JOURNAL OF MEMORY AND LANGUAGE 32, 517-535 (1993)

Splitting the Differences : A Structural Alignment View of Similarity

ARTHUR B . MARKMAN AND DEDRE GENTNER

Northwestern University

The similarity of a pair increases with its commonalities and decreases with its differences(Tversky, 1977, Psychological Review, 79(4), 281-299) . This research addresses how thecommonalities and differences of a pair are determined . We propose that comparisons arecarried out by an alignment of conceptual structures . This view suggests that beyond thecommonality-difference distinction, there is a further distinction between differences re-lated to the common structure (alignable differences), and differences unrelated to thecommon structure (nonalignable differences) . In two experiments, subjects were asked tolist commonalities and differences of word pairs and/or to rate the similarity of these pairs .Three predictions for this task follow from the structural alignment view : (I) pairs with manycommonalities should also have many alignable differences, (2) commonalities and alignabledifferences should tend to be conceptually related, and (3) alignable differences shouldoutnumber nonalignable differences . The data support the structural alignment proposal .The implications of these findings for theories of similarity and of cognitive processes thatinvolve similarity are discussed . C 1993 Academic Press, Inc .

Similarity is a vital part of cognitive pro-cessing . Models of categorization (Medin &Schaffer, 1978 ; Rosch & Mervis, 1975 ;Smith & Medin, 1981), skill acquisition(Singley & Anderson, 1989 ; Thorndike &Woodworth, 1901), transfer (Logan, 1988),and affect (Kahneman & Miller, 1986) as-sume that new items are processed basedon their similarity to previous experiences .Because of this centrality, similarity itselfhas been the focus of extensive research .

Much current research in similarity hasits roots in Tversky's seminal contrastmodel (Tversky, 1977) . The contrast modelformalized the fundamental insight that the

Please send all correspondence and reprint requeststo Arthur B . Markman, Department of Psychology,Northwestern University, 2029 Sheridan Rd ., Evan-ston, IL 60208 . After July 1, 1993, send to Arthur B .Markman, Department of Psychology, Columbia Uni-versity, Schermerhorn Hall, New York, NY 10027 .This work was supported by NSF Grant BNS-87-20301 and ONR Grant N00014-89-J1272 given to thesecond author . We thank Linda May for tirelesslytranscribing the protocols in this study . We also thankLarry Barsalou, Evan Heit, Mutsumi Imai, Eva Kit-tay, Laura Kotovsky, Doug Medin, Mary Jo Ratter-mann, Lance Rips, Ed Wisniewski, Phil Wolff, thewhole Similarity and Analogy group, and three anon-ymous reviewers for helpful comments and sugges-tions during the evolution of this project .

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psychological similarity of a pair of objectsincreases with its commonalities and de-creases with its differences . However,there is no general procedure for decidingwhat counts as a commonality and whatcounts as a difference . The scenes in Fig . Iillustrate this problem . When determiningthe similarity of these pictures, we couldfocus on the similarity between the two ro-bot arms . Given this match, the fact thatone robot arm is repairing something whilethe other is being repaired would be a dif-ference . Alternatively, we could focus onthe similarity that both scenes depict "re-pairing." In this case, the fact that the robotperforms the repair in one scene while aman performs the repair in the other scenewould be a difference . To model similarity,we need an account of the comparison pro-cess that arrives at the commonalities anddifferences between two items .

In this paper, we will outline a structuralalignment account of similarity in whichthe commonalities and differences of a pairare determined via the comparison of struc-tured representations (Gentner & Mark-man, in press ; Goldstone, Medin, & Gent-ner, 1991) . This approach is based on pre-vious research in analogical reasoning that

0749-596X/93 $5 .00Copyright ® 1993 by Academic Press . Inc .All rights of reproduction in any form reserved .

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has focused on methods for finding corre-spondences between representations(Gentner, 1983, 1989 ; Holyoak & Thagard,1989) .

STRUCTURE IN SIMILARITY

The approach here is an extension ofGentner's (1983, 1989) structure-mappingtheory of analogy . The structural alignmentprocess takes a pair of structured represen-tations and computes the correspondencesbetween them by seeking the maximalstructurally consistent match (Gentner,1983, 1989 ; Falkenhainer, Forbus, & Gent-ner, 1986, 1989) . A structurally consistentmatch is one that has one-to-one correspon-dences and parallel connectivity . One-to-one matches are those for which each ele-ment (e .g ., attribute, relation or object)' inone representation is placed in correspon-dence with at most one element in the otherrepresentation . Parallel connectivity ap-plies when the arguments of correspondingpredicates can themselves be placed in cor-respondence . According to this view, ob-ject mappings are determined not only onthe basis of their intrinsic similarities, butalso on the basis of their playing similarroles in like relational structures. Finally,

' Predicates that connect two or more arguments(e .g ., repair(x,y)) are called relations . For example,the central action in the top scene of Fig . 1 could berepresented as repair(robot, car) . This notation explic-itly encodes the connection between the action beingperformed and the objects involved in the action . Thearguments of a relation can be objects, as here, orother predicates . Relations taking other relations asarguments (higher-order relations) are important be-cause they represent causal or logical connections be-tween first-order assertions . In addition to relations,there are predicates that have only one argument . Wecall these predicates attributes, because they often de-scribe properties of particular objects (e .g ., red(carl)),These distinctions are psychological, not logical . Forexample, the same information (e .g ., that carl is red)can be represented as a relation (e .g ., color-of(carl,red)), as an attribute (e .g ., red(carl)), or as afunction (e .g ., color(carl) = red) . Each of these rep-resentations captures a different psychological inter-pretation of a situation, The representations that weoffer here are intended as typical construals .

mappings involving coherent higher-ordermatches (i .e ., systematic mappings) arepreferred to correspondences involvingonly isolated relational matches .

For example, the match between the pic-tures in Fig. I could be organized aroundthe relational similarity that both scenes de-pict something repairing something else .On this interpretation, parallel connectivityrequires that the robot arm in the first scenebe placed in correspondence with the manin the second scene, because both are re-pairing something. Likewise, the car in thefirst scene is placed in correspondence withthe robot arm in the second scene, becausethey are both being repaired . Despite theperceptual similarity between the robotarms, the robot arm in the first scene can-not be placed in correspondence with boththe man and the robot arm in the secondscene because of the one-to-one mappingconstraint .

The calculation of structurally consistentmatches is a computationally viable pro-cess . For example, the Structure-MappingEngine instantiates structural alignmentwith a local-to-global alignment algorithmthat first matches all identical predicates(and functions) in two representations(Falkenhainer et al ., 1986, 1989) . This ini-tial mapping may be inconsistent, but in thenext phase these local matches are coa-lesced into a global structure . Structuralconsistency is enforced by requiring thatthe arguments of matching predicates alsomatch and that each object in one represen-tation is placed in correspondence with atmost one object in the other representation .As in human comparison, this algorithmmay yield more than one consistent inter-pretation for a pair such as the robot pic-tures . Forbus and Gentner (1989) discusshow competing matches may be evaluated .A local-to-global process has been incorpo-rated into other models of comparison aswell (Goldstone & Medin, in press ; Hof-stadter, 1984 ; Hofstadter & Mitchell, inpress ; Holyoak & Thagard, 1989) .

