Running head: ISOLATED AND INTERRELATED CONCEPTS

A continuum between purely isolated and purely interrelated concepts is described. A concept is interrelated to the extent that it is influenced by other concepts. Methods for manipulating and identiying a concept's degree of interrelatedness are introduced. Relatively isolated concepts are empirically identified by a relatively large use of nondiagnostic features, and by better categorization performance for a concept's prototype than for a caricature of the concept. Relatively interrelated concepts are identified by minimal use of nondiagnostic features, and by better categorization performance for a caricature than a prototype. A concept is likely to be relatively isolated when: subjects are instructed to create images for their concepts rather than find discriminating features, concepts are given unrelated labels, and the categories that are displayed alternate rarely between trials. The entire set of manipulations and measurements supports a graded distinction between isolated and interrelated concepts. The distinction is applied to current models of category learning, and a connectionist framework for interpreting the empirical results is presented.

Modern research on concept representation and learning has evolved from two traditions. One tradition connects concept acquisition with language in general and word learning in specific (Lakoff, 1986; Saussure, 1915/1959). Concepts are approximately equated with single words or phrases. In this tradition, for example, evidence that a child has acquired the adult concept of dog comes from the child's use of the word "dog" to designate dogs. The other tradition connects concept acquisition with object recognition (Biederman, 1987). From this perspective, concept learning involves learning to correctly categorize perceptual inputs into classes.

These two approaches, linking concepts to language and perception respectively, are not mutually exclusive, and a full account of the nature of conceptual representation will most likely borrow from both approaches. Still, the approaches emphasize different methods for representing and processing concepts. The three aims of this paper are: to describe these different characterizations, to develop empirical methods for distinguishing between them, and to devise a framework that integrates both characterizations into a single formal framework.

Much of the work that ties concepts to language is concerned with the presence of (McNamara & Miller, 1989; Saussure, 1915/1959) or absence (Fodor, Garret, Walker, & Parkes, 1980) of interconceptual connections. Conversely, much of the work that ties concepts to object recognition is concerned with the links between concepts and perceptual inputs rather than between concepts. Indeed, concepts seem to be cognitively self-contained bundles of knowledge on the one hand, and intricately interconnected entities on the other. Concepts appear to be isolated from each other, each acting as an independent detector polling the world (Selfridge, 1959), and yet also seem to influence each other in an interacting network (Collins & Quillian, 1969). For example, while certain shapes seem to be directly recognized as examples of dog, the concept dog also appears to be closely associated with and influenced by other concepts such as mammal, tail and domesticated . Most models of concept representation and use try to account for one or the other of these types of conceptual behavior. The central purpose of this paper is to make a case for considering a continuum of interrelatedness in concept characterizations. The characterization of a concept refers to the way the concept is described, and the members that belong to it. A concept's characterization will depend both on its representation, and the cognitive processes that operate on that representation. A concept is interrelated to the extent that its characterization is influenced by other concepts. A concept is isolated to the extent that its characterization is not influenced by other concepts.

The proposed continuum of interrelatedness is supported by results of five experiments that systematically affect the degree of interrelatedness of laboratory-acquired concepts by human subjects. Three manipulations of conceptual interrelatedness and two empirical indicators of conceptual interrelatedness are evaluated. In addition, a computational simulation of concept learning is presented. The simulation demonstrates how degrees of conceptual interrelation can be modeled in a formal network. In the model, the use of a concept can reflect intermediate degrees of interrelation, depending upon the strength of the connections that other concepts have to it. Such links are potentially determined both by the context of concept acquisition and the nature of the current processing demands. In order to understand the continuum of conceptual interrelatedness, idealized concepts at the extreme poles of the continuum are first considered individually.

There are several ways in which the characterization of concepts might be influenced by other concepts (Goldstone, 1991). First, a concept might be characterized as a modified version of another previously acquired concept. Such modifications could include adding or deleting properties, increasing or decreasing the quantity of a property, or rearranging properties. For example, one's concept of toy poodle might be a modified version of one's concept of standard poodle, with a modification to size. Or consider the concept unicorn . At first pass, one might think of unicorns as horses, with the addition of the features magical and horns. If unicorn is characterized by its relation to the concept horse then altering one's concept of horse would likely also alter one's concept of unicorn. For example, if a new fact were learned about horses (e.g. the pad in the middle of a horse's hoof is called a "frog"), then it might be incorporated into the unicorn concept as well (Potts, St. John, & Kirson, 1989). At the very least, it would be difficult for a person in this culture to have a full concept of unicorn without also possessing a horse concept (cf. Stich, 1983).

A second way that concepts can be influenced by other concepts is suggested by the work of Barr and Caplan (1987; Caplan & Barr, 1991). These researchers report evidence from feature-listing tasks that people's concepts typically contain both intrinsic and extrinsic features. Intrinsic features refer to parts or properties of the concept under scrutiny. Extrinsic features are "represented as the relationship between two or more entities" (p. 398). For example, an extrinsic feature of hammer is that it is "used to strike nails." This feature refers to a concept other than hammer. If this feature is part of one's concept of hammer, then one cannot possess a hammer concept without also possessing nail.

In all of the above examples of interrelatedness among concepts, the intension, or internally represented meaning (see Johnson-Laird, 1983), of a concept is influenced by other concepts in the system. The extension of a concept is the set of items that is covered by the concept. In arguing for complete interrelatedness among concepts, Saussure (1915/1959) stated that "concepts are purely differential and defined not in terms of their positive content but negatively by their relations with other terms in the system" (p. 117). That is, he contended that all concepts are "negatively defined," or defined solely in terms of other concepts. Several current theories of word and concept representation from linguistics and computer science similarly assume that concepts' meanings are interrelated. In semantic network representations (Collins & Quillian, 1972), concepts are represented by their relations (e.g. part-of, is-a, and has-a relations) to other concepts. For example, the meaning of cat is represented by its has-a relation to claw, its is-a relation to pet and animal, and its part-of relation to household (see McNamara and Miller (1989) for a review of evidence for theories of conceptual representation that posit interrelations between concepts). And in linguistics, there is a widespread notion that the lexicon is organized as a semantic field, in which words applicable to a common conceptual domain are organized by relations of similarity and contrast (Grandy, 1987; Lerher & Kittay, 1992; Lyons, 1963; Martin & Billman, 1994). Thus, the semantic relations that a word enters into at least partially constitute the meaning of that word. For example, one's understanding of walk is influenced by one's possessions of the concepts jog, skip, run, and drive.

The reported experiments and simulations do not evaluate all the varieties of interrelated concepts. The research does not consider concepts that are interrelated by their semantic associations, or by their cohabitation in a single theory or system (Field, 1978; Fodor, 1983). Rather, the research focuses on artificial, laboratory-created concepts that are interrelated because they are mutually exclusive categories, and consequently, membership in one category prevents membership in the other. Although visual concepts were used in the experiments to be reported, linguists have discussed this relation of mutual exclusivity between concepts. In linguistic theory, a mutually exclusive set of terms that are organized under an inclusive covering term is called a contrast set (Grandy, 1987; Lehrer & Kittay, 1992; Martin & Billman, 1994). For example, Sunday, Monday, and Tuesday belong to a common contrast set: days of the week. Concepts within a contrast set evoke each other, and once evoked, influence each others' interpretation. In Saussure's example (1915/1959), mutton is influenced by the presence of other neighboring concepts. mutton's use does not extend to refer to sheep that are living because there is another concept that covers living sheep (sheep), and mutton does not extend to refer to cooked pig because of the presence of Pork. If one did not possess the concept mutton , then "all its content would go to its competitors" (Saussure, 1915/1959, p. 116) and cooked sheep would be encompassed by sheep. Thus, concepts compete to the extent that they are conceptually related "neighbors."

