the2-R condition. Therefore, the necessary discrimination net is built more rapidly,and learning is more efficient. This prediction is contradicted by Bower's (1962)finding that the same learning parameter could be used to fit learning curves forlists having different numbers of responses; however, the prediction was confirmedby Smith, Jones, and Thomas (1963), and in an experiment summarized below(Hintzman, 1967).

Of greater theoretical interest is the model's precriterion performance in the twoconditions (Fig. 5). The 9-R curve is consistently above chance (-J) and increasingover trials. However, the 2-R curve does not deviate significantly from the a priori

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guessingrate of J. This finding can be explained as follows. An error by SAL indicatesthat at least twostimuli are still being confused; therefore theprobabilityof a correctresponse prior to the last error cannot exceed .50. This value is a theoretical upperlimit for precriterion curves. Hence, as learning progresses, the 9-R curve rises,approaching .50, while the 2-R curve, which begins at .50 on early trials, remainsstationary.

Note that the precriterion stationarity in the 2-R condition does not mean thatSALis not learning prior to the last error. It means only that learning is not evidenced inperformance on that item. Learning appears in performance only with the buildingof the final critical test node—the one that can discriminate that stimulus from allother stimuli in the list. An attempt to fit the one-elementmodel to SAL's 2-R datawas fairly successful except for the one-element model's prediction of independenceof precriterion responses. SAL produced longer response runs than the independenceassumption would predict. Failures of the one-element model to fit human 2-R datahave often involved the prediction of precriterion independence, rather than that ofstationarity(e.g., Kintsch, 1965). It should be noted also that in thepresentexperimentSAL predicted stationarity even though one assumption of the one-element model—that of perfect stimulus discriminability—was violated. SAL predicts 2-R stationarityregardless of the degree of stimulus similarity.

Some Experimental Confirmation. APA study with human subjects was done totest several of the above predictions (Hintzman, 1967). Both intralist stimulussimilarity (high vs low) and number of responses (2 vs 14) were varied in a 2 X 2design involving 4 different lists of 14 pairs each. Stimuli were trigrams and responseswere numbers between 1 and 14; subjects learned by the anticipation method, andwere always allowed time to respond. The basic findings were in agreement withSAL's predictions: (1) low similarity lists were learned faster than high similaritylists; (2) 14-response lists were learned faster than 2-response lists; (3) precriterioncurves for both 2-response lists were stationary and those for both 14-response listswere nonstationary; and (4) precriterion stationarity was not accompanied by trial-to-trial response independence.

Experiment 3. Probability Learning

Voss, Thompson, and Keegan (1959) report a study of probabilistic PA learning,in which a stimulus could have two different associates, R x and R 2 . The probabilityof an R x reinforcement was controlled, and varied systematically over the pairs inthe list. Thus, subjects learned several different probabilistic associations simul-taneously. The following study was patterned after that of Voss et al. (1959), todetermine how SAL would perform in a similar situation.

Twelve stimulus trigrams of minimal similarity were paired with 1 1 differentnumbers as responses. Two of the stimuli (100% associates) were paired with the

same response on all 10 trials in each block of 10. Two other stimuli (90-10%) werepaired with one response (Rj) on 9 trials and with the other (R2) on one trial in eachblock. Similarly, two stimuli were assigned to each of the remaining possible R l-R 2splits: 8-2, 7-3, 6-4, and 5-5. Ten simulated subjects (a = .30, b = .50) were runfor 60 trials each. The first 10acquisition trials were discarded, leaving 5 blocks of 10trials per subject. There were thus 500 trials in all, each associative split occurringtwice per trial, for a total of 1000 observations per condition.

Response proportions were calculated as a function of reinforcement probabilities.These data are presented in Table 2. Clearly, none of the obtained values deviatesignificantly from the reinforcement probability; there is nearly perfect matching.Given probabilistic associations, SAL matches probabilities in its responses. Thereason for this is simple. After about 10 trials, the net has elaborated sufficiently todiscriminate all stimulus terms, so that item interactions are no longer occurring.Thus only the response images in terminalnodes are being altered. If SAL respondscorrectly, it keeps the same association; if it responds incorrectly, it changes to thereinforced response with probability b. Thus, asymptotically SAL I is the same asthe one-element model for this situation (Suppes and Atkinson, 1960), and it willhave the same defects regarding sequential statistics—for example, predicting perfectrepetition of a response which was given and reinforced on the previous trial.

TABLE 2

Results of Experiment 3. Probability LearningA Samples SAL Protocol

Responseproportion

Inputprobability

0.0 0.000.100.1

0.2 0.210.300.3

0.4 0.380.5 0.500.6 0.620.7 0.700.8 0.790.9 0.901.0 1.00

Actually, the Voss et al. (1959) study obtained considerable "overshooting"at highprobabilities and "undershooting" at low probabilities, showing that humans do not

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strictly probability match, as SAL I does. It is not clear what kind of modificationswould enable SAL to predict overshooting. It should be noted, however, that thisphenomenon poses problems for other models as well (Estes, 1964b).

Experiment 4. Massed vs Spaced Item Repetition

An experiment by Greeno(1964) has shown that the amount ofPA learning producedby the second exposureofa pair depends on howmany other itemsintervened betweenthe two presentations. If the second exposure of the pair took place immediatelyafter the first, later, long-term retention was not much better than it was followingonly a single exposure. If the second exposure was delayed, on the other hand, laterretention of the pair was enhanced. Greenoconcluded that spacedrepetitions resultedin better learning than massed repetitions. In the following experiment, SAL waspresented with a PA task similarto the one used by Greeno.

Eight stimulus trigrams having maximal similarity were paired with the first 8digits. Four of thesepairs were assigned to the Massed condition and 4 to the Distri-buted condition. On each trial, every Massed item appeared twice, the second exposureimmediately following the first. Each Distributed item appeared only once per trial.Presentation order was the same on all trials. Thus, on any given trial, the Massedpairs had been exposed twice as often as the Distributed pairs, and, if learning werea function only of frequency of repetitions and not of their spacing, onewould predictsuperior performance on the massed items. Parameters were a = .30, h = .50.

The results are presented alongwith Greeno's data in Fig. 6. For the Massed items,two percentages are plotted for each trial; proportion of errors on first presentationsand on second presentations (which immediately followed). It can be seen thatperformance on first presentations of items was not consistently better thanperformance on Distributed items. Despite the fact that the Massed items wereexposed twice on each trial, about the same number of trials were needed to reachmastery in both conditions. Figure 6 also shows the effect of Massed presentation 1on presentation 2 performance. A considerable drop in number of errors occurredon the second exposure,but the number increased again on presentation 1 of the nexttrial. These results are remarkably similar to those of Greeno (1964).

The fact that SAL behaves much like Greeno's subjects tends to confirm hisdiscrimination-learning interpretation of his results. SAL's performance on Masseditems improves greatly from presentation 1 to presentation 2 because eitherdiscrimination learning or replacing the old response at the terminal node results ina correct presentation 2 response given an error on presentation 1. In fact, the trueerror probability on presentation 2 is just (\-a)(\-b) times the error probability onpresentation 1 (note that the SAL data would look more like Greeno's if SAL'sMassed presentation 2 performance could be improved; this could be done by simplyraising the value of parameterb—in effect, boosting the model's short-termretention).