The structurally consistent match yielded

Grant s Robot Repair Service

by the alignment process is used to deter-mine the commonalities and differences ofthe pair . These comparisons give rise tothree types of elements : matches, mis-matches that are connected to the matchingstructures, and mismatches that are not re-lated to the matching structures . For exam-ple, in the scenes in Fig . 1, the objectscould be placed in correspondence basedon the relational similarity of the scenes .Then, the fact that both scenes depictsomething repairing something else wouldbe a commonality of the scenes . Further-more, this interpretation places some dis-similar objects in correspondence . For ex-ample, in Fig . 1 the robot repairing the carin the top scene is mapped to the man re-pairing the car in the bottom scene . Be-

DIFFERENCES IN SIMILARITY

Jack's Robot Repair Service

SpareParts

T : ° 1

i

e t'~\

FIG . 1 . Sample pair of scenes containing cross-mappings, like those used by Markman and Gentner(1990) .

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cause this difference occurs within ele-ments connected to the common structure,we refer to it as an alignable difference(AD) . In contrast, other differences are in-dependent of the matching structure . Forexample, the box of spare parts in the bot-tom scene does not match any object in thetop scene. We call this type of difference anonalignable difference (NAD) .

In the experiments that follow, we willexamine four predictions of structuralalignment . First, there should be a numeri-cal link between commonalities and align-able differences . Because alignable differ-ences are defined in terms of correspon-dences, pairs with many commonalitiesshould also have many alignable differ-ences and pairs with few commonalities

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should have few alignable differences . Sec-ond, alignable differences should be morenumerous than should be nonalignable dif-ferences . This prediction results from theassumption that similarity comparisons fo-cus on matching information . Third, thereshould be a conceptual relationship be-tween the commonalities and alignable dif-ferences . This prediction is derived fromthe fact that links between predicates andtheir arguments represent conceptual con-nections between elements . The fourth pre-diction, which also follows from Tversky(1977), is that the similarity of a pair in-creases with its commonalities and de-creases with both its alignable and non-alignable differences.

We can contrast these predictions withthose of a feature matching view that as-sumes that mental representations consistof sets of independent features . On thisview, commonalities are the intersection ofthe feature sets, and differences are thosefeatures not in the set intersection : there isno distinction between alignable and non-alignable differences . Pairs with many com-monalities are predicted to have few differ-ences, and pairs with few commonalitiesare predicted to have many differences . Fi-nally, commonalities and differences arenot predicted to be conceptually related .

EXPERIMENT I

To test these predictions, we asked sub-jects to list commonalities and differencesof 20 highly similar word pairs and 20 highlydissimilar word pairs . Subjects were given1 min to list either as many commonalities,or as many differences (but not both) asthey could for each word pair . According tothe predictions of structural alignment out-lined above, more commonalities and align-able differences should be listed for similarpairs than for dissimilar pairs . In addition,more alignable differences should be listedoverall than should nonalignable differ-ences . Finally, similarity (as assessed byratings obtained from a separate group of

subjects) should increase with commonali-ties and decrease with differences, althoughalignable and nonalignable differences mayhave different strengths of effect .

With the commonality and differencemethodology we hope to tap the output ofthe comparison process involved in similar-ity ratings . Furthermore, this task allows usto see the kinds of features subjects believeto be relevant to particular comparisons, asopposed to attribute-listing tasks that onlymake use of properties subjects list for theitems in isolation (Tversky, 1977) . Thus,this methodology allows for the possibilitythat the features of an object that are rele-vant to a particular comparison may not berelevant for other comparisons in which thesame object is paired with something else .These advantages have led other research-ers to use a commonality and difference-listing methodology as well (Medin & Gold-stone, in press ; Tourangeau & Rips, 1991) .

Method

Subjects . Subjects in the similarity ratingtask were 22 undergraduates at the Univer-sity of Illinois . Subjects in the commonalityand difference listing task were 32 studentsfrom the same population . All subjectswere native speakers of English . They re-ceived course credit in an introductory psy-chology course for their participation .

Materials . The stimuli were 40 wordpairs : 20 highly similar pairs and 20 highlydissimilar pairs . The experimenters gener-ated the similar and dissimilar pairs, buttheir intuitions were confirmed by subjects'ratings . For the similarity rating task, tworandom orders of the words were gener-ated . Beneath each word pair was a simi-larity scale ranging from I (Highly Dissim-ilar) to 9 (Highly Similar) . There were 8word pairs on each page .

For the commonality and difference list-ing task, each word pair was printed on twowhite index cards . At the top of one cardwere the words "Commonalities of" and atthe top of the second card were the words

"Differences between ." The word pairs arepresented in Appendix 1,

Procedure . Subjects in the similarity rat-ing task were given booklets with the simi-larity rating sheets . Subjects were told thatthey would see pairs of words and wereasked to rate their similarity using the nine-point scale provided . Subjects in this taskwere run in small groups .

Subjects in the commonality and differ-ence listing task were run individually at atable with a tape recorder and a stack ofcards placed face down in front of them .Each subject was presented with 20 Com-monalities cards and 20 Differences cards .Subjects listed commonalities for 10 HighSimilarity and 10 Low Similarity pairs .They also listed differences for 10 HighSimilarity and 10 Low Similarity pairs .Thus, it took two subjects to get a completeset of listings for the entire stimulus set .Subject to these restrictions, 8 randomstimulus orders were generated .

Subjects were instructed to turn over thefirst card on the stack, and to list out loudeither the commonalities or differences ofthe pair, depending on the card's instruc-tions . There were no practice trials, as sub-jects were comfortable doing this task fromthe beginning . The experimenter timedeach trial with a watch. Each trial was ter-minated after 1 min, or 30 s of silence,whichever came sooner. Subjects were al-lowed to finish an utterance if they spokefor the full minute, but then the trial was

DIFFERENCES IN SIMILARITY

TABLE ISAMPLE PROTOCOLS FROM EXPERIMENT I

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ended . A short break was given after half ofthe trials were completed . The entire exper-iment was recorded on an audio cassettetape, which was then transcribed . A ses-sion took approximately 45 min to com-plete .Design . There were two levels of Simi-

larity (Low and High) . For the commonal-ity listings, the dependent measure was thenumber of commonalities listed . For thedifference listings, the number of alignabledifferences and nonalignable differenceswere counted, The total number of differ-ences listed was also recorded .

Scoring . The full set of transcripts wasscored by one rater who knew the hypoth-esis under study (the first author) . A ran-dom 20% subsample of the data was thenscored by a naive rater . The raters agreedon 92% of their scorings, and analysis of thedifferences yielded no consistent tendencyfor one rater to overestimate or underesti-mate the number of commonalities or dif-ferences relative to the other .

In scoring the commonality listings, onecommonality was counted for each itemthat subjects listed as true of both objects .Generally, each utterance beginning with"Both (items) are x" was counted as a sin-gle commonality . For example, in the sam-ple commonality protocol in Table 1, lineslike "They both have sirens" were countedas one commonality . Commonalities of theform "Both [items) are not x" (e.g ., Both [apolice car and an ambulance] are not grape-

Commonalities of Police Car and Ambulance (6 Commonalities)

They both have sirens . They both have lights on the top and they're both driven by people with authority .[pause] They both have preference over other cars on the road, so if you see one, you should pull over .They're both automobiles . They both have four tires .

Differences between Police Car and Ambulance (3 ADS, I NAD, 1 Word Surface Difference)

An ambulance is involved with carrying someone who is hurt to a hospital, a police car is involved withcarrying a criminal, or someone who is alleged to commit a crime to a police station or a jail . A police caris involved with law enforcement, an ambulance is involved with rescuing injured people . Police car is acar, an ambulance is usually a van . Police car usually has weapons in it, ambulance doesn't . [pause]Police car is two words, ambulance is one .

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fruits) were also scored as commonalities . ResultsIn contrast, commonalities (and differ-ences) in the surface form of the words, orof their grammatical category (e.g ., "Bothhave the letter 'a' in them" or "Both arenouns") were not counted as commonali-ties . Finally, associations between the ob-jects were not counted as commonalities(e .g ., "A police car could pass an ambu-lance on the street") .