Theoretical grounds for doubting the ubiquity of completely interrelated concepts derives from a reappraisal of Saussure's notion of competition between concepts. In his view, concepts compete with neighboring concepts to cover specific instances. In this way, concepts are completely defined by their neighbors. However, the question remains: how are the neighbors of a concept determined in the first place? It seems that concepts must usually have an independent characterization in order to have neighbors. Harnad (1991) and Barsalou (1993) have argued that concepts cannot simply gain their meaning from other concepts; concepts also be grounded by perceptual, non-symbolic properties (see also Goldstone, 1994c). In most cases, a concept can only have neighbors if it first has some location. This location is its isolated or concept-independent characterization. Such reasoning suggests that a good diagnostic for locating objects on the isolated/interrelated continuum is, "Would this concept be used in this way if some/most/all other concepts were eliminated?"

One way to conceive of an isolated concept is as a feature detector. In the classical conception of feature detectors, a detector becomes activated when an input with a particular feature is displayed. For example, there exist neurons in primate striate cortex that act as feature detectors for straight lines of particular orientations (Hubel & Wiesel, 1968). There is also evidence that some neurons respond selectively to stimuli as complex as triangles, hands, and faces (Bruce, Desimone, & Gross, 1981). In order for a neuron to become active when a line of a particular orientation is presented to the visual field, the feature detector does not need any information from other detectors, concepts, or theories in the system. Although the particular specialization that a feature detector develops can be influenced by the states of other neighboring neurons at the same cortical level (Malsburg, 1973), once the specialization of a neuron has been set, the feature detector is isolated from the influences of other neurons for the most part.

The lately unfashionable (but, see Ullman, 1989) template approach to pattern recognition provides another possible representation for isolated concepts. If patterns are categorized by being compared to stored category templates, then the representation of the category does not depend on other category representations. A category's representation is simply the image that is compared to the input to be recognized. For example, instead of characterizing Unicorn by making reference to Horse, one's representation may simply be photograph-like image.

Researchers interested in concept learning from the perspective of categorization of perceptual stimuli have proposed prototype and exemplar representations. Posner and Keele (1968) and Reed (1972) advocate prototype representations. Medin and Schaffer (1978) and Nosofsky (1986) argue that concepts are represented by their individual exemplars. At a first pass, these internal representations do not depend on other concepts. That is, the prototype or exemplars that create a category's representation are not typically altered by other categories. However, researchers advocating these representations have discussed shifts in the weighting of stimulus dimensions due to their categorical diagnosticity (Kruschke, 1992; Nosofsky, 1986). The resulting stretching and shrinking of psychological space (Nosofsky, 1986) can be viewed as altering conceptual representations.

Concept X is interrelated to Concept Y to the degree that X's characterization is influenced by Y. The isolated/interrelated continuum, as described so far, still has five theoretical ambiguities. These ambiguities pertain both to the interpretation of the continuum and to the experimental realization of tests of the continuum. In the five distinctions below, I describe the particular interpretation of the continuum that motivated the currently reported experiments.

Dichotomy versus Dimension. The distinction between isolated and interrelated concepts may be thought of as a dichotomy for describing concepts, whereby concepts are either isolated or interrelated. Instead, the difference between isolated and interrelated concepts is here conceptualized as a continuum with purely isolated and purely interrelated concepts at the two extremes. Given that the distinction is treated as a continuum, questions arise of "What property of concepts varies along the continuum?" and "How can two concepts be only partially interrelated?" In the RECON model of isolated and interrelated concepts described in the General Discussion, category units are connected by weighted links to other category units and to external, perceptual inputs. In this approach, the continuum from isolated to interrelated concepts is obtained by varying the connection strengths between categories from weak to strong, relative to the influence of external inputs. Partially interrelated or partially competing concepts do have connections to each other, but their connection strengths are relatively weak. In this conception, most concepts will be partially interrelated and partially isolated, in that influences on a concept come from both other concepts and from external inputs.

Definition Versus Influence. Concept X is clearly interrelated to Concept Y if X's definition or characterization makes recourse to Y. For example, the definition of Gentile is related to Jew because not being Jewish is part of Gentile's definition. However, Concept X's representation can be influenced by Y even if X is not defined or characterized in terms of Y. The presence of Y may change the representation of X by competing with X or facilitating X. The current experimental tests of interrelatedness only assess whether one concept influences another, and not whether one concept is explicitly defined in terms of another. Active Versus Past Interrelation. There is a difference between concepts that are currently dependent on other concepts for their characterization, and concepts that were dependent on other concepts during their development but not in their current state. The measures used in the current experiment do not distinguish between these options. As such, evidence for interrelatedness in the experiments will only be taken as evidence that the concepts influenced each other's characterization at some time, and may still actively influence each other. One potential way to obtain evidence for active dependencies between concepts is to systematically alter one of the concepts, and observe changes in the other. After two categories are learned, new information can be provided about one of the concepts. If the other concept has an "active" link to the concept or if the two concepts share representational units, then the other concept's representation should change.

Concepts that were originally isolated may become interrelated, or vice versa. Providing information about a link between concepts, or simply providing exposure to the concepts' members in the context of each other, may cause them to become interrelated. Conversely, prolonged experience with a concept may cause it to become separated or modularized. One of the purposes of the experiments is to explore the relation between the amount of experience with concepts and their degree of isolation.

Representation Versus Process. Concepts that have not influenced each other's representations can still influence each other's use. For example, in prototype and exemplar models, if Concept A is introduced into an experiment, then classifications of objects into Concept B may decrease because of response competition from A during categorization, even though subjects' representation of Concept B itself is unchanged.

It is notoriously difficult to study representations separately from the processes that operate on those representations (Anderson, 1978). Empirical data support process-representation pairs rather than representations alone. For this reason, if evidence suggests that Concept Y influences the extension of Concept X, it cannot be inferred that Concept X's intension has changed. The RECON model that is described in the General Discussion accounts for differences in conceptual interrelatedness in terms of processing differences that have repercussions for category characterizations. As such, the claim will not be made that conceptual interrelatedness is a purely representational matter. The characterization of a concept depends on both the concept's representation and processes on that representation. In order to model a category characterization task (such as "draw the best possible example of Category A"), the relevant category unit is activated and then the activation is spread to the perceptual units from the category unit. The resulting perceptual image is the model's characterization of the category, but it depends on processing (activation passing) in addition to static representations. One advantage to using characterization to refer to both concept representation and processing is that momentary contextual cues can influence the characterization of a concept without requiring permanent representational changes.