Acot_

° .2aca.

Greeno, 1964.Fig. 6. Distributed vs massed presentation data, Experiment 4. Inset from

The subsequent drop in Massed item performance between trials occurs because ofinterference from interpolated items. Finally, performance on Massed presentation 1is about the same as performance on Distributed items because SAL learns a list asa whole. No pair can be "learned" independentlyof the other pairs in the list, sincelearning depends on errors, and these are contributed by other, similar items.

Experiments 5 and 6 demonstrate two situations in which SAL fails to make thecorrect prediction.

Experiment 5. Whole vs Part Learning

Experiments using a variety of materials have been done to determine whether atask is more efficiently learned as a whole or in parts which can then be integratedinto the whole (McGeoch and Irion, 1952). In order to determineSAL's predictionsconcerningthe whole and part methods, the modelwas run in a simulation of a recentstudy using PA lists (Postman and Goggin, 1966) which compared three learningmethods, Whole, Part, and "Repeated Part" (explained below). That study foundthe Whole and Part methods to be of about equal difficulty, but both inferior to theRepeated Part method. The essential variables were duplicated in the followingexperimentwith SAL.

The 9-pair list shown in Table 1 was again used. The list was subdivided intothree equal parts or sublists: F1 ,P2 , and P3 . In the Part condition these sublistswere mastered successively, followed by learning of the integrated 9-pair list, i.e.,(Pt ,P2 ,P3,Pj + P2 + P3)- In the Repeated Part condition, the length of the list

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0 I 1 . 1 . 1 s_ s_ s VT^ I1 2 3 4 5 6 7 8 9 10 11

TRI A I

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hintzman discrimination net model

was gradually increased by adding a new sublist each time mastery was attained, i.e.,(P 1 ,PT +P2 ,Pj -f- P2 + P3 ). In the Whole condition, the entire list was learned inthe normal manner, i.e., (P 1 +P2 + P3 ). There were 15 simulated subjects in eachcondition with parameters a = .30, b = .50.

The total number of errors made, including all stages of learning, was used as themeasure of difficulty. Mean errors by conditions were: Whole, 33.2; Part, 29.0;Repeated Part, 31.2. None of the differences were significant. The model thus failedto predict the superiority of the Repeated Part method found by Postman and Goggin(1966). Apparently,a fixed number of confusions must occur before SAL can discrimi-nate among a given set of stimulus items. The order in which particular confusingitems are encountered is not an important variable.

Experiment 6. List Length

A powerful determinant of the difficulty of a PA list is list length or the numberof pairs (Calfee and Atkinson, 1965; Runquist, 1965, 1966;

Sand,

1939). In order todetermine the effects of this variable on SAL's performance, two design problemsfirst have to be dealt with. Thefirst is that in manyexperiments, list length and numberof response alternatives are confounded. This problem was handled simply by holdingconstant the number of responses (as did Calfee and Atkinson, 1965). The secondproblem is that when trigrams are used, it is impossible to manipulate list lengthwithout either increasing the number of letters or increasing the degree of similarityof the trigrams. It was decided in this case to hold the number of letters constant,allowingsimilarity to vary.

Condition 8-P consisted of the data of condition Mcd in Experiment 1 above.The eight trigrams used, it will be recalled, were generated from a set of 4 alternativeletters for each position. In condition 16-P, the same sets of 4 letters per positionwere used to generate 16 different trigrams. Number of responses was equated inthe two conditions by randomly pairing two 16-P trigrams with each of the first 8digits. All simulated subjects (20 per condition) were run to mastery, with a

-~

.40,b = .50. Mean number of errors per pair were: 8-P, 1.59; 16-P, 1.55. Clearly, listlength is not the important variable to SAL that it is to human subjects. The factthat more test nodes are required to learn a longer list is apparently counteracted bythe fact that there are more opportunitiesper trial for the test nodes to be grown.

The fact that longlists are not more difficult than short lists for the model to learncan be considered a major failing, for the effect of list length on human learning isvery consistent and must reflect some basic feature of the memory mechanism. Twopossible solutions to this problem have suggested themselves. One possibility wouldbe to postulate a kind of "cognitive strain," such that the larger the discriminationnetbecomes, the smaller is the probability a of adding a new test node. This notion isclearlyad hoc, however, and might result in undesirable sideeffects, such as distortions

in the learning curve. The other possible solution would involve adding a short-termmemory mechanism. Calfee and Atkinson (1965) have shown in their work on the"trial-dependent-forgetting" model that a short-term mechanism helps explain thelist-length effect. It might also clear up the difficulties encountered in handling wholevs part learning (Experiment 5) and errors occurring after an errorless trial.

Other human learning phenomena which we have not yet considered, such asoverlearning, proactive interference, etc. are clearly outside the scope of the simpleversion of SAL presented above. However, they can be dealt with by some slightmodifications of SAL I. The remainder of this paper presents two elaborations ofthe SAL model.

SAL 11. THE OVERLEARNING MODEL

In extending application of SAL to the problem of retroactive interference (RI),the model was found to be inadequate without at least one additional assumption.In version II of

SAL,

it is postulated that learning can take place following a correctresponse, as well as following an error. The probability of this occurring is c, where ccan take on values between 0 and a. It can be seen that the simpler version of SALis a special case of this model, wherec — 0. Also, note that if c = _, that is, if learningis equally likely following correct and incorrect responses, the difference in learningrates between conditions 9-R and 2-R in Experiment 2 would disappear.

The parameter c can be considered an "overlearning" parameter, which allowsdiscrimination learning to continue even though performance may show completemastery of the list. Followinga correct response, with probability c, SAL constructsa newtest node. This test node incorporates the letter of thepresented trigram whichis next in the noticing order. The correct response is stored at the positive terminalof the new test node, while nothing is stored at the negative terminal. Because thenegative terminal is left blank, an empty terminal node may be encountered duringa later attempt at recall of some pair. When this happens, SAL guesses randomlyfrom the set ofresponses appropriateto the list and thenstores thereinforced responseat the empty node with probability 1 .

Experiments 7-9 were run with SAL II as subject.

Experiment 7. Interlist Similarity and Retroactive Interference

The operations for producing and testing retroactive interference (RI) are: learnlist 1, then learn list 2, then relearn list 1. These steps will be designated originallearning (OL), interpolated learning (IL), and relearning (RL), respectively. SinceSAL II doesnot spontaneously forget overtime, the amount of RI can be determineddirectly by counting the number of errors made on trial 1 ofrelearning (RL-1). Thisis only true, of course, in situations in which list 1 was originally learned to mastery—

140 hintzman141discrimination net model

otherwise a control condition is needed (as in Experiment 8 below). The followingexperiment was done to demonstrateRI and to determinehow RI varies with interliststimulus similarity. With human subjects more RI is found the more overlap thereis between stimuli of the original and interpolated lists (McGeoch and Irion, 1952).

SAL's RL rates are higher is that the discriminationnet built up during OL is entirelyadequate to discriminate among the list 1 stimuli. Thus, the relationship betweenintralist and interlist (retroactive) interference can be characterized as follows. DuringOL, SAL must deal with confusions from within the list. The confused pairs recur,trial after trial, so that the list cannot be mastered until all the proper discriminationtests have been incorporated into the net. Interference causedby interpolated learning,while due to the same mechanisms as intralist interference, does not recur duringrelearning. The learning system can dispose of interference from list 2 responses bothby building new test nodes and by replacing the list 2 responses with list 1 responsesin terminal nodes. Relearning can proceed rapidly because intralist interference wasdealt with during original learning.