In scoring the difference listings, we useda conservative measure of alignable differ-ences. Subjects had to make explicit or im-plicit mention of a different value alongsome dimension for both objects . Thus, "Apolice car is a car, an ambulance is a van"and "Police cars and ambulances are differ-ent kinds of vehicles" would be alignabledifferences . All other differences (e .g ., "Apolice car has weapons in it, an ambulancedoes not") were considered nonalignabledifferences . The total number of differ-ences for a pair was simply the sum of thealignable and nonalignable differences . Theprimary advantage of this criterion is that itcan be applied simply . One disadvantage ofthe criterion is that it probably underesti-mates the number of alignable differencesactually listed, because subjects could say"Cars have four wheels, and motorcyclesdon't" when they actually mean "Carshave four wheels, motorcycles have two ."However, since we predicted large num-bers of alignable differences, we preferredto err on the conservative side. Finally, wedropped items for which the subject did notknow the meaning of one of the words inthe pair, or used a different sense of theword than the one that we intended .

* p < .05 t test

As expected, the mean rated similaritywas significantly higher for pairs in theHigh Similarity group (m = 7 .4) than forpairs in the Low Similarity group (m =1 .8), t(38) = 30 .28, p < .001 . Table 2 pre-sents the mean number of commonalities,total differences, alignable differences, andnonalignable differences listed for Low andHigh Similarity pairs . As predicted, morecommonalities were listed for High Similar-ity pairs (m = 6.63) than were listed forLow Similarity pairs (m = 2 .78), t(38) =9.60, p < .001 . More alignable differenceswere listed for High Similarity pairs (m =4 .14) than were listed for Low Similaritypairs (m = 3 .32), t(38) = 3 .11, p < .005 .This evaluation was specific to alignabledifferences : fewer nonalignable differenceswere listed for High Similarity pairs (m =0.62) than were listed for Low Similaritypairs (m = 2 .07), t(38) = 5.57, p < .001 .Interestingly, the total number of differ-ences listed for High Similarity pairs (m =4.91) and Low Similarity pairs (m = 5 .23) didnot differ significantly, t(38) = 1 .40, p > .10 .As predicted, the commonalities and

alignable differences were numerically re-lated, as is evident in a correlational analy-sis. There was a significant positive corre-lation between the number of commonali-ties and number of alignable differenceslisted for each pair, r(38) = 0 .45, p < .05 . Incontrast, there was a negative correlationbetween the number of commonalities andthe number of nonalignable differencesr(38) = -0 .58, p < .05 . The correlationbetween the number of commonalities and

TABLE 2MEAN NUMBER OF LISTED PROPERTIES FOR LOW AND HIGH SIMILARITY PAIRS IN EXPERIMENT 1

Listed properties

Similarityof pair

Ratedsimilarity Commonalities

Alignabledifferences

Nonalignabledifferences

Totaldifferences

Low 1 .8 2 .78 3 .32 2 .07 5 .23High 7.4* 6 .63* 4.14* 0 .62* 4 .91

the total number of differences was not sig-nificant, r(38) = -0 .13, p > .10 .

The data also support the prediction thatalignable differences should be more nu-merous than nonalignable differences . Asshown in Table 2, more alignable differ-ences were listed than were nonalignabledifferences for both High and Low Similar-ity items. Paired t tests treating items asindividuals support this interpretation, t(19)= 15.69, p < .001 for the High Similaritypairs ; t(19) = 4 .13, p < .005 for the LowSimilarity pairs .

A regression analysis was carried out totest the assumption that similarity increaseswith commonalities and decreases with dif-ferences . Considering similarity as a func-tion of commonalities, alignable differencesand nonalignable differences we find that(using standardized regression weights)

Similarity = 0 .75 (Commonalities)- 0.06 (AD)- 0.22 (NAD) .

[1]

Thus similarity does indeed increase withthe number of commonalities and decreasewith the number of alignable and nonalign-able differences . The multiple correlationfor this equation is .87 . The finding thatcommonalities receive more weight in theregression than do either alignable or non-alignable differences is consistent with thatof previous studies of similarity that havefound that commonalities are more impor-tant to rated similarity than are differences(Krumhansl, 1978; Sjoberg, 1972 ; Tversky,1977) .

DiscussionThe results supported the view that sim-

ilarity comparison is fundamentally a pro-cess of finding aligned systems of common-alities, and that differences related to thosecommon systems (alignable differences) arepsychologically distinct from unrelated dif-ferences (nonalignable differences) . First,commonalities and alignable differenceswere numerically linked . As demonstratedby the correlation between commonalitiesand alignable differences, when a pair had

DIFFERENCES IN SIMILARITY 523

many commonalities, it also had manyalignable differences . Second, alignable dif-ferences were more numerous than werenonalignable differences . Finally, the re-gression analyses suggest that rated similar-ity increased with the number of common-alities of a pair and decreased with the num-ber of differences .

There are some aspects of Experiment 1that require clarification . First, this studyonly used pairs of High and Low similarity .Thus, the correlations we obtained may beinflated by our use of the ends of the simi-larity scale, and not the middle . In addition,words were used in either a High Similarityor a Low Similarity pair, but not both .Thus, the similarity of the pairs was com-pletely confounded with the words used .Finally, we have not yet provided any sup-port for the prediction that commonalitiesand alignable differences are conceptuallyrelated . In order to address these issues, werepeated the methodology of the first studyusing a wider range of stimuli . In addition,we performed a detailed analysis of theconceptual relationships between the listedcommonalities and differences which wepresent in Experiment 2b .

EXPERIMENT 2This study extends the first experiment

by using word pairs that span a range ofsimilarities. Similarity was manipulated byconstructing a simple ontology like thoseused by Sommers (1959), Keil (1979), andLenat and Guha (1990) . We assume that therepresentations of items that are close inthis ontology are more easily alignable thanare the representations of items that are dis-tant in the ontology . Thus, we expectedsimilarity to vary inversely with ontologicaldistance . 2

The ontology tree used in this experiment

We are not attempting to test the psychologicalreality of this ontology . Work by Gerard and Mandler(1983) has demonstrated that, at best, there are multi-ple ontological hierarchies . However, the basic as-sumption that ontologically similar pairs will be moresimilar than ontologically dissimilar pairs is still tena-ble for these stimuli .

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Thing

Tangible

Intangible

Living

Non-Living

Animal

Plant

Furniture

Vehicle

is shown in Fig. 2. Eight objects wereplaced at each leaf of the tree : four fromeach of two categories that satisfied theconstraints of that path in the tree . For ex-ample, land and air vehicles are under the"vehicles" node of the tree . The ontologi-cal distance of a pair was measured as thenumber of nodes in the tree that had to betraversed to get from one word to the other,For example, a pair consisting of two vehi-cles (e.g ., a car and a motorcycle) was ofdistance 0. A pair with a vehicle and a pieceof furniture was of distance 1, a pair with avehicle and an animal was of distance 3,and a pair with a vehicle and an abstractobject was of distance 5 . From this tree, wemade two stimulus sets of 32 word pairs .Each set had 16 pairs of distance 0 and 16pairs of distance greater than 0 . This pre-ponderance of high similarity pairs was de-sirable, because the results of Experiment 1suggested that listing commonalities anddifferences for dissimilar pairs can be diffi-cult and frustrating for subjects .

The predictions for this task are the sameas those for Experiment 1 . We expect toobtain evidence that commonalities andalignable differences are numericallylinked . We also expect to find that alignabledifferences are generally more numerousthan are nonalignable differences . In addi-tion, we should obtain evidence that simi-larity increases with commonalities and de-creases with differences . Finally, we willexamine the properties listed by subjects to

MARKMAN AND GENTNER

External

InternalEvents

Events

Events

Processes

Cognitions

EmotionsFIG . 2. Ontology used to generate stimuli in Experiment 2 .

see whether the commonalities and align-able differences are conceptually linked .