Negative Relations Versus Any Relation. Conceptual influences may be positive or negative. The Saussurian notion of competition between concepts for control of conceptual regions is a negative influence. As one concept gains control of a conceptual area, its competitor concepts lose control of the area. However, concepts can also be positively interrelated if they are inductively or hierarchically related to each other. Properties that are found to be true of one concept will frequently be transferred to similar concepts (Osherson, Smith, Wilkie, Lopez, & Shafir , 1990), more general concepts, and more specific concepts.

In the RECON model to be developed, concepts exert negative influences on each other because there are negative connection strengths between category units. This is appropriate for categorization tasks where objects belong to one and only one category. Positive connection strengths between categories would be required to handle situations where categories can be embedded in other categories (linebacker is embedded in football player), or one category can signal membership in another category (things that are cats are often pets, Hampton, 1987, 1988).

The majority of concepts are probably neither purely isolated nor interrelated. The research of Harnad, Barsalou, and psychologists investigating concept learning, points to the insufficiency of concepts that are solely defined in terms of other concepts. However, there is also substantial evidence for rich interconceptual relations (e.g. Winston, Chaffin, & Herrmann, 1987). The proposed empirical methods are aimed at locating concepts along the isolated-to-interrelated continuum. The empirical methods to be described only diagnose the subset of interrelated characterizations wherein a concept is influenced by competition from other simultaneously acquired concepts.

The overall research strategy is to use converging operations (Garner, Hake, & Erikson, 1956) to identify isolated and interrelated concepts. Experimental manipulations are developed that are expected to alter the interrelatedness of the concepts to be learned. At the same time, empirical indicators of interrelatedness are also developed. The reason for testing multiple manipulations and indicators is that each indicator, by itself, provides only an indirect and fallible lens on interrelatedness. Confidence that a particular manipulation or indicator is related to interrelatedness increases if it provides results that are consistent with the other methods. Considered individually, what each manipulation is affecting, and what each indicator is measuring is not precisely specifiable. Considered together, the pattern of results strongly suggests a common underlying construct of concept interrelatedness. Table 1 presents an overview of the converging manipulations and indicators that are explored.

The experiments will focus on three methods for experimentally manipulating concept interrelatedness, and two methods for measuring interrelatedness. The notion that concepts vary systematically in their interrelatedness will be supported if the experimental manipulations and measures consistently cohere together in locating particular concepts on the continuum of interrelatedness. Interrelatedness is manipulated by: instructing subjects to either create independent images of the concepts to be learned (isolated) or to look for features that discriminate between the concepts (interrelated), alternating presented concepts frequently (interrelated) or rarely (isolated), and by giving the concepts related (interrelated) or unrelated (isolated) labels. Concept interrelatedness is measured by the degree to which nondiagnostic features are used for categorizing and depicting categories, and by the relative ease of categorizing instances that are prototypical or distorted in particular ways. The justification for associating each of these manipulations and measures with concept interrelatedness will be discussed as they are introduced.

Nondiagnostic Features in Categorization

One method for identifying isolated and interrelated concepts is to observe the influence of nondiagnostic features on categorization accuracy. A nondiagnostic feature is a feature that does not, by itself, provide any information to choose between candidate categories. When categorizing a shape as a triangle or square, knowledge that the shape has the feature "straight line" does not provide any grounds for choosing between the categories. If a feature F is nondiagnostic, then P(C|F) = P(C) for all categories C; that is, the probability of a category given that the feature is present is equal to the probability of the category given no additional information. The category validity of a feature is P(F|C), the probability of the feature, given a particular category. Although "straight line" is not diagnostic for choosing between a triangle and square, the feature is certain [P(F|C) = 1.0] for both categories.

The difference between a diagnostic and nondiagnostic feature is only relevant for interrelated concepts. For purely isolated concepts, any feature that has high category validity will likely be a part of the template, or image, of the concept, and may be used for categorization purposes. Furthermore, if the categorization decision rule involves a similarity criterion, then nondiagnostic features can increase categorization accuracy. An example of such a rule is: "If the similarity of the item to the prototype of Category Y is greater than X, then place the item into Category Y. If the item's similarity to any category never exceeds X, then respond at random." Such rules are commonly used in pattern recognition domains. Nondiagnostic features can increase categorization accuracy because they cause an item's similarity to a category to exceed the criterion X.

The diagnosticity of a feature only becomes an issue when there is a set of candidate categories, and an attempt is being made to distinguish between the possible choices. Nondiagnostic features, by definition, do not distinguish between candidate categories, and would not be included in a concept that is characterized purely by its negative relation to its competitor concepts. The experimental question then becomes: How much does the presence of non-diagnostic features with high category validity increase the accuracy of categorization? For relatively isolated concepts nondiagnostic features should increase accuracy because they will be part of the concepts' characterization, assuming that the probability of finding the correct category for an item increases as the item's similarity to the correct category's template increases (see General Discussion for details regarding this assumption). For relatively interrelated concepts, nondiagnostic features should have a small influence on accuracy because they will not be a large part of the concept's characterization. For concepts that are influenced by competition with other concept, features that discriminate between concepts will play a large role.

Overview of Experiment

In Experiment 1, the influence of nondiagnostic relative to diagnostic features is used as the indicator of interrelatedness. An instructional manipulation is used in an attempt to vary concept interrelatedness. One group of subjects is told to create an image of the two concepts to be learned, and another group of subjects is told to seek out stimulus features that serve to distinguish the concepts. The "Image" instructions are aimed at promoting isolated concepts; if an image/template if formed for each concept, then there should be relatively little influence of one concept on another concept's characterization. The second set of instructions is aimed at promoting interrelated concepts. A concept's distinguishing features are only diagnostic relative to another concept. While an image can be generated for a concept without any knowledge of the other concepts being acquired, the selection of distinguishing/diagnostic features for a concept requires knowledge of the other candidate concepts.

Thus, the prediction for the first experiment is that subjects who are given "image" instructions will develop concepts that are relatively isolated, as indicated by a large influence of nondiagnostic features on categorization accuracy. In addition to the categorization accuracy measure, clues about the nature of a concept's representation are also obtained by asking subjects to pictorially describe their concepts.

Method

Materials. Sample materials are shown in Figure 1. Stimuli were composed of the twenty horizontal, vertical, and diagonal line segments that connect a 3 by 3 grid of dots. The line segments, but not the dots, were displayed to subjects. The background for all the materials was white. For each of the two concepts to be learned, a prototypical pattern of line segments was generated, consisting of 9 black lines. Out of the 20 positions for line segments, 10 of the positions were diagnostic and 10 were nondiagnostic. A line segment was diagnostic if it provided evidence in favor of one of the concepts - i.e. if it was present in one concept prototype but not the other. A line segment was nondiagnostic if its presence did not make one concept more likely than the other. White (absent) line segments could also be nondiagnostic or diagnostic, although post-experimental interviews revealed that they were not as salient as the black line segments for most subjects. Most analyses were unchanged when they were excluded as features. Out of the 10 diagnostic line segments, 5 were black and 5 were white; out of the 10 nondiagnostic line segments, 4 were black and 6 were white.