There were three conditions varying in degree of interlist stimulus similarity.List 1 was identical in all three conditions, consisting of 9 trigrams of mediumsimilarity paired with the numbers 11 through 19. In list 2, the first 9 digits werepaired with stimuli which differed in each condition. For every list 1 trigram, list 2of condition High contained a trigram having the same first two letters. List 2 ofcondition Medium repeated only first letters from list 1 . Those of condition Lowwere generated from an entirely different set of letters. Both lists were learned tomastery by 10 simulated subjects in each condition. Parameter values were: a = .40,b = .50, c = .20.

SAL escapes the chief criticism Underwood (1961) has aimed at Gibson's theoryfor the same reason. Gibson (1940) proposed that generalization among stimulusitems could recover, causing forgetting. It follows that high intralist similarity shouldlead to poorer retention than low intralist similarity, a prediction that Underwoodwas not able to confirm. Although SAL is similar to Gibson's theory in many respects,it does not predict recovery of intralist generalization,for the discrimination net isa permanent structure, and once a list has been mastered, forgetting can be causedonlyby interference from external (e.g., interlist) sources.

A positive relationship is generally found between number of "reinforcements"during original learning and resistance to RI or forgetting (Runquist, 1957;Underwood, 1953a, 1953b, 1964). In general, pairs which have been correctlyanticipated most often during OL are least susceptible to interference. Such findingsare extremely difficult to reconcile with simple all-or-none learning notions; theinterpretation has always been that associative strength can vary, and that reinforcinga response strengthens the S-R bond, making the association more permanent.

2345678 12345TRIALS ORIGINAL LEARNING

RELEARNING

RELEARNINGSAL 11, with its overlearning feature, offers an alternative interpretation in terms

of stimulus discrimination learning. A stimulus which has been discriminatedfromthe others in its list can continue to be learned while the more troublesome pairs arebeing mastered. Thus, with uniform intralist similarity, SAL will have learned moreabout the stimuli of rapidly learned pairs than about stimuli of pairs which have beenbarely mastered by the end of original learning. The effects can be demonstrated inthe data of condition High. Proportion correct on RL-1 was .36 for pairs correctlyanticipated 1 to 3 times during OL, and was .68 for those correctly anticipated 4 to6 times.

Fig. 7. Inflects of three degrees of interlist stimulus similarity on RI, Experiment 7,

Performance on list 1 in the three conditions, both original learning (OL) andrelearning (RL), is shown in Fig. 7. The chance variation among conditions in OLwas about the amount which could be expected with human subjects run in groupsof 10. The effects of the interpolated learning (IL) differed considerably, as can bejudged from performance decrements on RL-1 (Fig. 7). As expected, condition Highsuffered the greatest retention loss, and condition Low the least. Mean number oferrors on this trial were: Low, 0.1; Medium, 2.2; High, 4.6.

i

Experiment 8. RI and Amount of Original LearningThe RL curves of conditions High and Medium demonstrate another interestingfact aboutSAL's behavior. The RL rates are higher than OL rates (this has alsobeenfound with EPAM, cf. Feigenbaum, 1959). This finding agrees with the literatureregarding relearning following RI (Thune and Underwood, 1943; Underwood, 1945)and following a forgetting interval (Underwood and

Schulz,

1961). The reason that

An effect similarto the one just described shows up in investigations into the effectsof various degrees of original learning on RI. The parameterc allows SAL II to learnmore about the stimulus items than is necessary for perfect performance on the list.To the extent that the additionaltest nodes so created helpto differentiate list 1 stimuli

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hintzman discrimination net model

from those of list 2, increased learning of list 1 should make it more resistant to RI.This is true of human learning of both serial (McGeoch, 1929) and PA lists (Briggs,1957).

Numberof errorson RL-1 is plotted as a function of trials of IL in Fig. 8. It can beseen that as IL increases, total RI increases rapidly at

first,

then more gradually.The number of these RI errors which were intrusions from list 2, on the other hand,shows a sharp initial increase followed by a considerable decline. The differencebetween these two curves, the number of RI errors which cannot be attributed tolist 2 intrusions, thus gradually increases with trials of IL, as shown in the thirdcurve of Fig. 8. These results compare favorably with those presented by Briggs(1957) and by Thune and Underwood (1943). The obtained discrepancy betweenthe curves of total RI and intrusions is the same as that which inspired the "two-factor" theory of RI (Melton and Irwin, 1941) by showing that response competitionalone cannot account for all RI. The additional factor in RI was assumed to be"unlearning" or extinction of list 1 responses during IL. The unlearning theory hasbeen criticized on the grounds that intrusions during IL are rare and are concentratedin the first few trials (this is also true of SAL's data), while the unexplained RI factorincreases most at high degrees of IL(McGeoch and Irion, 1952).

For this simulation, lists I and 2 of condition Medium Experiment 7, were used.Three conditions were run, 10 simulated subjects per condition. Groups 4-OL,8-OL, and 12-OL received 4, 8, and 12trials of original list 1 learning, respectively.List 2 was learned to mastery, followed by relearning of list 1 . Parametervalues were:a = .40, b = .50, c = .20.

IIn order to determine how manyof the errors on trial RL-1 were due to RI, it was

first necessary to arrive at an indication of what the performance in each conditionwould have been on an additional OL trial, had one been given. This was done byusing 8-OL performance on trial 5 as control for 4-OL, and 12-OL performance ontrial 9 as control for 8-OL. All errors in condition 12-OL were due to RI, as perfectperformance was reached by trial 10. Subtracting these correction values gives themean numbers of errors due to RI on RL-1. They were:

4-OL,

2.7;

8-OL,

1.3;

12-OL,

0.5. RI is thus a decreasingfunction of the number of OL trials.We may state as a general principle of SAL ll's learning that the amount of RI

produced by an interpolated list is inversely related to the amount of stimulusdiscrimination learning which has gone on during list 1 acquisition. Since one wayof assuring a high degree of OL is to have high intralist similarity, the followingprediction may be made: if intralist similarity on list 1 is manipulated and interlistsimilarity held constant, the amount of RI should be inversely proportional to thedegree of intralist similarity. This prediction could easily be tested.

Experiment 9. RI and Amount

of

Interpolated Learning

In a similar manner, one can manipulate the number of trials on the interpolatedlist. Experiments with both serial (Melton and Irwin, 1941) and PA learning (Briggs,1957; Thune and Underwood, 1943) have produced complex results. In general, asIL increases: (1) totalRI increases exponentially; (2) the number of actual intrusionsfrom list 2 first increases, reaches a maximum at intermediate degrees of IL, thendecreaseswith overlearningof list 2; and (3) as a consequence, the amount of RI whichcannot be explained by specific response interference rises. In addition, it has beenfound that the shape of the RI function depends on what measureis being used. Theexponentialincrease inRI justmentionedholds onlyfor errorson RL-1

;

if the numberof RL trials needed to master the list is taken as the RI measure, it is found first toincrease and then to decrease with the number of trials on list 2. The followingexperimentwas run to determineto what extent SAL II could match this complexpattern of findings.