MethodSubjects . Subjects in the similarity rat-

ings task were 40 undergraduates from theUniversity of Illinois . Subjects in the com-monality and difference listing task were 44undergraduates from the University of Illi-nois . All subjects received course credit inan introductory psychology course for theirparticipation .

Materials . Two stimulus sets were gen-erated from the words we placed into theontology tree shown in Fig . 2 . Words thatwere placed in high similarity pairs (dis-tance 0) in one set, were placed in low sim-ilarity pairs (distance greater than 0) in theother set . Each stimulus set contained 16pairs of distance 0, 8 pairs of distance 1, and4 pairs each of distances 3 and 5 . 3 Eachword pair was printed on two index cards .Subjects received an equal number of com-monality and difference listings for pairs ateach distance . The complete set of materi-als is presented in Appendix 2 .

Procedure and scoring . The procedureand scoring were identical to those used in

3 Two errors were made in the creation of the stim-uli . First, one pair of distance 5 (hang glider-fear) be-came a pair of distance 3 (hang gliding-fear) . Second,the words "moral" and "promise" were each used intwo pairs of distance 0 in Set 1 and one pair of distancegreater than 0 in Set 2. For this reason, the words"secret" and "thought" did not appear in Set 1 .

the previous experiment . One rater whoknew the hypothesis under study (the firstauthor) scored the complete data set . Arandom 20% subsample of the data wasthen scored by a naive rater . The ratersagreed on 89% of their judgments . The dif-ferences in scoring did not appear to be sys-tematic .Design . This study had four within-

subject distance conditions (0, 1, 3, and 5) .The two stimulus sets were run betweensubjects . The dependent measures wereCommonalities, Alignable Differences, andNonalignable Differences .

Results and DiscussionSimilarity and ontological distance . The

assumption that the distance of a pair in theontology was inversely related to the simi-larity of the pair was supported by subjects'similarity ratings as shown in Table 3 . Aone-way ANOVA indicated that the mean-rated similarity decreased significantly asdistance in the ontology increased, F(3,60)= 25.18, p < .001 . Further analysis indi-cated that higher similarity ratings weregiven to pairs of distance 0 than to pairs ofdistance greater than 0, F(1,60) = 75.12, p< .001 . 4 No other differences were signifi-cant .

Numerical link between commonalitiesand alignable differences . The mean num-ber of commonalities and differences listedfor pairs at each ontological distance isshown in Table 3 . A one-way ANOVA on

4 The significance levels for all post hoc tests re-ported in this paper are corrected using the Bonferroniinequality .

DIFFERENCES IN SIMILARITY

TABLE 3MEAN NUMBER OF LISTED PROPERTIES FOR PAIRS AT EACH ONTOLOGICAL DISTANCE IN EXPERIMENT 2

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the number of commonalities listed forpairs at each distance indicates that thenumber of listed commonalities varied withdistance, F(3,60) = 11 .65, p < .001 . Posthoc tests indicate that significantly morecommonalities were listed for pairs of dis-tance 0 than were listed for pairs of greaterdistance, F(1,60) = 31 .36, p < .001 . Simi-larly, significantly more commonalitieswere listed for pairs of distance I than werelisted for pairs of distance 3 and distance 5,F(1,60) = 9.79, p < .05 . The number ofcommonalities listed for pairs of distance 3and distance 5 did not differ significantly,F(1,60) = 0 .83, p > .05 .

The graph in Fig . 3 shows that subjectstended to list more alignable differences forontologically close pairs than did for onto-logically distant pairs, although these dif-ferences were only marginally significant,F(3,60) = 2 .33, p = .08 . However, the pre-diction that commonalities and alignabledifferences should be numerically linked issupported by the significant positive corre-lation between the number of listed com-monalities and the number of listed align-able differences for items in this study,r(62) = 0 .71, p < .001 .

As predicted, nonalignable differencesshow a different pattern than do alignabledifferences : subjects listed increasinglymore nonalignable differences as ontologi-cal distance increased, F(3,60) = 6 .93, p <.001 . Fewer nonalignable differences werelisted for pairs of distance 0 than were forpairs of greater distance, F(1,60) = 17 .2 1, p< .001 . Similarly, fewer differences werelisted for pairs of distance 1 than were forpairs of distance 5, F(1,60) = 7 .77, p < .05 .

Listed properties

Distanceof pair

Ratedsimilarity Commonalities

Alignabledifferences

Nonalignabledifferences

Totaldifferences

0 5 .1 3 .56 2 .67 0 .73 3 .401 3 .0 2 .50 2 .34 1 .01 3 .353 2 .0 1 .17 2 .18 1 .25 3 .435 1 .6 0 .48 1 .65 1 .71 3 .36

526 MARKMAN AND GENTNER

-x- AD

0 NAD

-•- Total

0

1

3

5

Distance in the Ontology

FIG . 3 . Total number of listed differences, as well as number of alignable and nonalignable differ-ences at each ontological distance in Experiment 2 .

No other differences were significant . Fi-nally, no correlation was found between thenumber of listed commonalities and thenumber of listed nonalignable differencesfor each pair, r(62) = -0 .12, p > .10 .When combined, the total number of differ-ences listed did not differ significantly atdifferent ontological distances, F(3,60) =0 .01, p > .10. However, the correlation be-tween commonalities and total differenceswas significantly greater than 0, r(62) _0.53, p < .05 .Alignable differences more numerous

than nonalignable differences . As pre-dicted, significantly more alignable differ-ences were listed overall (m = 2.41) thanwere nonalignable differences (m = 0.98),t(63) = 9.76, p < .001 (paired t test treatingitems as individuals) . As shown in Table 3significantly more alignable differencesthan nonalignable differences were listedfor pairs of distance 0, t(31) = 9.65, p <.001 ; distance 1, t(15) = 5.80, p < .001 ; anddistance 3, t(8) = 3 .36, p < .05 . For thehighly dissimilar pairs of distance 5, the

number of listed alignable and nonalignabledifferences did not differ significantly, t(6)=0.34,p> .10 .Commonalities, differences and rated

similarity . The relationship between ratedsimilarity and listed commonalities and dif-ferences was examined in a regression anal-ysis. We found that

Similarity = 0 .67 (Commonalities)- 0 .16 (AD)- 0.52 (NAD) .

[2]

Thus, as for Experiment 1, rated similarityincreased with commonalities and de-creased with both alignable and nonalign-able differences . Once again, the regressioncoefficient for nonalignable differences waslarger than was the coefficient for alignabledifferences . The multiple correlation forthis regression analysis was 0.82 .

Concrete and abstract pairs . One strik-ing aspect of the data was that subjects hadmuch greater success listing properties forconcrete pairs than for abstract pairs . Sub-jects listed significantly more common-

alities for concrete pairs (m = 4 .04) than forabstract pairs (m = 1 .68), t(55) = 6 .61, p.001 . 5 Subjects also listed more alignabledifferences for concrete pairs (m = 3 .23)than for abstract pairs (m = 1 .75), t(55) =7 .64, p < .001 . In addition, they listed morenonalignable differences for concrete pairs(m = 1 .23) than for abstract pairs (m =0 .54), t(55) = 5 .23, p < .001 . Although wedid not predict this result, many studieshave found that subjects are more fluentwith concrete concepts than they are withabstract concepts (Schwanenflugel, 1991) .We analyzed the data for abstract and con-crete pairs separately to determine whetherthe overall pattern was the same for bothsets of items .