Subjects were presented with distortions of the two prototypes. Three possible distortions of category A are shown in Figure 1. Distortions were formed by randomly switching (from white to black, or from black to white), with a probability of 0.2, each of the 20 line segments of the concept prototypes. Thus, on average, distortions contained 80% of the line segments of their prototypical pattern. Individual nondiagnostic and diagnostic line segments were switched equally often, and the two prototypes were used as the basis for the distortions equally often. Thus, the category validity [P(cue|category)] of all line segments in the prototype was 0.8, the diagnosticity [P(category|cue)] of diagnostic line segments was 0.8, and the diagnosticity of nondiagnostic line segments was 0.5.

Procedure. Twenty-eight undergraduates from the University of Michigan were divided into two groups. One group of subjects (the "Image" group) was given the instructions, "While you are learning the two categories, you should try to form an image of what each category looks like. Use these images to help you categorize the pictures that you see." The other group of subjects (the "Discriminate" group) was given the instructions, "While you are learning the two categories, you should try to find features in the pictures that help you distinguish between the two categories."

Six hundred randomly generated distortions of the two prototypes were displayed. On each trial, a distortion of a concept's prototype was displayed, and subjects pressed one of two keys to indicate their categorization decision. The image remained on the screen until the subject entered a response. Subjects then received feedback indicating whether their choice was correct and what the correct response was. The feedback was displayed for 1.5 seconds, and a blank screen between trials was displayed for 1 second. All materials were presented on Macintosh SE computers.

Subjects were given breaks after every one hundred trials. During the break, subjects were reminded to either form images or look for discriminating features. Following the categorization task subjects were instructed to "draw pictures that best capture the nature of the two concepts" on empty 3 by 3 grids.

Results

The data of principal interest concern the use of diagnostic and nondiagnostic features by subjects in the two instruction groups. The number of diagnostic and nondiagnostic features that were altered from a concept's prototype was measured on each trial. Figure 2 illustrates the unsurprising finding that categorization performance decreased as the number of altered line segments increased, F(4, 104) = 17.5, mse = 0.18, p < .01. Separate results are shown for alterations of nondiagnostic and diagnostic features, for both instruction groups. For example, the 85% accuracy rate for Discriminate instructions when no diagnostic features were changed includes all of the stipulated data, regardless of the number of nondiagnostic features altered.

In addition to the main effect of the degree of distortion on accuracy, altering diagnostic features was more detrimental to categorization accuracy than was altering nondiagnostic features. The slopes of the lines relating number of altered features to categorization accuracy, -5.2 for diagnostic lines and -2.3 for nondiagnostic lines, were significantly different, F(1, 26) = 8.8, mse = .09, p < .01.

The result of principal interest was the significant three-way interaction between segment diagnosticity, number of features changed, and instruction type, F(4, 104) = 3.59, mse = 0.21, p < .05. When subjects were given Image instructions, then nondiagnostic features were more important than when subjects were given Discriminate instructions. When subjects were given Discriminate instructions categorization accuracy was only slightly affected by alterations to nondiagnostic features. These nondiagnostic features had a greater influence when subjects were told to form images of the concepts.

The influence of a type of feature was also quantified by measuring the slope of the line that related the number of alterations of a particular type of feature to categorization accuracy. For the Discriminate group, slopes were -1.4 and -5.6 for nondiagnostic and diagnostic features, respectively. For the Image group, the respective slopes were -3.2 and -4.8. These slopes reveal a significant interaction between instruction group and feature diagnosticity on accuracy, F(1,26) = 5.45, mse = 0.30, p < .05. For both groups, even nondiagnostic features had a significant influence on categorization accuracy, as measured by comparing the obtained slopes to a population mean of 0.0, F(1, 26) > 6.15, mse < 0.16, p < .05.

The relative influence of nondiagnostic and diagnostic features did not remain constant across training. There was a marginally significant trend in which concepts in the Image group became increasingly isolated with practice, as indicated by a marginally significant interaction between trial number and feature diagnosticity on the slope of the line relating number of altered features to categorization accuracy, F(1, 13) = 4.4, mse = .21, p < .06. For the first half of the trials, the influence of nondiagnostic features (again quantified by the slopes of the lines relating number of feature changes to categorization accuracy) was 49% of the influence of diagnostic features (nondiagnostic slope = -1.73, diagnostic slope = -3.53). For the second half of trials, the influence of nondiagnostic features rose to 77% of the influence of diagnostic features (nondiagnostic slope = -4.67, diagnostic slope = -6.07). In contrast, concepts in the Discriminate group became more interrelated with practice, F(1,13) = 5.50, mse = 0.25, p < .05. For the first half of the trials, the influence of nondiagnostic features was 33% of the influence of diagnostic features (nondiagnostic slope = -3.57, diagnostic slope = -10.81). For the second half of trials, nondiagnostic features were only 10% as influential as diagnostic features (nondiagnostic slope = -0.039, diagnostic slope = -0.386).

Although there was not a significant overall difference between the accuracies of the two instruction groups (72% and 71% for Image and Discriminate conditions respectively), F(1, 26) = 0.49, mse = .03, p > 0.1, their interactions with two factors were slightly different. First, the Image instructions led to higher accuracy rates (67%) than the Discriminate instructions (64%) for the first half of trials, but the Discriminate instructions led to higher accuracy rates (78%) than the Image instructions (77%) on the second half of trials, yielding a significant block by instructions interaction, F(1, 26) = 4.15, mse = 0.09, p < .05. Second, the Image instructions led to relatively high categorization accuracy when the items presented were not highly distorted. Ignoring whether nondiagnostic or diagnostic features were changed, the presented items were divided into two groups, depending on their degree of distortion from their original prototype. Items that were highly distorted (more than four line segments altered) were more successfully categorized by the Discriminate group (65%) than by the Image group (62%). Items that were less distorted (fewer than five segments altered) were more successfully categorized by the Image group (82%) than by the Discriminate group (76%), F(1, 26) = 6.5, mse = 0.10, p < .05.

An examination of the pictures drawn by subjects to exemplify concepts provided additional evidence for different characterizations developing in the two instruction groups. Subjects' pictures were analyzed in terms of the numbers of diagnostic and nondiagnostic features correctly depicted (i.e. part of the concept's prototype). Image instructions yielded a marginally significant higher proportion of correctly drawn features (an average of 14.6 out of 20 correct segments) than did Discriminate instructions (13.9 correct segments), t(26) = 1.94, p =.06. Importantly, the difference was particularly large for nondiagnostic features (Image = 8.2 out of 11 correct segments, Discriminate = 6.7 correct), t (26) = 2.25, p < 0.05.

Discussion

Experiment 1's results were predicted by the following set of assumptions: 1) nondiagnostic features are more likely to influence categorization accuracy for relatively isolated than for relatively interrelated concepts, 2) imagery, as opposed to discrimination, instructions are more likely to promote isolated concepts, and 3) the individual line segments are the basic features of the stimuli. Discussion and justification of the first two assumptions will be postponed until the General Discussion. A possible objection to the third assumption is that individual line segments may not be the correct unit of analysis. There is no a priori reason why the psychologically relevant features must coincide with the experimenter-defined features. Subjects might develop features that are compositions of several line segments (Hock, Tromley, & Polmann, 1988; Palmer, 1978; Schyns, Goldstone, and Thibaut, in press). For example, subjects may encode Concept A in Figure 1 as possessing the feature "X-shape in the lower left quadrant." This feature is diagnostic in that B examples will not typically have this feature. Furthermore, by taking away a so-called "nondiagnostic" line, we eliminate this diagnostic feature. According to this objection, nondiagnostic line segments may only influence categorization accuracy because they serve to define psychologically salient, diagnostic, complex features.