I 12 4 7 12

TRIALS

OF INTERPOLATED LEARNING

Fig. 8. The RI errors as a function of degree of IL, Experiment 9. Inset from Thuneand Underwood, 1943.

The lists used were lists 1 and 2 of condition High, Experiment 8. Five conditionswere run, 15 simulated subjects per condition. In all cases, list 1 was first mastered.List 2 was then presented for 1, 2, 4, 7, or 12 trials, followed by relearning of list 1.

The feature of SAL II which is essential for producing these results is the emptynegative terminal node created whenever learning takes place following a correctresponse. After small amounts of IL, the model confuses list 1 and list 2 stimuli,

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discrimination net model

thus producing response intrusions. With increased differentiation of list-2 stimuliduring overlearning, however, the discrimination net grows more and more emptynegative terminalnodes. Thus, when tested for RI, the list-1 stimulus becomes morelikely to be sorted to an empty terminal, an event which will not produce a list 2intrusion, but one which will produce either an omission or a random error. The oldlist-1 associations are no longer available because they have been bypassed by thecontinued elaboration of the discrimination net.

The paradoxical finding that relearning is faster with high than with intermediatedegrees of IL is also predicted by the model. Stated simply, SAL finds it easier to fillan empty terminal node than to deal with an interfering response, and empty terminalsare more frequent after high degrees of IL. In the present experiment, the meannumbers of trials to relearn for conditions 1, 2, 4, 7, and 12, respectively, were:1.67, 1.93, 2.07, 2.13, and 1.27. Thus, whether 7 or 12 trials of IL appear to producemore RI depends on whether RI is measured by errors on RL-1 or by thenumberof RL trials required to regain mastery of the list; and this was the effect to beexplained.

Another finding which is consistent with SAL has been reported by Underwood(1945). Holding the number of IL trials constant, he found that the more IL listswere presented, the greater was the resulting RI. It can be seen in Fig. 8 that theamount of RI produced by one interpolatedlist reaches a maximum in a few trials.This happens because a point is reached early in IL at which interlist confusions havebeen completely eliminated. Further practice on the interpolated list beyond thatpoint has no effect on list-1 retention. This would not be true, however, if duringILseveral lists were presented, all of high similarity to list 1. In such a case, one wouldexpect RI to increase with the number ofIL lists, as Underwood(1945) found.

The List Identification Problem. It should be noted that the overlearning resultsof Experiments 8 and 9 would not have been obtained if the A-B, A-C paradigm hadbeen used— that is, if the stimuli of the two lists had been identical. Overlearning isonly effective for SAL insofar as it increases differentiation between list-1 and list-2stimuli, and SAL cannot discriminate stimuli which are formally identical.

To make the model applicable to overlearning in the A-B, A-C situation, onewould have to assume that the model can add to a stimulus some kind of identifyingtag or label which serves to differentiate the two lists. This identifying label couldbe incorporated into the discrimination net much as letter tests are. But list identi-fication would ultimately have to be derived from temporal cues or from "contextcues"—stimuli not obviously part of the immediate nominal stimulus situation(other pairs in the list, etc.). Indeed, there is much evidence that a completemodel ofverbal learning would have to make use of contextcues (e.g., Bilodeau and Schlosberg,1951), but it is not clear how a mechanism to do this efficiently could be incorporatedinto the present model.

Experiment 10. Predifferentiation

of

Stimuli

Like Gibson's theory (Gibson, 1940) and EPAM (Simon and Feigenbaum, 1964),SAL predicts that prior discrimination training with the stimuli will facilitate sub-sequent acquisition when these same stimuli are used in a standard PA task. Theeffect should be stronger the greater is the degree to which the prior task requireselaboration of the discrimination net. Thus, prior PA learning or free recall of thestimulus terms (predifferentiation) would be expected to have more consistent positiveeffects than would mere observation or pronunciation of the stimulus terms (pre-familiarization).

In his review ofthe predifferentiation literature, Arnoult (1957) concludes that such"Relevant S" pretraining does indeed usually produce positive transfer to the secondtask, especially when the responses in the two tasks come from entirely unrelatedclasses. In discussing theories of the predifferentiationeffect, Arnoult notes that oneprediction of Gibson's theory has not been borne out in experiments: that transfershould be negative after a few pretraining trials and positive after many trials. Insituations where a predifferentiation effect is obtained, it increases monotonicallywith pretraining trials to an asymptote. This is the outcome predicted by SAL.

An alternative explanation of predifferentiation effects, offered by Miller andDollard (1941), states that learning to respond to stimuli with distinctive labelsreduces generalization and thereby produces positive transfer. Thus, transfer shouldbe greater the greater the specificity of the responses learned to the stimuli in thepredifferentiation training. Regarding this prediction, an experiment by Hake andEriksen (1955) found no effect of pretraining response specificity. Their subjectswere pretrained to label each of 16 random patterns (5 lights in a 5 X 5 matrix) withone of either 2, 4, or 8 labels. The labels were assigned at random to the 16 stimuli,with no simple "concept" rule to describe thepairings. Subsequent learning of a newset of labels for the 16 patterns was independentofthe numberoflabels in pretraining.

Similar independence from pretraining response specificity was shown by SALin a simulation of the Hake and Eriksen study using trigrams instead oflight patterns.Using the 8 trigrams of Experiment 1 having high intralist similarity, one group of15 simulated subjects learned a PA task with 8 responses; another group of 15 learnedwith 2 responses. In the latter case, the 2 responses were so assigned to the stimulithat no single letter or pair of letters would enable complete discrimination. This wastaken to approximate the random, unstructured pairings used in the Hake andEriksen study. Following initial training to mastery, both groups learned a new setof 8 responses to the stimuli. There were no differences between groups on thetransfer task; subjects pretrained with 8 responses made an average of 1 1.8 errors onthe second task; those pretrained with 2 responses made 13.0 errors (t = 0.44).Thus, SAL can simulate the Hake and Eriksen results when the task 1 responses areassigned so that no simple rule describes the pairings. If, on the other hand, a simple

146 HINTZMAN

DISCRIMINATION

NET

MODEL

147

conceptual rule had characterized the 2-response pairs in task 1 (e.g., "all stimulibeginning with 'X' are paired with 2"), then SAL would expect less positive transferthan in the 8-response condition. This suggests repeating the Hake and Eriksenparadigm with variations in the complexity of the rule describing the S-R pairs intask 1.

Transfer Paradigms

At this point, it would seem reasonable to extend application of SAL to paradigmsof transfer as related to similarity, such as those summarized by the Osgood transfersurface (Osgood, 1949). This has not been done, for two reasons. First, SAL does notdeal with response similarity or associative mediation between two responses, so themodel would be applicable only to changes on the stimulus similarity dimension.Second, it is quite clear that SAL would not always behave as human subjects do,since SAL never produces negative transfer. With low interlist stimulus similarity,transfer may be nearly zero, but with medium or high similarity, transfer is positive.In fact, SAL shows maximum positive transfer in the A-B, A-C paradigm, due tothe predifferentiation of the stimuli in the A-B task; the "response competition"inherent in the design is dealt with by SAL without difficulty, and is a minor factorin relation to the positive effects of predifferentiation. Apparently, a simplediscrimination net cannot account for the complexities of the transfer literature.In order to get negative transfer, special assumptions must be made—assumptionswhich weigh response competition more heavily than stimulus-discriminationlearning. The fact that EPAM 111can predict negative A-B, A-C transfer (Simon andFeigenbaum, 1964) apparently arises from the way time charges are assigned tocertain EPAM subprocesses; the end result is that the time taken to replace a terminalnode response image with a new image is greatrelative to the time consumed growingnew test nodes.