Overall, the same general pattern of datawas obtained for both abstract and concretepairs. To illustrate, Table 4 presents thecorrelation between listed commonalitiesand listed alignable and nonalignable differ-ences . These correlations are presented forall the data combined, and also separatelyfor abstract and concrete pairs . These cor-relations for abstract and concrete pairs arealways of the same sign as for the data as awhole . The only difference we found wasthat the correlation between commonalitiesand nonalignable differences was signifi-cantly less than 0 for concrete pairs, butnonsignificant for abstract pairs . The re-gression analyses relating similarity torated commonalities and differences alsoshow a similar pattern as the combineddata . For concrete pairs, the regressionequation was

Similarity = 0.54 (Commonalities)- 0 .04 (AD)- 0 .40 (NAD),

[31

and for abstract pairs the regression equa-tion was

s Pairs of distance 5 were not used in these analyses,because they contain one abstract and one concreteword. In general, subjects listed very few commonal-ities or differences for these items .

DIFFERENCES IN SIMILARITY

TABLE 4CORRELATIONS BETWEEN NUMBER OF LISTEDCOMMONALITIES AND NUMBER OF LISTED

ALIGNABLE AND NONALIGNABLE DIFFERENCES FORALL DATA, AND SPLIT BY ABSTRACT AND

CONCRETE PAIRS

527

* p < .05

Similarity = 0.63 (Commonalities)- 0 .21 (AD)- 0.42 (NAD) .

[4JThus, for both concrete and abstract pairs,rated similarity increases with commonali-ties and decreases with differences .

Conceptual link between commonalitiesand alignable differences . Inspection ofsubjects' protocols supports the claim thatcommonalities and alignable differences areconceptually linked . For example, 92% ofthe subjects listing commonalities for thepair bus-bicycle said that both havewheels, but 82% of the subjects listing dif-ferences said that buses have more wheelsthan do motorcycles . Similarly, 80% of thesubjects listing commonalities for the pairtoad-cardinal said that both are animals,while 45% of the subjects listing differencesnoted that toads are amphibians, while car-dinals are birds . In Experiment 2b, we ex-amined this pattern more systematically .We assembled all of the commonalities anddifferences of the concrete pairs that werelisted by at least three subjects and askedother subjects to match the commonalitiesand differences that they felt were concep-tually related . According to structuralalignment, subjects should often link align-able differences with commonalities, butshould rarely link nonalignable differenceswith commonalities . Note that a simple fea-tural view does not predict any relation-ships between commonalities and differ-ences .

Pair type

CorrelationAlldata

Concreteonly

Abstractonly

r(Comm,AD) 0.71* 0 .38* 0.51*r(Comm,NAD) -0.12 -0.62* -0.18

528

EXPERIMENT 2bMethod

Subjects . Subjects were 12 undergradu-ates at Northwestern University who re-ceived course credit in an introductory psy-chology course for their participation .Materials . This study included common-

alities and differences from 26 of the 28 con-crete pairs from Experiment 2 . 6 For eachitem, every commonality and differencelisted by at least three subjects in Experiment2 was written on an individual index card .

Procedure . Half the subjects were givena stack of cards corresponding to the com-monalities of one of the items (the other halfof the subjects performed the reverse task) .The difference cards were spread haphaz-ardly on the table in front of the subject .For each commonality card, subjects wereasked to point to all of the differences thatthey felt were conceptually related to thatcommonality. Subjects were told explicitlynot to select items as related simply be-cause they had the same number of words,or used the same letters . They were told tofeel free to say that none of the pairs wererelated . When subjects completed this pro-cedure for all of the commonalities for agiven pair, they were given the stack ofcards for the next pair, and the procedurewas repeated .Design . All subjects described the rela-

tionship between commonalities and differ-ences for all pairs . Stimuli were presentedin a different random order for each sub-ject .

Results and Discussion

To assess the claim that commonalitiesand alignable differences should be concep-tually related, we counted only those com-monality-difference pairs that 9/12 (75%) of

6 Two of the concrete items did not have any com-monalities listed by at least three subjects . The ab-stract items were excluded from this study, becausesubjects listed few properties for abstract items, sothere were few commonalities or differences listed bymore than three subjects for these items .

MARKMAN AND GENTNER

the subjects selected . This conservative cri-terion biases our results against the possi-bility that subjects simply selected somepairs at random because of the demands ofthe task . In all, there were 688 possiblecombinations of commonalities and differ-ences, and, on average, subjects found re-lationships between 104 (15%) pairs of com-monalities and differences . Using a bino-mial distribution with the probability ofselecting a commonality and difference as0 .20, the probability of a particular com-monality and difference being selected by 9or more subjects is approximately .0001 .

Despite the low chance probability, therewere many conceptually related common-alities and differences : 36 pairs of common-alities and differences were deemed relatedby at least 9 subjects . These items are pre-sented in Appendix 3 . Indeed, 21/26 (81%)of the pairs had linked commonalities anddifferences . The central hypothesis thatcommonalities and alignable differenceswould be conceptually related was alsosupported . Of the 36 pairs of related com-monalities and differences, 34 (94%) relateda commonality and an alignable difference,even though alignable differences made uponly 79% of the differences included in thestudy .'

An examination of the 36 pairs indicatessome interesting regularities . Of thesepairs, 10/36 (28%) turn on taxonomic con-nections (e .g ., Both [roses and pines] areplants/Roses are flowers, pines are trees) .Nine of the 36 pairs (25%) involve func-tional relations (e .g ., Both [chairs anddressers] are useful to man/Chairs are forsitting, dressers hold clothes) . Seven of the36 related (19%) pairs turn on part-wholerelations (e .g ., Both [cars and motorcycles]have wheels ; Cars have four wheels, mo-torcycles have two wheels) . These three

' The same pattern emerges if we consider all pairsdeemed related by only 6/12 subjects . Under this cri-terion, there are 67 pairs of related commonalities anddifferences, of which 61 (91%) included a commonalityand an alignable difference .

categories-taxonomic relations, functionsand part-whole relations-may be perva-sive relational types that provide align-ment, even between dissimilar items .

GENERAL DISCUSSION

Commonalities, Differencesand Alignment

The results found here provide evidencefor the view that similarity comparisons in-volve the alignment of structured represen-tations. Our first prediction was that com-monalities and alignable differences wouldbe numerically linked . In both experiments,we found that pairs with many commonali-ties also had many alignable differences,while pairs with few commonalities had fewalignable differences . This pattern wasmost evident in the strong positive correla-tions between the number of listed com-monalities and alignable differences in bothstudies . Second, we predicted that com-monalities and alignable differences wouldbe conceptually related . In Experiment 2b,we found conceptual relationships betweenmany commonalities and alignable differ-ences, and few relationships between com-monalities and nonalignable differences .Third, we predicted that alignable differ-ences would be more numerous than wouldnonalignable differences . In both experi-ments, more alignable differences werelisted than were nonalignable differences .Finally, our results were consistent withprevious research (Tversky, 1977), in thatrated similarity increased with the com-monalities of a pair and decreased with thedifferences . Regression analyses in bothexperiments supported this claim .

As described above, a simple featuralmodel of similarity would make differentpredictions for this task . If items are repre-sented as collections of independent fea-tures, similar pairs should have manycommonalities and few differences, whiledissimilar pairs should have few common-alities and many differences . Further, sincethis view makes no distinction between

DIFFERENCES IN SIMILARITY 529

alignable and nonalignable differences,there is no basis for predicting the patternsof correlation found here . Finally, on thisaccount, we would not expect to find rela-tionships between commonalities and dif-ferences . Thus, an independent featuresmodel does not provide a satisfying accountof our results . Our findings suggest thatsimilarity comparisons operate across rep-resentations consisting of interconnectedelements rather than across representationsconsisting of independent elements .