However, the obtained results provide a provisional validation of line segments as important functional features in some cases. Under some circumstances, subjects' analyses of features clearly did coincide with the experimenter-determined analysis. Specifically, when subjects were instructed to look for discriminating/diagnostic features, the lines that were experimentally defined as nondiagnostic did not have much influence on categorization accuracy relative to diagnostic lines. The nondiagnostic line segments never lost their influence completely, and this can be taken as some support for an influence of complex features that are constructed from simpler units. Simply arguing that subjects' features may not have agreed with the experimenter's features does not explain why sometimes the two did agree. The isolated/interrelated conceptual analysis that has been developed gains some support because it provides an account for when and why the experimenter's and subject's features coincide at the level of individual line segments. Although an alternative "complex features" account for the effect of the experimental manipulation in Experiment 1 is possible, later experiments will cast doubt on the generality of this explanation.

The data from the subjects' drawings of the concepts are potentially important, because they provide relatively direct information about the concepts' characterizations. The forced-choice nature of categorization decisions creates a heavy bias for relational judgments; categorizations will often be based on the relative appropriateness of one category over another. Subjects' drawings, on the other hand, are absolute measures of the qualities of one category irrespective of the other. Subjects from the Image group, posited to produce concepts that are relatively isolated, were more likely to include nondiagnostic features in their visual depictions of concepts than were subjects who were told to find discriminating features. These results provide converging evidence to the categorization accuracy results.

Experiment 2 is an attempt to obtain evidence converging with Experiment 1, using a second task manipulation intended to vary the interrelatedness of concept representations. In this experiment, the frequency of category alternation is varied. The presentation of different categories is alternated frequently or rarely. If categories are alternated rarely, then subjects will see long clusters of items that belong to the same category; a subject may, for instance, see six pictures that belong to Category 1 followed by five pictures belonging to Category 2. If categories are alternated frequently, then most often a Category 1 picture will be followed immediately by a category 2 picture, and vice versa.

The apriori assumption for this experiment is that frequent alternation of categories will yield concepts that are interrelated, and infrequent alternation will yield isolated concepts. The justification for this assumption is that if several distortions of the same concept's prototype are presented in a series, then the concept's characterization will most likely be based on the common properties of the distortions. Influences from the other concept will be relatively modest. If categories are alternated frequently, then there will be more opportunity for interplay between the developing concepts. In short, an item's categorization is likely to depend disproportionally on its immediate context; if that context contains members from other categories, then the item will likely be encoded in terms of those other category members (Medin & Edelson, 1987). If its context contains members from the same category, then the item will likely be encoded in terms of its overlap with these items.

Method

Materials. The same type of materials used in Experiment 1 were used here. Again, two concept prototypes were created that each had 8 diagnostic and 12 nondiagnostic line segment positions.

Procedure. Twenty-six Indiana University undergraduates were given the same categorization task used in Experiment 1. Subjects were given no strategy instructions; they were simply instructed to select a category for each of the presented pictures. The only other departure from Experiment 1's procedure was that categories were alternated frequently for half of the subjects, and rarely for the other half. For both groups, Category 1 and Category 2 items were each presented on one half of the trials. For the frequent alternation group, the probability of displaying an item from the same category as the preceding item was 0.25. For the infrequent alternation group, the probability was 0.75.

Results

The results from Experiment 2 showed a similar pattern to those from Experiment 1, as presented in Figure 3. Diagnostic line segments influenced categorization accuracy more than did nondiagnostic lines, as measured by the slopes of lines relating the number of features altered from the prototype to categorization accuracy (nondiagnostic slope = -1.5, diagnostic slope = -2.8), F(1, 24) = 14.7, mse = 0.15, p < .05. More importantly, the differential influence of diagnostic lines was greater when the category of the displayed item was alternated frequently rather than infrequently, as measured by the slopes (nondiagnostic frequent slope = -1.2, nondiagnostic infrequent slope = -1.8, diagnostic frequent slope = -4.0, nondiagnostic infrequent slope = -2.8), F(1, 24) = 5.79, mse = 0.12, p < .05.

A similar pattern of results was obtained from subjects' drawings. Subjects who received frequently alternating concepts drew an average of 6.5 correct diagnostic lines (out of 9 possible), and 7.3 correct nondiagnostic lines (out of 11 possible). Subjects who received infrequently alternating concepts drew an average of 6.7 correct diagnostic lines and 8.5 correct nondiagnostic lines. These results indicate that significantly more nondiagnostic features were drawn as part of a concept's representation when categories were infrequently alternated, F (1, 24) = 5.58, mse = 1.2, p < .05.

Categorization accuracy was significantly higher for infrequently altered categories than for frequently altered categories, F(1, 24) = 8.3, mse = .09, p < .05. With increasing practice, both groups of subjects' concepts became increasingly interrelated, as measured by a significant blocks (first half, second half) by feature (nondiagnostic, diagnostic) interaction using slopes as the dependent measure, F(1, 24)=4.4, mse = 0.10, p < .05. The slopes representing the influence of diagnostic features were -3.2 and -3.8 early and late in training, respectively, F(1, 24) = 1.2, mse = 0.25, p > .1. The slopes for early and late nondiagnostic features were -2.0 and -0.8 respectively, F(1, 24) = 5.0, mse = 0.11, p < .05.

Discussion

Experiment 2 provides support for a coherent set of manipulations and measures of concept interrelatedness. Similar categorization accuracy and concept depiction results were obtained when subjects were asked to depict images of concepts (Experiment 1) and when displayed categories alternated infrequently. The similar pattern of results was predicted by the hypothesis that both of these manipulations encourage the creation of isolated concepts -- concepts that are not influenced by the other concepts that are being acquired. Similarly, frequent category alternation produced results that were similar to those elicited by instructions to attend to distinctive features. Both of these manipulations were hypothesized to yield interrelated concepts - concepts with representations that are influenced by the other learned concepts.

The finding that categorization accuracy is greater for infrequently alternated categories than for frequently alternated categories corroborates results from Whitman and Garner (1963). Each of the two alternation conditions has an advantage over the other. Within the isolated/interrelated framework, frequent alternation of categories has the advantage of highlighting features that serve to distinguish categories. Conversely, infrequent alternation of categories has the advantage of highlighting information that remains constant across the members within a category (Hunt & McDaniel, 1993; Medin, Wattenmaker, & Michalski, 1987). Infrequent alternation may have resulted in better categorization performance because there were no features that perfectly distinguished the categories, several features were completely nondiagnostic, and the materials allowed for the relatively efficient creation of image-like category characterizations. Subjects who viewed several examples of a category successively may have adopted the efficient strategy of uncovering frequent commonalities between the examples rather than trying to discover partially diagnostic features that distinguished the categories from each other.