The experimental literature is still incomplete regarding what kinds of terms canbe substituted in the A, B, and C locations so that the A-B, A-C paradigm producespositive, negative, or zero transfer. For example, if A is a nonverbal stimulus andB andC come from entirely unrelated response classes (e.g., a motor response and a CVC),then the predifferentiation literature shows that transfer is predominantly positive(cf. Experiment 10). Similarly, transfer has been reported to be positive when theA, B, and C terms were unrelated nouns (Postman, 1963), negative when they wereunrelated adjectives (Postman, 1962), and positive when B or C were either similarCVCs or associatively related adjectives (Barnes and Underwood, 1959; Young, 1955).Studiesby Goulet (1965), Houston (1965), Jung (1963), and Merikle and Battig (1963)have shown a complex pattern of negative and positive transfer effects dependingon the meaningfulness (ni) of the B and C response terms. It has also been shown thatif the C items are thefirst-list B responses, re-paired with the stimuli (the A-B, A-Brparadigm), negative transfer is even more pronounced (cf. Postman, 1962). Factors

related to response integration, associative mediation, and list differentiationseem tobe important for understandingthese complexresults. It is clear that SAL is deficientin just such factors. It is also deficient in not showing nonspecific transfer effects, suchas learning-to-learn or warm-up, for which controls are routinely introduced in thestandard transfer paradigms.

SAL 111. THE PUSH-DOWN STACK MODEL

Version 111 of SAL eliminates a major flaw in SAL I and SAL 11. In those twoversions of the model, only one response could be associated with a stimulus at anygiven time. Evidence from studies of proactive interference (PI) and from "modifiedfree recall" procedures demonstrates that several associations to the same stimuluscan and often do coexist. Accordingly, another slight modification was made in

SAL,

involving the addition of a "push-down stack" at each terminal node.Items are stored in a push-down stack (PDS) in their order of recency. That is,

the most recent item is always stored at the topmost position in the stack, the nextmost recent item is stored in the second position, and so on. Storage of a new iteminvolves pushing the other items in the stack down, making a place for the new one.In thepresentmodel, thePDS replaces the single-occupant terminal nodes of versionsI and II as theresponse storagemechanism. At any terminalpoint in the net, theremaynow be stored a response hierarchy, with the most available associate in the topmostposition.

Little modification of SAL II was needed to incorporate thePDS feature. Whereasin SAL I and II an error was followed, with probabilityb(\ — _), by the reinforcedresponse replacing the old response at the terminal node, SAL 111 assumes that withthe same probabilitythe reinforced response is stored at the top position of thePDS.The new model differs from SAL II onlyin the fate of the old response. It is not lost,but is merely pushed down from the number one position by the new response.SAL 111is thus able to store a hierarchyof associationsat each terminalnode, arrangedin their order of recency. The topmost response is assumed to be the most available;it will be thefirst response retrieved, and unless special procedures such as modifiedfree recall, second guess, or recognition are used, it will be the onlyresponseretrieved.

As a list is mastered and the depth of the net increases, PDS's locatedat the bottomof the net are found to contain fewer and fewer response images, reflecting thedecrease in confusions that accompanies net growth. Like the two simpler versionsof the model, SAL 111 can "lose" responses due to growthof the net around a terminalnode. An entire PDS hierarchy can thus become unavailable for cued recall bya stimulus item which once could elicit that hierarchy.

Having introduced a mechanism for simultaneous storage of associates, we nextconsider the question of "recovery" of old responses; how do they get back to the

149

148 DISCRIMINATION NET

MODEL

HINTZMAN

top of the hierarchy once they have been displacedfrom thatposition ? The assumptionadopted in SAL 111 is that responses at lower levels in the PDS tend to "rise" overtime, pushing the higher or more recent responses out the top of the PDS, andthereby causing them to be lost from memory. This means that any terminal nodewhich contains more than one response image is in an unstable condition. As timepasses, it becomes more and more likely that only the oldest response will remainat a terminal node, in the topmost position of the PDS.

In the SAL 111 program this assumption takes the form of a stochastic process.For any PDS containing more than one response image existing over time intervalAt, there is a probability d that the topmost response will be lost and each responselower in the hierarchy will rise one level. The probability of retaining the topmostresponse for T such time intervals, therefore, is a decreasing exponentialfunction,(1 — d)T. Since At is undefined, specific values of T and d are meaningful only relativeto other values.

The following experiments demonstrate some of the consequences of the PDSaddition to the model.

Experiment 11. Recognition vs RecallRecognition measures generally lead to higher estimates of retention of verbal

materials than do recall measures (Brown, 1964, 1965; Luh, 1922; Postman, JenkinsandPostman, 1948;Postman and Rau, 1957). This finding poses a problem for simpleall-or-noneretention theorieswhich allow only one associate per stimulus. In SAL 111,more than one response maybe associated with a stimulus, and the correct responseneed not be the most available. With scanning of the response alternatives stored atthe

PDS,

therefore, recognition can often succeed where recall fails. The followingexperiment demonstrates this fact.

Fifteen simulated subjects (a — .30, b = .50, c = .15) learned the 9-pair mixedsimilarity list of Table 1 . On each presentation, a recognitiontest was given, followedby the usual recall (anticipation) test. Thus, for each subject-item on every trial,there were two retention measures, recognition and recall, which could be directlycompared. On the recognition test, the stimulus was presented along with a responsedigit which was either correct (50% of the time) or incorrect. Incorrect pairings weredrawn randomly from the other 8 digits. The model determined its recognitionresponse by sorting the stimulus to a terminal node and searching the PDS at thatterminal for the presented response. If the presented response was found at any levelof thePDS, SAL responded "yes," otherwise "no." In the recall test which followedimmediately, SAL always responded with the topmost response in thePDS. Followingthe recall test, learning took place in the usual manner. Recognition tests had noeffect on learning.

Results on trials 2 through 5 were analyzed. Recognition responses were talliedin 4 categories: hits ("yes" | correct pairing), false alarms ("yes" | incorrect pairing),

correct rejections ("no" 1 incorrect pairing), and incorrect rejections ("no" j correctpairing). These categories were further analyzed according to whether the recallattempt was correct or incorrect. Pr(__ ), the probability of a hit, andPr(F), the prob-ability of a false alarm, were then computed. Summingoverboth correct and incorrectrecalls, these values were Pr(i_) = .72, Pr(F) = .12. For items recalled correctly,¥r(H) = 1.00, Pr(F) = .05; and for items recalled incorrectly, Pr(/_) == .41,Pr(F) = .22. Note that Pr(//) > Pr(.F) on pairs which were recalled incorrectly,indicating the superiority of recognition to recall. This superiority can also be shownby applying a correction for guessing to the proportions correct obtained by bothmeasures. Corrected proportions correct were: recognition, .60; recall, .49.

SAL 111 is thus able to explain the qualitative difference between recognition andrecall without the ad hoc assumption of different "thresholds" for the two measures.