One potential weakness of this method-ology is that we cannot identify the proper-ties listed by subjects as the ones they ac-tually use when rating similarity (or whenperforming some other task that involvessimilarity) . Further research will have toaddress whether our belief that the proper-ties listed by subjects in the commonalityand difference-listing task are those that areused as the basis for their similarity judg-ments .

Similarity and Structural Alignment

These data are consistent with an emerg-ing view that similarity involves the align-ment of conceptual structures (Medin,Goldstone, & Gentner, in press ; Gentner &Markman, in press) . For example, it hasbeen demonstrated that similarity compari-sons are sensitive to relations in stimuli .Rattermann and Gentner (1987) found thatstories with similar plots and different char-acters (and hence common relational struc-tures) were often rated as more similar thanwere stories with different plots and similarcharacters . Similarly, proverbs with similarmorals and different surface objects weregenerally given higher similarity ratingsthan were proverbs with different moralsand similar surface objects (Schumacher &Gentner, 1987) . In addition, it has beendemonstrated that attributes and relationsare psychologically distinct (Goldstone etal ., 1991) . They found that adding a newrelational commonality to a pair (e .g ., mak-ing the shading of all items in a configura-

530

tion the same) was more effective when thepair already had many relational common-alities (e .g ., both configurations were sym-metric) than when it was added to a pairthat shared mostly attribute commonalities(e.g., same patterns on objects) .

Additional research has demonstratedthat similarity comparisons heighten sensi-tivity to matching relational structure(Markman & Gentner, 1990, in press) . Sub-jects were presented with pairs of sceneslike those in Fig . 1 . These scenes containeda cross-mapping (Gentner & Toupin, 1986) :perceptually similar objects (e .g ., the robotarms) played different relational roles ineach scene . In one condition, the experi-menter pointed to the cross-mapped objectin one scene (e .g ., the robot arm) and askedthe subject to select the object in the otherscene that went with that object . Subjectsgenerally selected the perceptually similarobject (e .g ., they mapped the robot arm tothe other robot arm) . A second group ofsubjects rated the similarity of the scenesbefore doing the same one-shot mappingtask. These subjects selected the objectplaying the same relational role signifi-cantly more often than did the first group(e .g ., they mapped the robot arm to the manrepairing the robot) . This finding suggeststhat similarity comparisons involve struc-tural alignment .

Not only do comparisons promote a fo-cus on relations, but these comparisonsgenerally yield structurally consistent map-pings . Spellman and Holyoak (1992) gavesubjects the premise that the conflict be-tween Iraq and the United States was sim-ilar to that of World War II . They askedsubjects who corresponded to George Bushif Saddam Hussein corresponded to Hitler .Subjects who said that Bush was likeRoosevelt also tended to say that theUnited States in the recent conflictmatched to the United States in World WarII . In contrast, subjects who said that Bushwas like Churchill also tended to say thatthe United States in the recent conflictmatched Great Britain .

MARKMAN AND GENTNER

It has also been shown that the impor-tance of a particular match to similarity isrelated to the connection between that fea-ture and other correspondences . Goldstoneand Medin (in press) presented subjectswith pairs of scenes each containing twoschematic butterflies . For these stimuli,they defined a match-in-place as a featurematch between butterflies that would beplaced in correspondence based on theprobable overall alignment . A match-out-of-place was a cross-mapped featurematch : one occurring between butterfliesthat would not have been placed in corre-spondence based on overall similarity .They found that matches-in-place had agreater impact on rated similarity thanmatches-out-of-place . A parallel findingwas obtained by Clement and Gentner(1991), who demonstrated that the contri-bution of a pair of matching facts to thestrength of an analogy was greater when thecausal antecedents of the facts alsomatched than when they did not match .The work by Clement and Gentner (1991)

also demonstrated that systems of con-nected relations are a crucial determinantof further analogical inferences . They pre-sented subjects with pairs of stories thatwere analogically similar (e.g ., an organismthat eats rock, and a robot probe that takesin data) . The base story had two key factsthat had no corresponding facts in the otherstory, but which could readily be mappedto the target story . One of these facts wasconnected to a causal antecedent thatmatched a fact in the other story, but theother had no matching causal antecedent .In a free prediction task, in which subjectswere asked to predict some new fact aboutthe second story, subjects were signifi-cantly more likely to project the causallyconnected fact than the unconnected fact .

The Role of Structural Alignment inCognitive Processes

Although the present experiments pro-vide evidence that similarity judgments in-

volve an alignment process, subjects rarelyneed to put a rating on their feelings of sim-ilarity, and determining the degree of simi-larity is generally not the end goal of theircognitive processing . Rather, subjects of-ten make comparisons to subserve othercognitive processes including categoriza-tion and decision making . In the followingsections, we discuss the role of alignmentand the distinction between alignable andnonalignable differences in other cognitiveprocesses .

Alignment and Categorization

Categorization is an area for which com-parisons are crucial . When a new item isencountered, the features of the new exem-plar must be compared to the features ofstored category representations (be theyexemplars or prototypes) . Alignment ismodeled in different ways . In vector mod-els of categorization, the alignment of fea-tures is based on the position of featureswithin the vector (Estes, 1986 ; Gluck &Bower, 1988 ; Hintzman, 1986) . In modelsbased on mental distance, alignment takesplace via positions in a mental space(Nosofsky, 1986). For models based on fea-ture lists, identical features are placed incorrespondence (Barsalou & Hale, 1993) .All of these alignment processes assumeless complex representations than doesstructural alignment . Simplification of thealignment process is a valuable assumptionfor these models, because it allows them tofocus on other factors that are important tocategorization . For example, it is easier tofocus on the role of cue validity in categorylearning when the alignment of features isassumed to be automatic . Consistent withthis assumption, the stimuli in many studiesof categorization are explicitly designed tohave a limited number of easily alignabledimensions. (See Wisniewski & Medin (inpress) for a review of this work .)

However, in the general case, the rele-vant features of new items may not be im-mediately obvious . In these cases, a more

DIFFERENCES IN SIMILARITY

complex alignment process that allows ele-ments to be placed in correspondencebased on their position in a matching rela-tional structure may assist categorization .Structural alignment may be particularlyimportant when categorizing novel exem-plars. For example, Wisniewski and Medin(in press) have examined the way collegestudents categorize children's drawings .This work suggests that features must beconstructed during categorization, and thatoften elements in two drawings are placedin correspondence because they play thesame role in subjects' theoretical beliefsabout the categories . For example, whensubjects believed that one category ofdrawings contained items with missinglimbs, a missing hand in one drawing wasplaced in correspondence with a missingfoot in another drawing. This kind of rela-tional match is a central part of structuralalignment .

Alignable and Nonalignable Differencesin Decision Making

Structural alignment, and particularly thedistinction between alignable and nonalign-able differences, may provide an importanttheoretical framework for studies of deci-sion making . Extensive work has been de-voted to understanding how people choosebetween alternatives and how they justifytheir decisions. Much of this work can berecast as suggesting that subjects focus onalignable differences between alternativeswhen choosing between them (Tversky,1972 ; Tversky, Sattath, & Slovic, 1988) .For example, according to Tversky's (1972)elimination-by-aspects model, individualschoosing between a set of items focus onone common aspect or dimension of the al-ternatives at a time . The probability thatthey will focus on a particular dimension isroughly equivalent to its importance . Afterfinding a relevant aspect, subjects eliminateany alternatives with unsatisfactory valuesalong that dimension . This process is re-peated until only one alternative remains .

531

532

Research by Johnson (1988, 1989) on con-sumer choice behavior also demonstratesthe importance of alignment . He finds thatwhen people select between two similarproducts (e.g ., two toasters) they engage ina choice strategy based on aligning andcomparing the particular attributes of theproducts involved (e .g ., number of breadslots or time to toast bread) . When theproducts are dissimilar (e .g ., a toaster and asmoke alarm), and therefore difficult toalign, subjects revert to other strategies .