Until now, we have considered manipulations that influence the isolation/interrelation of both concepts to be acquired. It is also possible to devise asymmetric manipulations - manipulations that produce concepts that are not equally interrelated. One of the most straightforward ways to do this is by assigning different labels to the concepts to be learned. In the asymmetric condition of Experiment 3, concepts were essentially labeled "Concept A" and "Not Concept A," whereas in the symmetric condition the two concepts were labeled "Concept A" and "Concept B." Within the asymmetric condition, the concept labelled "Not Concept A" is predicted to be more influenced by "Concept A" than the concept labelled "Concept A" is influenced by "Not Concept A" (Clark, 1990). The concept that has a label that refers to another concept is predicted to be highly influenced by the referenced concept. Although logically identical categories were used in the two asymmetric groups and in the symmetric condition, the labels themselves were predicted to influence the degree of interaction between the acquired concepts. In addition, the "Not Concept A" concept is predicted to be more interrelated to its competitor concept than either concept in the symmetric labels condition, because concepts in the symmetric labels conditions receive labels that are independent of each other. Some grounds for predicting an influence of labeling comes from work on hypothesis testing (Van Wallendael & Hastie, 1990). Information which is presented as "A is not guilty" influences judgments of "A is guilty" far more than it influences "B is guilty" judgments, even when A and B are the only suspects. That is, when the negative contingency between two hypotheses is explicit in their labelling, then the two hypotheses influence each other more than when the two hypotheses are simply mutually exclusive (Goldstone, 1993 discusses a related labeling bias). More generally, the efficacy of labelling manipulations in inducing changes to learned concepts has been shown by Wisniewski and Medin (1994).

Method

The same materials and procedures used in the previous experiments were used in this experiment, with a few exceptions. Twenty-four Indiana University undergraduates were evenly split into two groups: symmetric and asymmetric labeling. Subjects in the symmetric-labels group were instructed, "You will see abstract paintings from two different imaginary artists, Yarpleaux and Noogan. If you think a painting was created by Yarpleaux, press the 'Y' key, and press the 'N' key if you think it was painted by Noogan." Subjects in the asymmetric-labels group were instructed, "You will see paintings by the imaginary artist Yarpleaux, and several forgeries by other artists. If you think a painting was created by Yarpleaux, press the "Y" key. If you do not think the painting is authentic, press the 'N' key." As before, subjects received feedback about the correctness of their responses. Subjects in the symmetric-labels groups were corrected with the phrase "No. This painting is a Yarpleaux [Noogan]." Subjects in the asymmetric-labels groups were corrected by the phrase "No. This painting is NOT a Yarpleaux" or by "No. This painting IS a Yarpleaux."

The particular prototypes that were labeled Yarpleaux, Not Yarpleaux, and Noogan were counterbalanced. Thus, for half of the subjects in the asymmetric-labels group, one prototype was labeled "Yarpleaux" and the other prototype was labeled "Not Yarpleaux." These labels were swapped for the other subjects.

Results

The results of principal interest, shown in Table 2, pertained to the influence of nondiagnostic and diagnostic features on categorization accuracy within the asymmetric labelling condition. The table shows categorization accuracies when 0 or 4 nondiagnostic or diagnostic features were altered from the prototype. Although more than 4 features were altered occasionally, there were not sufficiently many of these cases to assure statistical reliability. When concepts were asymmetrically labeled, there was a larger influence of nondiagnostic features on the "Yarpleaux" concept than on the "Not Yarpleaux" concept, based on the slopes of lines relating number of features altered (0, 1, 2, 3, or 4) and categorization accuracy , F(1, 11) = 5.3, mse = 0.18, p < .05 (Yarpleaux nondiagnostic = - 2.6, Not Yarpleaux nondiagnostic = -0.8). The concepts from the symmetric labels conditions showed an influence of nondiagnostic features that was intermediate to the two asymmetrically labeled concepts (symmetric diagnostic = -6.2, symmetric nondiagnostic = -1.5), and was not significantly different from the influence of nondiagnostic features in either of the asymmetric conditions, F(1, 22) = 2.1, mse = 0.39, p>0.1. There was no difference between the three groups in the influence of diagnostic features on categorization accuracy (Yarpleaux = -6.2, Not Yarpleaux = -4.8, symmetric = -6.2), F(2, 22) = 1.7, mse = 0.34, p >.1.

Marginally significant corroborating results were found when subjects were asked to draw their best representation of each of the concepts. Subjects drew an average of 6.3, 6.6, and 6.2 correct diagnostic lines (F(2, 22) = 1.1, mse = 0.87, p > 0.1) and 7.9, 8.2, 7.0 nondiagnostic lines (F(2, 22) = 3.1, mse = 1.1, p = 0.07) for the symmetric, "Yarpleaux," and "Not Yarpleaux" conditions respectively.

As shown in Table 2, the influence of nondiagnostic features decreased, F(1, 22) = 5.9, mse = 0.35, p < .05, and the influence of diagnostic features increased, F(1, 22) = 4.9, mse = 0.23, p < .05, with practice, collapsing across labeling conditions. These results are consistent with those obtained in Experiment 2.

Discussion

Experiment 3 illustrates one method for creating asymmetrically interrelated concepts. When labeling concepts A and Not A, the A concept appeared to be relatively isolated and the Not A concept appeared to be influenced by the other concept, even though the actual prototypes were logically equivalent. Nondiagnostic features that were equally likely to occur for both A and Not A concepts were much more likely to be associated with A. When concepts were learned with labels that were not related to each other, they became represented in a fairly isolated manner.

The success of the labeling manipulation casts doubt on the generality of the alternative account for Experiment 1. The alternative account was that complex features that involve more than one line segment are more likely to develop with Image than Discriminate instructions. Although this account is plausible for Experiment 1, for Experiment 3 there is little reason to think that complex features are more likely to develop for asymmetric positively labeled categories than for symmetric categories, or for symmetric categories than for negation-labeled categories.

Taken in total, the first three experiments show that concept interrelatedness, as indicated by reliance on nondiagnostic and diagnostic features, can be promoted by a number of experimental manipulations. Concepts are relatively interrelated when subjects are instructed to look for discriminating features, when categories are alternated often, and when categories are labeled as negations of other categories. Concepts are relatively isolated when subjects are instructed to create concept images, when categories are alternated infrequently, and when categories are given unrelated or standard labels.

The second method for measuring the degree of concept interrelatedness involves comparing the categorization accuracy for a concept's prototype and caricature. Consider the simple case in which two concepts can be distinguished by their values on a single dimension. Concept A has instances that are 2, 3, and 4 inches wide, while Concept B has instances that are 6, 7, and 8 inches wide. The prototype of Concept A is the 3 inch item; the caricature of Concept A is the 2 inch item. The prototype of a concept is the item that possesses the central tendency of dimension values, averaging over all of the concept's instances. Caricatures of a concept assume dimension values that depart from the central tendency in the opposite direction from the central tendency of other concepts to be simultaneously acquired. Thus, 3 inches is the central tendency of concept A because it is the average of 2, 3, and 4, but 2 inches is a caricature of concept A because it is less than A's average of 3 inches and B's average of 7 inches is greater than A's average. Just as a caricature of a politician in a cartoon exaggerates certain distinguishing features of the politician, so a caricature of a concept makes the dimension value that distinguishes the concept from other concepts more extreme.