Experiment 12. Second and Third GuessesSimilar to studies of recognition vs recall are experiments which give the subject

more than one try at recalling the correct response (Binford and Gettys, 1965; Bower,1967; Bregman, 1966; Brown, 1964, 1965). A simple all-or-none association modelpredicts that second and third attempts at recall will be no better than chance.Experimental results unanimously refute this notion. The following experimentshows what happens when SAL 111 is given more than one attempt at recall on eachpresentation.

The list and parameters were the same as Experiment 9. Learning was by theanticipation procedure, but if the first response given was incorrect, the model wasallowed a second or third attempt at recall before being shown the correct response.Thus, the stimulus was sorted to a terminal, and the first, second, and third responsesin thePDS were retrieved and output if needed. Ifany of these levelswere unoccupieda random guess (a digit between 1 and 9) was output instead. The chance probabilityof a correct response was therefore I, or .1 1 on all 3 attempts (lower than for humansubjects, who are able to eliminate earlier incorrect guesses).

TABLE 3

Proportion Correct on First, Second and Third Guesses, Experiment 1 2

AttemptTrial no.

321

.144.161.1722

.287.256.3503

.283.418.5614.348.489.7505.467.531.8226.111.526.8947

150 hintzman

151

discrimination net model

The proportions correct on first, second, and third attempts for trials 2 through 7arepresented in Table3.Performance onall 3 attempts was abovechance, and improvedas the list was learned. First attempts were more accurate than second, and secondweremore accurate than third and these differences increased as the list was mastered.

Experiment 13. "Unlearning" and Modified Free Recall

Very similar to the second guess technique for the study of single list learning isthe "modified modified free recall" (MMFR) method developed by Barnes andUnderwood (1959) for the study of interlist transfer and interference. By asking thesubject to give both B and C responses in an A-B, A-C transfer paradigm, they wereable to trace the changes in availability of the two response sets which take placeduring list 2 learning. As list 2 responses became more available, list 1 responsesbecame less available, but this drop in availabilitywas never complete. The commonlyaccepted interpretation of thesefindings (extinctionorunlearning of list 1 associations)will be discussed after we see what SAL 111 predicts in this situation.

An A-B, A-C paradigm was used. The stimuli were of high intralist similarity,and both lists were 9 pairs in length. Responses for the A-B list were the numbers11 to 19; those for list A-C were 1 to 9. Ten simulated subjects were run (a = .30,

b = .50, c — .15); each learned A-B to mastery and then transfered to list A-C.During the learning of A-C, the model retrieved 2 responses whenever possible, bysorting the stimulus and then responding with both the first and second items storedin the PDS. If no second response was present, only thefirst was given.

Responses made during the learning ofA-C werecategorizedas either B or C items.The frequencies of B and C itemsare shown as a function of the number of trials onA-C in Fig. 9.

These results are in substantial agreement with those of Barnes and Underwood(1959). As A-C availability increased and reached its maximum, A-B availabilitydeclined, but the decline was much slower than the A-C increase. Even after mostof thesimulatedsubjects had performed perfectly on list A-C for 2 trials in succession,nearly I of the first-list responses were still available.

SAL 111 is also consistent with other features of MMFR results. First, when SALrecalls both responses to a stimulus, they are emitted in the order C, then B, whichis the predominant order used by human subjects. Second, order of responses in thePDS could be used to identify list membership of a response, and human subjectsarecapable ofhighly accurate list identification in MMFR (e.g., Ceraso and Henderson,1965). Third, if the A-B and A-C lists are both originally learned to a criterion ofmastery, then in MMFR SAL never recalls a response to an incorrect stimulus; inhuman data involving mastery of both lists (e.g., Ceraso and Henderson, 1965), suchmisplaced responses in MMFR are quite infrequent, less than 1% on an immediatetest, less than 6% on a 24-hour retention test.

TRIALS ON LIST A-C

Fig. 9. The MMFR results, Experiment 13. Inset from Barnes and Underwood, 1959.

A list 1 response which remains available to SAL throughout the learning of list2 does so by residing in the second level of a

PDS,

the list 2 response for the samestimulus having taken over the first position. Why, then, do many B items becomeunavailable ? This is caused by continued discrimination learning. If during A-Cacquisition SAL responds with a B item (an error), then with probability a a newtest node will be built, and the B response will be stored at the negative terminalof this test node. Thereafter, sorting stimulus A through the net will lead to responseC alone, andB will be bypassed. A similar occurrence is possible if B has been pusheddown one level in the PDS by response C. Now, a correct response is given, but withprobability c (the overlearning parameter) a new test node is added which, again,isolates the B response in the net. It is no longer possible to retrieve B by sortingstimulus A. Thus, availabilityof B responses in MMFR will graduallydecline, evenafter list A-C has been mastered and is being overlearned. Note that the level ofMMFR A-B performance by SAL will depend greatly on the parameter values.If a is

very

high, A-B recall will be low. If a is low, A-B recall will be an increasingfunction of b.

The most common interpretation of the Barnes and Underwood (1959) study hasbeen that A-B associations are "unlearned" as the A-C associations are learned(Postman, 1961). The idea is that occurrences of response B during A-C learning areconsistently nonreinforced and hence eventually unlearned, or extinguished. Therehave been several difficulties with this particular account. First, overt intrusions of Bduring A-C learning are in fact infrequent and are concentrated within the first few

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trials, while the unavailability of B responses grows progressively with trials, longafter overtB intrusions have ceased. This discrepancy has been handled by supposingthat B responses occur implicitly but are withheld by a "selector mechanism" thatchecks their list membership. A second difficulty for the unlearning theory is toaccount for the many B responses which remain available even after the A-C listhas been practiced well past mastery; why has the unlearning not been complete ?This has been explained by supposing that the A-C associate becomes so dominantthat B stops occurring(even implicitly),and unlearningofB responses thereforeceases.

Perhaps the critical test of the unlearning theory comes with application of theMMFR technique to the study of long-term changes in availability of the B and Cresponses. Unlearning theory predicts that A-B associations will spontaneouslyrecover, and the B responses will therefore increase in MMFR availability. SAL 111,on the other hand, predicts no such increase in MMFR availability. Only those Bresponses which are available to MMFR at the end of A-C learning will be availableon later tests. Therefore, the number of B items recalled should remain approximatelyconstant with changes in time. The availabilityof C responses, in contrast, shouldshow a sharp drop, as they are being displaced from the PDS's by recovery of theremaining B responses. Thus, contrary to the unlearning theory, a delayed MMFRtest should show proactive interference. These predictions are more in line withexperimental results (Birnbaum, 1965; Ceraso and Henderson, 1965; Houston, 1966;Koppenaal, 1963; Slamecka, 1966) than are those of the unlearninghypothesis.

We noted earlier that A-B will become unavailable to MMFR during interpolatedlearning if a new test node is grown for sorting the A stimulus. This happens withprobability a following an error or with probability c following a correct response,and we have assumed throughout that a is larger than c. The difference in theseparameters suggests that for a fixed period ofinterpolated learning, the A-B associationwould be less available following those procedures which maximize errors to the Astimulus. One such procedure is to present several successive interpolated lists.This was done in a study by Postman (1965). All experimental subjects had a totalof 16 IL trials, but these 16 trials were divided among 1 , 2, or 4 different lists, eachbearing an A-B, A-C relationship to the first. A later MMFR test showed lessavailability of A-B the more interpolated lists used. Also, with amount of learningheld constant, the availability of responses from a given list varied directly with itsrecency to the MMFR test. These results are as expectedby SAL 111.