There is also evidence that, when bothalignable and nonalignable differences areavailable, subjects give greater weight toalignable differences . Slovic and MacPhil-lamy (1974) asked subjects to guess whichone of a pair of students had a higher fresh-man GPA given two test scores for eachindividual . One score was from the sametest (e .g ., an English proficiency test),while the other score was unique for eachindividual (e .g ., SAT for one person andthe ACT for the other) . They found thatsubjects in the prediction task attended

MARKMAN AND GENTNER

APPENDIX 1 : WORD PAIRS IN EXPERIMENT I

more heavily to the score on the commontest than to the score on the unique test .These examples suggest that processes ofalignment and the identification of alignabledifferences may be crucial to the processesof decision and choice .

CONCLUSIONS

The results described here suggest thatsimilarity comparisons are carried out byan alignment process akin to analogicalmapping that places parts of structured rep-resentations in correspondence . Accordingto this view, comparisons yield commonal-ities, alignable differences and nonalignabledifferences . These elements can be used todetermine the overall similarity of the ob-jects or can serve as the input to anothercognitive process . By focusing on the pro-cess of comparison, rather than simply thedegree of likeness, the study of similaritycan be extended to encompass the generalrole of alignment and comparison in cogni-tive processing .

Similar pairs Dissimilar pairs

Yacht Sailboat Curtain Ball BearingHotel Motel Eggplant GiraffeVCR Tape Deck Restaurant Strobe LightKite Hang Glider Bank Check Light BulbBroom Mop Magazine KittenWatch Clock Mug SpeakerIce Cream Sundae Banana Split Phone Book Lamp ShadeSculpture Painting Postage Stamp MicrophonePolice Car Ambulance Lock AsphaltRocket Missile Blanket BowlChair Stool Cab Driver AntennaCalculator Abacus Air Conditioner Cloud

Army Navy Door SidewalkBed Couch Stove Dumpster

Casino Horse Track Notebook Piano

Store Boutique Traffic Light Shopping MallHammock Lounge Chair Freezer Personal Computer

Stairs Escalator Trapeze Fork

McDonald's Burger King Parade Tennis

Football Hockey Handcuffs T-Shirt

APPENDIX 2 : WORD PAIRS USED INEXPERIMENT 2

Stimulus set I

APPENDIX 3

Related word pairs in Exp . 2b

DIFFERENCES IN SIMILARITY

Number ofsubjects

APPENDIX 3-Continued

533

Related word pairs in Exp . 2bNumber ofsubjects

Lizard-Frog

none

Robin-Bluebird

Both are found in North AmericaBoth are found in different locations 9

Helicopter-Cabinet

Both are manufacturedChairs are made of wood .

Helicopters are made of metal 10

Toad-Maple

Both are part of natureToads are animals . Maples are plants 10

Both are living thingsToads are animals . Maples are plants 12

Plane-Blimp

Both flyPlanes have wings, Blimps do not 9

Both carry peoplePlanes hold more people than blimps 9

Maple-Palm

Both have leavesMaples and Palms have different leaves 11

Desk-Blimp

Both are man madeDesks and Blimps are madefrom different materials 10

Table-Bench

none

Rose-Robin

Both are livingRoses are plants, Robins are animals 9

Chair-Car

You can sit in bothChairs hold one person, Cars hold many I1

Helicopter-Hang Glider

none

Oak-Lizard

Both are greenOaks and Lizards can be different colors 10

Cardinal-Orchid

Both are part of natureCardinals are birds, Orchids are flowers 10

Stool-Bicycle

Both have seats to sit onYou sit on a Stool, you pedal a Bicycle 9

Both are made of many materialsBicycles are made primarily

of metal . Stoolsare made primarily of wood 9

Table Overseeing

Promise TheoryPromise Moral

Salamander BenchDesk Sofa

Writing TalkingSparrow Discussion

Palm BusBlimp Plane

Robin BluebirdHang Gliding Fear

Carnation CompromiseRegret Apathy

Love GenerosityToad Maple

Marching TrustStool Bicycle

Secret HonestyCar Motorcycle

Lizard FrogCabinet Helicopter

Party ThoughtVacation Striding

Class GameRose Pine

Cardinal OrchidSpeech Reading

Oak DaffodilIdea Moral

Jogging RunningDebt Selfishness

Chair Dresser

Stimulus set 2Toad Cardinal

Running TheoryStool Cabinet

Chair CarTable Bench

Helicopter Hang GliderRobin Rose

Lizard OakSparrow Salamander

Bluebird MeetingSelfishness Fear

Game GenerosityMaple Palm

Pine MotorcycleThought Compromise

Bicycle BusPlane Apathy

Discussion PartyFrog Sofa

Orchid CarnationClass Writing

Idea LoveHonesty Trust

Reading OverseeingDresser Moral

Secret DebtStriding Marching

Daffodil TalkingPromise Regret

Vacation SpeechTV Show Jogging

Desk Blimp

Sofa-Desk

Both are made of woodDesks have drawers, Sofas do not . 9

You can sit at bothYou sit at a desk, you sit on a sofa . 10

Salamander-Sparrow

Both are animalsSalamanders are reptiles,

Sparrows are birds 12

Both moveSalamanders walk, Sparrows fly 12

Chair-Dresser

Both are useful to manChairs are for sitting, Desks hold clothes 10

Rose-Pine

Both have sharp pointsRoses have thorns, Pines have needles

Both are plantsRoses are flowers, Pines are trees

II

11

534

APPENDIX 3-Continued

Bench-Salamander

Both have wheelsCars have four wheels, Motorcycles

have two wheels

Cabinet-Stool

none

MARKMAN AND GENTNER

REFERENCES

BARSALOU, L. W., & HALE, C . R. Components ofconceptual representation : From feature lists torecursive frames . In V . Mechelen, J . Hampton, R .Michalski, & P. Thewns (Eds .), Categories andconcepts : Theoretical views and inductive data .San Diego, CA : Academic Press, 1993 .

CLEMENT, C. A ., & GENTNER, D . (1991) . Systematic-ity as a selection constraint in analogical mapping .Cognitive Science, 15, 89-132 .

ESTES, W . K . (1986) . Array models for category learn-ing . Cognitive Psychology, 18, 500-549,

FALKENHAINER, B ., FoRBUs, K . D., & GENTNER, D .(1986) . The structure-mapping engine . In Proceed-ings of AAAI-86, Philadelphia, PA .

FALKENHAINER, B ., FoRBUS, K . D., & GENTNER, D .(1989) . The structure-mapping engine : Algorithmand examples . Artificial Intelligence, 41(1), 1-63 .

FORBUS, K . D., & GENTNER, D . (1989) . Structuralevaluation of analogies : What counts? In The Pro-ceedings of the Eleventh Annual Conference ofthe Cognitive Science Society . Ann Arbor, MI :Erlbaum .

GENTNER, D. (1983) . Structure-mapping : A theoreticalframework for analogy . Cognitive Science, 7, 155-170 .

GENTNER, D . (1989) . The mechanisms of analogicallearning . In S . Vosniadou & A . Ortony (Eds .),Similarity and Analogical Reasoning . London :Cambridge Univ . Press .

GENTNER, D., & MARKMAN, A . B . Similarity is likeanalogy . In C . Cacciari (Ed .), The Proceedings ofthe Workshop on Similarity at the University ofSan Marino . Milan : Bompiani, in press .

GENTNER, D ., & TouPIN, C . (1986) . Systematicity andsurface similarity in the development of analogy .Cognitive Science, 10, 277-300 .