A question of interest is: is the prototype or caricature of a concept more accurately categorized as belonging to the concept? On the one hand, it might be argued that the prototype will be better categorized. The prototype is the item that is closest to the most other category items, assuming either normal or uniform item distributions. According to prototype theorists, a concept's representation is based on the prototype of the concept, and the degree to which an item belongs to a concept is directly related to the item's proximity to the concept's prototype (Posner & Keele, 1968; Rosch, 1975). Some researchers have extended the notion of a prototype to include concepts that are defined in terms of an ideal or exaggerated item (Lakoff, 1987). However, in this discussion the notion of a prototype will be restricted to the central tendency or most average member of a category.

On the other hand, an argument can also be made that the caricature is better categorized. Several researchers have found a caricature advantage in categorization accuracy and/or speed (Rhodes, Brennan, & Carey, 1987; Hearst, 1968; Nosofksy, 1991). Caricatures emphasize distinguishing category features (Rhodes et al, 1987), and are further removed from the boundary between categories than are prototypes (Ashby & Gott, 1988; Nosofsky, 1991).

The framework developed thus far predicts that whether a prototype or caricature advantage is found will depend, in part, on the degree to which concepts are interrelated. If a concept is purely isolated, an advantage for the concept's prototype is expected. In the absence of interconceptual influences, the representation that best exemplifies a concept will be its prototype. However, if a concept is characterized relative to other concepts, then rules of the sort "Concept A items are smaller than Concept B items" or "Concept A is small, relative to Concept B" will be likely to develop. Caricatures better fit these relational rules than do prototypes. While items of 2 or 3 inches both satisfy the rule "smaller than Concept B items," the item of 2 inches more clearly satisfies this rule. Thus, if a concept is purely isolated and categorization speed or accuracy is a function of the proximity of the item to the concept's best representation (Rosch & Mervis, 1975), then the prototype is expected to be more accurately or quickly categorized than caricatures. Whether an item is a caricature or simply a distortion of a concept's prototype can only be answered when the other concepts to be acquired are considered. Consequently, as the interrelatedness of concepts increases, so should the categorization advantage of the caricature relative to the prototype.

Experiment 4 tests the prediction that prototypes will be categorized relatively easily with instructions that bias subjects toward isolated concepts, whereas caricatures will be categorized relatively easily with instructions that bias subjects toward interrelated concepts. The experimental manipulation used is identical to the one used in Experiment 1. Thus, Experiment 4 is an attempt to provide converging evidence to the results from Experiment 1, using a previously supported manipulation that affects concept interrelatedness, and a new empirical indicator based on the ease of prototype/caricature categorization.

Experiments 1 and 2 indicated that nondiagnostic features were more likely to be used for categorization when few diagnostic features were altered from category prototypes. One explanation for this effect is that subjects were more likely to use a template-matching (an isolated representation) strategy for categorization when the overall similarity of the object to be categorized and its best-fitting category was high. Experiment 4 further explored this hypothesis by varying the overall similarity of objects to prototypical category representations. On the majority of trials, displayed objects had particular nondiagnostic features. When these standard nondiagnostic features were present in a stimulus, it was predicted that subjects would more effectively use a template-matching strategy, because of the greater overlap between the item and the categories. The use of a template-matching strategy, in turn, would translate into greater facility with categorizing objects with prototypical, relative to caricatured, dimension values.

Also, in this experiment, four rather than two categories were used. One objection to Experiments 1-3 is that two-category conditions unnaturally bias subjects to use a special case of interrelated concepts in which one concept is characterized simply as "whatever is not the other concept." Creation of this type of "leftovers" category is discouraged in Experiment 4 by increasing the number of categories to learn.

Method

Materials. Sample materials are shown in Figure 4. Stimuli consisted of seven vertical bars joined together to form a histogram-like shape. Each bar assumed one of 6 different values (1.0= shortest, 6.0=tallest, each unit corresponding to 1.5 cm). The histograms belonged to one of four categories. Each category was associated with one long bar, and three short bars with values of 1.0. All four of these bars were diagnostic because if they had a height value above 1 then they provided information in favor of one and only one of the categories. The lengthened diagnostic bar for a category had a value of 2.0 on one quarter of the trials, 3.0 on one half of the trials, and 5.0 on one quarter of the trials. Thus, a value of 3.0 for a lengthened diagnostic bar was considered the prototypical value, because it occurred most frequently, and because its value was intermediate to the other possible values. A value of 5.0 for a diagnostic bar was considered a caricature because it exaggerated the length of the bar that was particularly long for the category, and it exaggerated the length in the direction opposite to the other categories' bars.

The other three bars were nondiagnostic. At the beginning of an experiment, three randomly determined bar heights were generated. These were the standard values for the nondiagnostic bars. The bars were nondiagnostic because all four categories shared the same standard set of values for these bars. On one half of the trials, a histogram was presented with the standard values for the nondiagnostic bars. On the other half of the trials, new random heights were generated. Thus, subjects received a great deal of experience with one set of three nondiagnostic bar heights, and received less experience with all other sets of nondiagnostic bar heights.

Procedure. Twenty-six undergraduates from Indiana University were divided into two instruction groups. The two sets of instructions corresponded to Image and Discriminate instructions used in Experiment 1. Subjects were reminded every 96 trials to use imagery or discriminating features to guide their categorization. At the beginning of the experiment, subjects were instructed to make their categorization decisions as quickly as possible without sacrificing accuracy.

There were 384 trials in all. On each trial, a histogram appeared and subjects pressed one of four keys to indicate their proposed categorization for the object. Subjects then received feedback indicating whether their choice was correct and the correct response. All materials were presented on Macintosh SE computers. After all categorization trials were completed, subjects were asked to draw as good representations as possible of the four categories on 7X8 grid paper.

Results

The results of Experiment 4 are shown in Figure 5. Given that accuracy rates were above 93%, the dependent variable of greatest interest was response time for correct categorization. There was a general speed advantage for categorizing caricatures (height = 5, RT = 1.74 sec) relative to prototypes (height = 3, RT = 2.07 sec), F(1, 24) = 14.7, mse = 0.47, p < .05. In addition, subjects were faster to categorize instances when the nondiagnostic bars were in their standard configuration (standard RT = 1.72, random RT = 2.27 sec), F(1, 24) = 23.6, mse = 0.49, p < .05. Finally, there was a main effect of instructions, with Discriminate subjects categorizing more quickly than Image subjects (Discriminate RT = 1.91 sec, Image RT = 2.20 sec), F(1, 24) = 11.1, mse = 0.26, p < .05.

Figure 5 shows two interactions of interest - between height of lengthened diagnostic bar and instructions, F (2, 48) = 5.7, mse = 0.28, p < .05, and between height and configuration of nondiagnostic bars, F(2, 48) = 6.5, mse = 0.19, p < .05. These interactions were still significant when only bar heights of 3 (prototype) and 5 (caricature) were considered, F(1,24)=5.0, mse = 0.35, p < .05, and F(1, 24) = 5.2, mse = .40, p < .05, respectively. Both of these interactions are predicted by the isolated/interrelated framework. The first interaction indicates that the speed advantage of caricatures over prototypes was particularly pronounced when subjects were given Discriminate rather than Image instructions. The second interaction indicates that the caricature advantage was greatest when items were presented with a random configuration of nondiagnostic features. One interpretation of this result is that when the overall stimulus configuration was similar to a familiar item, then a process similar to template-matching transpired. Conversely, when the item, because of unfamiliar values for nondiagnostic features, was not similar to many previous items, then rules of the form "third bar is relatively long" were used.