Experiment 14. Retroactive vs Proactive InterferenceThe operations for producing and testing for proactive interference (PI) are: learn

list 1, then learn list 2, then rest, and finally, relearn list 2. As with RI, the amountof interference can be measured on trial 1 of relearning. The purpose of the presentexperiment was to simulate varying lengths of the rest interval—in the SAL 111program, varying values of T—to determine how this variable affects the amount

of PI produced when an A-B, A-C paradigm is used. Since SAL does not censorits responses according to their list membership, theexperiment canalso be interpretedas a test of theeffects of rest interval on the amount of RI. That is, if stimulus A werepresented and it elicited response C, this could be called RI of list 1; alternatively,if it elicited response B, we could interpret this as PI of list 2. The amount ofPI forSAL 111 is therefore the amount of RI subtracted from the total number of oppor-tunities to respond, and RI and PI for any rest interval of length T can easily becompared. The following experiment is thus roughly comparable to studies by Briggs(1954) and by Underwood (1948).

Lists were the same as those of Experiment 13.Parameters were: a = .30, b = .70,c = .15, d = .30. Four conditions were run, with T (the number of opportunitiesfor recovery) taking on values 1,4, 16, and 64. Ten simulatedsubjects in each conditionmastered list A-B, followed by A-C. Then, after T opportunities for old responsesin eachPDS to recover the topmost position, list A-C was relearned.

Mean numbers of B responses (PI) given on trial RL-1 in conditions T = 1,4, 16,and 64, respectively, were: 1.2, 3.0, 3.8, and 4.2. Since each subject had an average of9 opportunities to respond, corresponding numbers of C responses (RI) were: 7.8,6.0, 5.2, and 4.8. At T = 64, the difference between PI and RI was not significant(p > .25). Thus, as the retention interval lengthened RI decreased andPI increased,so that at the longest interval the two effects were approximately equal. This patternof outcomes is in substantial agreement with the results reported by Briggs (1954)and Underwood (1948). The study by Briggs is fit especially well by SAL's simulationsince he used the MFR procedure ("give the first response that comes to mind")which circumvents the selector mechanism that withholds recall of responses froman incorrect list.

SAL 111 will also show an accumulative PI effect, such that, in an A-B, A-C,A-D,... paradigm, the more prior lists have been learned, the poorer will be thedelayed recall of the last list in the series. This agrees with Underwood's (1957)findings concerning the relationship between forgetting and the number of priorlists learned. In SAL 111, the discrimination net becomes progressively elaboratedwith the learning of each successive list. Consequently, it becomes more and morelikely that mastery of an item will require use of the PDS rather than elaboration ofthe net. That is, there is a limit to the number of features of a given stimulus itemwhich can benoticed, and onceall thesefeatures have been used in sorting thestimulus,a new response can be associated with it only through use of thePDS. And, of course,it is the response stored in the PDS which is subject to forgetting during a retentioninterval. Thus, it follows that PI will increase with the number of prior lists learned.

Experiment 15. Distributed Practice and PIOne of the few consistent effects to be found in verbal learning studies comparing

distributed practice (DP) and massed practice (MP) has been reported by Keppel

154 hintzman discrimination net model

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i

ii

(1964) and by Underwood, Keppel, and Schulz (1962). If the last of a series of listshaving an A-B, A-Crelationship is learned by DP (i.e., having relatively long intertrialintervals), it is learned moreslowly and retained better than if learned by MP. In thefollowing experiment, a DP condition was simulated with SAL 111 by allowingrecovery to take place between trials.

Lists A-B and A-C of Experiment 13 were again used. Parameters were: a = .30,b = .50, c = .15, d = .30. List A-B was mastered in the usual manner(MP), followedby either MP or DP (20 subjects each) during the learning of list A-C. In the DPcondition, recovery was possible between learning trials (_T = 1), but not in the MPcondition. Mastery of the second list was followed in both conditions by a longretention interval (T = 9), and then by relearning of list A-C.

The mean numbers of errors per subject during the original learning of list

A-C,

trial 2 until mastery, were: MP, 5.90; DP 11.55. This shows a clear superiority forMP in acquisition. The meanerrors due toPI on trial RL- 1 were: MP, 2.75

;

DP, 1 . 15—showing that learning by DP increasedresistance to PI. Thus, the major effects of DPon acquisition and retention of an A-C list were simulatedby the model.

Again, SAL 111 may be compared with unlearning theory as an explanation for thefindings. According to the unlearning or extinction hypothesis (Underwood et al.,1962), A-B associations are extinguished duringA-C learning. Intertrialrest intervalsin the DP condition allow the extinguished associations to recover, interfering withA-C acquisition. But because of this interference, the A-B associations mustrepeatedly be extinguished, and this results in a more permanent extinction forcondition DP than for condition MP. Hence, spontaneousrecovery of A-B associations(PI) is greater after MP than after DP learning of the A-C list.

In SAL 111, the same results are produced by stimulus discrimination learning.In the MP condition, perfect A-C performance can be achieved either by buildingnew test nodes to bypass interfering B responses or by displacing B responses fromthe topmost PDS positions. The latter method is inefficient in the DP condition,however, as there is some probability that suppressed B responses will recoverbetween trials. When a B response recovers, it causes an error, interfering with A-Cacquisition. The error, in turn, mayproduce (with probability a) further discriminationlearning. A-C learning by DP thus results in a more elaborate discrimination net andfewer PDS hierarchies that contain more thanone response image. More PI is possibleafter MP because there are more B responses available to recover and displace A-Cassociates.

The present hypothesis, then, is that DP results in better retention because itproduces more stimulus learning. From this analysis, three further predictions canbe made. In the A-B, A-C paradigm, if one group learns the A-C list by DP andanother learns itby MP, DP learning shouldresult in: (1) poorerA-Brecall in MMFR,(2) better backward recall of the A-C list, and (3) more resistance of A-C to RI fromsubsequent learning.

Experiment 16. Response Latencies

In EPAM, response latencies are determinedchiefly by sorting time (Feigenbaum,1959). The moretests made during thesorting ofa stimulus, the longer it takesEPAMto retrieve the response. This assumption leads to the prediction that, as a PA listis mastered and the discrimination net grows deeper, mean response latency willincrease exponentially. In fact, human data (Millward, 1964; Suppes, Groen andSchlag-Rey, 1966) show only a sharp initial increase in mean latency; this is followedby a gradual and consistent decrease. Obviously, mere sorting time in a growing netcannot account for these findings. Although SAL was not intended as a model ofresponse latencies, it happens that the PDS mechanism of SAL 111 provides anunexpected explanation. This is illustrated by the following experiment.