GERARD, A . B ., & MANDLER, J . M . (1983) . Ontolog-ical knowledge and sentence anomaly . Journal ofVerbal Learning and Verbal Behavior, 22, 105-120 .

GLUCK, M . A., & BOWER, G . H . (1988) . From condi-tioning to category learning : An adaptive networkmodel . Journal of Experimental Psychology : Gen-eral, 117(3), 227-247 .

GOLDSTONE, R. L ., & MEDIN, D . L . Similarity, inter-active-activation and mapping . In K . J . Holyoak& J . A. Barnden (Eds .), Advances in connection-ist and neural computation theory . Vol . 2 : Ana-logical connections . Norwood, NJ : Ablex, inpress .

GOLDSTONE, R. L., MEDIN, D . L., & GENTNER, D .10 (1991) . Relational similarity and the non-

independence of features, Cognitive Psychology,23, 222-262 .

HtNTZMAN. D. L . (1986) . "Schema abstraction" in a

Related word pairs in Exp . 2bNumber ofsubjects

Both are usefulBicycles are transportation,

Stools are furniture 11

Orchid-Carnation

Both are given as giftsOrchids are more expensive

than Carnations 10

Both are flowersOrchids and Carnations

are different kinds of flowers

Cardinal-Toad

Both are animalsToads are amphibians,

Cardinals are birds

U

12

Both have homesToads live in the ground, Cardinals

live in trees 11

Frog-Sofanone

Daffodil-Oak

Both are livingOaks live longer than Daffodils 10

Both are plantsOaks are trees, Daffodils are flowers 12

Bicycle-Bus

Both have wheelsBuses have many wheels, Bicycleshave two wheels I1

Both are means of transportationYou drive a Bicycle, you are a

passenger on a Bus

Both are riddenYou ride on a Bicycle, you ride in a Bus I1

Both can be the same colorBenches are one color,

Salamanders change color

12

Car-Motorcycle

Both have enginesCars have bigger engines

than do Motorcycles

10

Both carry peopleCars carry more people

than do motorcycles

II

Both can be dangerousMotorcycles require helmets,Cars require seatbelts

II

multiple trace memory model . Psychological Re-view, 93(4), 411-428 .

HOFSTADTER, D . R. (1984) . The Copycat project: Anexperiment in nondeterminism and creative anal-ogies, No. Al memo 755 . The MIT Al Lab .

HOFSTADTER, D . R., & MITCHELL, M . An overviewof the Copycat project . In K . J . Holyoak & J. A .Barnden (Eds .), Advances in connectionist andneural computation theory . Vol . 2 : Analogicalconnections . Norwood, NJ : Ablex, in press .

HOLYOAK, K. J., & THAGARD, P. (1989) . Analogicalmapping by constraint satisfaction . Cognitive Sci-ence, 13(3), 295-355 .

JOHNSON, M . D . (1988) . Comparability and hierarchi-cal processing in multialternative choice . Journalof Consumer Research, 15, 303-314 .

JOHNSON, M . D . (1989) . The differential processing ofproduct category and noncomparable choice alter-natives . Journal of Consumer Research, 16, 300-309 .

KAHNEMAN, D., & MILLER, D . T. (1986) . Norm the-ory : Comparing reality to its alternatives . Psycho-logical Review, 93(2), 136-153 .

KEIL, F . C. (1979) . Semantic and Conceptual Devel-opment: An Ontological Perspective . Cambridge,MA: Harvard Univ . Press .

KRUMHANSL, C . L . (1978) . Concerning the applicabil-ity of geometric models to similarity data : The in-terrelationship between similarity and spatial den-sity . Psychological Review, 85(5), 445-463 .

LENAT, D., & GUHA, R . V . (1990) . Building largeknowledge-based systems . San Francisco : Addi-son-Wesley .

LOGAN, G . D . (1988) . Toward an instance theory ofautomaticity . Psychological Review, 95, 492-527 .

MARKMAN, A. B., & GENTNER, D . (1990) . Analogicalmapping during similarity judgments . In Proceed-ings of the Twelfth Annual Meeting of the Cogni-tive Science Society . Boston, MA : Erlbaum .

MARKMAN, A . B ., & GENTNER, D . Structural align-ment during similarity comparisons . CognitivePsychology, in press .

MEDIN, D . L., & SCHAFFER, M . M . (1978) . Contexttheory of classification . Psychological Review,85(3), 207-238 .

MEDIN, D. L., & GOLDSTONE, R . L. Predicates ofsimilarity . In C . Cacciari (Ed .), The Proceedingsof the Workshop on Similarity at the University ofSan Marino . Milan : Bompiani, in press,

NOSOFSKY, R . M. (1986) . Attention, similarity and theidentification-categorization relationship . Journalof Experimental Psychology : General, 115(1), 39-57 .

RATTERMANN, M . J ., & GENTNER, D . (1987) . Analogyand similarity : Determinants of accessibility and

DIFFERENCES IN SIMILARITY 535

inferential soundness . In The Proceedings of theNinth Annual Conference of the Cognitive Sci-ence Society . Seattle, WA : Erlbaum .

ROSCH, E ., & MERVIS, C . B . (1975) . Family resem-blances : Study in the internal structure of catego-ries . Cognitive Psychology, 7, 573-605 .

SCHUMACHER . R., & GENTNER, D . (1987) . Similarity-based remindings : The effects of similarity and in-teritem difference . In The Proceedings of the An-nual Meeting of the Midwestern PsychologicalAssociation, Chicago, IL .

SCHWANENFLUGEL, P . J, (1991) . Why are abstractconcepts hard to understand? In P . J . Schwanen-flugel (Eds .), The psychology of word meanings .Hillsdale, NJ : Erlbaum .

SINGLEY, M . K., & ANDERSON, J . R . (1989) . Thetransfer of cognitive skill . Cambridge, MA: Har-vard Univ . Press .

SJOBERG, L . (1972) . A cognitive theory of similarity .Goteborg Psychological Reports, 2,(10) .

SLOVIC, P., & MACPHILLAMY, D . (1974) . Dimensionalcommensurability and cue utilization in compara-tive judgment . Organizational Behavior and Hu-man Performance, 11, 172-194 .

SMITH, E . E ., &MEDIN, D . L . (1981) . Categories andconcepts . Cambridge, MA : Harvard Univ . Press,

SOMMERS, F . (1959) . The ordinary language tree .Mind, 68, 160-185 .

SPELLMAN, B . A., & HOLYOAK, K . J . (1992) . If Sad-dam is Hitler then who is George Bush? Analogi-cal mapping between systems of social roles .Journal of Personality and Social Psychology,62(6), 913-933,

THORNDIKE, E . L., & WOODWORTH, R . S . (1901) .The influence of improvement in one mental func-tion upon the efficiency of other functions . Psy-chological Review, 8, 247-261 .

TOURANGEAU, R., & Rips, L . J . (1991) . Interpretingand evaluating metaphors . Journal of Memoryand Language, 30, 452-472,

TVERSKY . A . (1972) . Elimination by aspects : A theoryof choice . Psychological Review, 79(4), 281-299 .

TVERSKY, A . (1977) . Features of similarity . Psycho-logical Review, 84(4), 327-352 ..

TVERSKY, A., SATTATH, S ., & SLOVIC, P. (1988) . Con-tingent weighting in judgment and choice . Psycho-logical Review, 95(3), 371-384 .

WISNIEwSKI, E . J ., & MEDIN, D . L . The fiction andnonfiction of features . In R. S . Michalski & G . D .Tecuci (Eds .), Machine Learning : A Multistrat-egy Approach . San Mateo, CA: Morgan Kauff-mann, in press .

(Received June 2, 1992)(Revision received December I . 1992)