Thirty simulated subjects were run on the list shown in Table 1. Parameters were:_ = .20, b = .50, c = .10, and the maximum PDS depth was arbitrarily set at 4.Each time the model sorted a stimulus to a terminal node it output the response atthe top level of thePDS, and also indicated the depth of thePDS—that is, the numberof levels occupied by stored responses. Mean PDS depth is plotted as a function oftrial number in Fig. 10. The sharp initial rise occurs as PDS's are being filled; thesubsequentdecline, approaching a limitof 1.0, results from growth ofthe net, graduallyapproaching a one-to-one stimulus-response mapping. By manipulating the maximumpossible PDS depth one could raise or lower the curve somewhat, but this would notchange its general shape. The curve of Fig. 10 looks much like the mean latencycurve obtained by Suppes et al. (1966). Moreover, an analysis of mean PDS depthconditionalized on errors and successes showed error values to be considerably largerthan success values, and this corresponds to differences observed in latency data.

From these results, it appears that SAL 111 may be applicable to PA responselatencies without the additionof a new mechanism. However, somerationale is neededfor identifying latency with PDS depth. Several rationales are possible; perhaps thesimplest is to assume that before the response is produced an exhaustive scan of alloccupied PDS levels takes place. Alternatively, the correspondence between moreresponses in a PDS and longer response times could be attributed to competition andpartial blocking among these responses at the time of retrieval. Whicheverinterpretation one chooses, he must assume that the process takes more time thandoes stimulus sorting.

DISCUSSION

The computer simulation approach to theory construction used here may bebriefly contrasted with "verbal" and with "mathematical" theories of human learning.On the one hand, verbal theories, which have predominated in the functionalisttradition, have developed a rich collection of explanatoryconcepts to deal with the

156 discrimination net model

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phenomena of human learning. The most prevalent theoretical approach to verballearning, the Hullian-interference approach (e.g., Postman, 1961, 1963), has evolvedthrough the interaction of theory and experimentation more as a set of workinghypotheses than as an integrated theory. Such "verbal" theories have been criticizedon several grounds: (a) lack of criteria for deciding which of several explanatoryconcepts are relevant to a particular result, (b) a consequent lack of parsimony, and(c) lack of demonstration that the explanations are internally consistent, completeor adequate. In contrast, a theory specified as a computer program can be "run"to see whether it will behave properly, whether enough parts and their operationshave been specified in sufficient detail, whether there are any unsuspected contra-dictions, etc. The assumptions must be complete and precise, and the derivationsnecessarily follow unambiguously from the assumptions. It is interesting that severalof the present model's successes (and some of its failures) came as a surprise to thoseworking with SAL—a fact which points out some of the flaws inherent in the "verbal"method of deriving predictions.

On the other hand, mathematical models, while well specified and quantitativelyprecise, seem at present to lack generality and scope. Typically, a particular modelhas a very restricted range of application—it is "situation specific"—and severaldifferent models would be needed to deal with the range of situations considered inthis paper. Mathematical models for verbal learning are also often unable to deal with

many of the complexities of a given situation. For example, acquisition of a singleitem is usually considered in vacuo, and thereare no very convincing ways to representitem interactions, which enter into so many of the predictions of the SAL program.

Finally, we may contrast the theoretical work presented here with other simulationattempts. The computer, of course, makes it possible for the theorist to postulatean extremely complex system of interactingmechanisms; predictions can be generatedno matter how complicated the program. For this reason, simulation models areoften constructed with little regard for parsimony. Points of ignorance are routinelyfilled in with fanciful details for which there is no evidence, and which are virtually

as part of the program. One consequence has been that programs tend tobecome very lengthy and complicated, to the point where communication to non-specialists in computerprogramming has been hindered (cf. Hilgard and Bower, 1966;Reitman, 1965). In theSAL model, an attempt has been made to avoid theseproblems;points of ignorance are stated as probabilities, and new mechanisms are added onlywhen tests of the model have found them necessary. It is hoped that the simplicityof the model will facilitate communication and make the theoretical notions moreaccessible to others.

It was suggested earlier that stimulus-discrimination learning processes had beenrelegated to a minor theoretical role before their explanatory power had been fullyexplored. It is primarily these processes, represented by the discriminationnet, whichallow SAL and EPAM to account for oscillation, stimulus generalization,retroactive

interference,

and the effects of stimulus similarity on list difficulty. EPAM containsassumptions not present in SAL, which make it applicable to problems of seriallearning, response integration, and presentation rate, and which allow it to predictnegative transfer. At the same time, SAL is able to simulate some phenomena thatpresentversions of EPAM cannot, mainly through the use of overlearning assumptions(SAL II)and the storage of multiple associations(SAL III).Although all subprocessesin SAL are all-or-none, it is consistent with a number of facts (such as the effects ofoverlearning on retention) which have always seemed to prove that an incrementalhabit strength notion was needed. At least qualitatively, SAL seems to agree withthe main findings on both sides of the "incremental vs all-or-none" controversy,including the response patterns obtained in the RTT studies of Estes (1960), theincreasing conditional probability that repeated reinforcements will produce a firstcorrect response to a failed item(Battig, 1962; Underwood andKeppel, 1962; Wollen,1962), and the outcomes of recognition vs recall and second guess experiments, aswell as the successes and failures in finding precriterion stationarity.

In the 16 experiments reported in this paper, a number of predictions were derivedfrom three versions of the SAL model. Not all of these predictions, of course, can betraced directly to the discrimination net structure; some result from specific learningassumptions of SAL I or II; others are produced by thePDS mechanism of SAL III;and still others arise from interactions among different processes. It should be instruc-

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tive, therefore, to summarize by indicating which processes are responsible for eachof the major predictions. This information is presented in the following outline. Eachprediction is described only briefly, with reference to the section of the paper wherea more detailed discussion may be found. In addition, each prediction is followed bya (+) or (—), indicating whether or not it is consistent with results reported in theverbal learning literature.

Predictions Arising Primarily from the Discrimination Net Memory Structure1. Increase in list difficulty with increase in intralist stimulus similarity

[Experiment 1] (+).2. Effects of the number of response alternatives on precriterion stationarity

[Experiment 2] (+).3. Effects of the spacing of item repetitions on learning and retention

[Experiment 4] (+).4. No differences in efficiency of whole, part, and repeated part learning methods

[Experiment 5] (— ).5. No effects of list length on learning rate [Experiment 6] (—).6. Effects of interlist similarity on RI [Experiment 7] (+).7. Faster relearning than original learning [Experimental7] (+ ).8. Positive transfer in A-B, A-C paradigm [Transfer Paradigms] (— ).

Predictions Arising Primarily from Learning Assumptions of SAL I1. Effects of number of response alternatives on learningrate [Experiment 2] (+).2. Probability matching in probabilistic PA task [Experiment 3] (— ).

Predictions Arising from the Interaction of the Discrimination Net and the OverlearningAssumptions of SAL II

1. Effects of degree of original learning on retention [Experiments 7, 8] (+).2. Pattern of findings relating degree of interpolated learning to total RI, types of

errors, and relearning rate [Experiment 9] (+).

Predictions Arising Primarilyfrom thePDS Mechanism of SAL 1111. Increase in PI and decrease in RI with time [Experiment 14] (+ ).2. Superiority of retention following distributed practice [Experiment 15] (+).

Predictions Arising from the Interaction of the Discrimination Net and the PDSMechanism

1. Superiority of recognition to recall [Experiment 11] (+).2. Evidence of learning on second and third recall attempts [Experiment 12] (+).3. General pattern of findings in studies of unlearning with the MMFR procedure

[Experiment 13] (+).4. Changes in response latencies during learning [Experiment 16] (+).

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Received: November 29, 1966

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