With increasing practice, the caricature advantage increased, as shown by a significant blocks (early vs late) X type of stimulus (prototype vs caricature) interaction, F (1, 24) = 6.7, mse = 0.32, p < .05. For the first half of the 384 trials, correct categorizations took 2.6 and 2.5 seconds for the prototypes and caricatures respectively. for the second half, these numbers fell to 1.6 and 1.0 respectively.

The instructional manipulation also influenced subjects' pictorial representations of their concepts. Each of the four categories had one diagnostic bar that was lengthened. The actual modal height of this bar was 3.0 units. Image subjects estimated, on average, the height of this bar to be 3.7, whereas Discriminate subjects estimated this height to be 4.3, t (24) = 3.3, p < .05. The heights of the three other diagnostic bars were 1.0. Image subjects estimated these bars to be 1.2, whereas Discriminate subjects gave an average estimate of 1.4, a non-significant difference, t(24) = 1.0, p > .1.

Discussion

The nature of the prototype/caricature advantage in categorization was influenced by both task and stimulus factors. When subjects looked for discriminating features, there was evidence of an strong advantage for categorizing caricatures relative to prototypes. This caricature advantage was also found when the item to be categorized did not share nondiagnostic features with previously categorized items. The caricature advantage was reduced when either of these factors was altered, that is, when subjects were given image instructions, or when nondiagnostic features were preserved. These results are consistent with those of the first three experiments and support the validity of a second indicator of concept interrelatedness.

Experiment 5 was conducted to obtain one final converging source of evidence, using the task manipulation of Experiment 2 and the indicator of interrelatedness developed in Experiment 4. Category instances were alternated either frequently or infrequently, and the effect of this manipulation on caricature/prototype categorization was observed.

Method

Procedure. The materials from Experiment 4 were used. The procedure from Experiment 4 was used, with a few exceptions. Subjects were given no instructions on the appropriate categorization strategy to use. Twenty-four Indiana University undergraduates were split into two groups. For one group of subjects, the frequent alternation group, the probability of presenting an item from the same category as the previous item was .07, and the probability of presenting an item from one of the three other categories was .31. For the infrequent alternation group, the probability of presenting an item from the same category as the previous item was .31 and the probability of presenting an item from one of the three other categories was .23. If subjects used an optimal guessing strategy and had no knowledge of an item's category, then the two conditions were equated for probability of correct categorization (.31).

Results and Discussion

The results for Experiment 5 are shown in Figure 6. As with Experiment 4, caricatures were generally categorized more quickly than prototypes (prototype RT = 1.78, caricature RT = 1.51), F(1, 22) = 13.2, mse = 0.22, p < .05. Subjects made faster categorizations when nondiagnostic features were given familiar values (as with Experiment 4), F(1, 22) = 12.9, mse = 0.32, p < .05, and when concepts were alternated infrequently (as with Experiment 2), F (1, 22) = 9.8, mse = 0.34, p < .05. Categorization accuracy was 94% for the infrequent alternation group, and 92% for the frequent alternation group, F(1, 22) = 1.1, mse = 0.58, p > .1.

There were also two interactions involving the height of the lengthened diagnostic bar. First, the speed advantage for caricature over prototype categorization was greater when concepts were alternated frequently rather than infrequently, F(2, 44) = 5.4, mse = .18, p < .05. Second, the speed advantage for caricature over prototype categorization was greater when nondiagnostic features were given familiar rather than unfamiliar values, F(2, 44) = 3.87, mse = .13, p <.05. These results are consistent with the predictions of the isolated/interrelated framework. Frequent alternation of categories was expected to yield interrelated concepts, because instances from different concepts would be more likely be compared to each other. By this hypothesis, the presence of familiar nondiagnostic bar values increased the likelihood of using isolated concepts because it facilitated an overall template match rather than a selective use of discriminating features.

As with Experiment 4, the caricature advantage increased with practice, as evidenced by a two-way interaction between block (early vs late) and type of stimulus (caricature vs prototype) on response time, F(1, 22) = 7.1, mse = 0.28, p < .05. For the first half of the 384 trials, correct categorizations took 2.0 and 1.9 seconds for the prototypes and caricatures respectively. For the second half, these numbers fell to 1.5 and 1.1 respectively.

The five experiments presented investigated predictions made by the claim that concepts vary in the degree to which they are influenced by other simultaneously acquired concepts. The suggested continuum between isolated and interrelated concepts motivated the development of new task manipulations and measurements. The degree of interrelatedness was quantified in terms of: the influence of nondiagnostic features on categorization, the prevalence of nondiagnostic features in subjects' drawings, the relative advantage to categorizing prototypes relative to caricatures, and the degree of caricaturization in drawings. These four measures were in close agreement in locating concepts on the continuum of isolation/interrelation.

Reciprocally, the manipulations are in close accord in their influence of the measures of isolation. Isolated concepts are promoted by: giving subjects imagery instructions, alternating concepts infrequently, assigning unrelated labels to concepts, testing subjects early in practice, and presenting familiar or less distorted instances. Predictions for the first three manipulations are established by simple analysis of the manipulations. If subjects are asked to create separate images for each concept, if instances from different concepts are not often presented together, and if labels are presented that do not relate the concepts, then we expect that the concepts will become relatively isolated from each other. The final two manipulations (increasing the amount of training produces relatively interrelated concepts, and decreasing the similarity between an object and its category produces relatively interrelated concepts) have weaker apriori associations with concept isolation, but consistently cohere with the other three manipulations. The empirical results, from all four measures of interrelatedness, argue that concepts are increasingly influenced by each other as concept learning continues, and as increasingly distorted concepts are displayed.

Other Tests of the Interrelated/Isolated Framework

Experiment 3 introduced a manipulation that created asymmetrically defined concepts. Asymmetries were also found from manipulations of frequency and presentation order. If one concept is presented more frequently or earlier than another concept, then it is predicted to be relatively isolated. The less frequent, later concept will tend to be influenced by the frequent, earlier concept. These predictions have been tested with nondiagnostic feature use as an indicator of concept isolation (Goldstone, in preparation). Nondiagnostic features were more likely to be used for categorization, and depicted in concept representations, for categories that were presented on 80%, rather than 20%, of trials. Similarly, nondiagnostic features had more of an influence on concept depictions and categorizations for categories that were presented in the first 200, rather than second 200, trials. Unfortunately, presentation order was confounded with practice effects in this experiment.

In addition to Experiment 3, a second labeling manipulation was tested (Goldstone, in preparation). Stick-figure prototypes similar to those in Figure 1 were constructed for three categories. These three prototypes can be called A, B, and C. Every pair of category prototypes (A and B, A and C, and B and C) had two line segments in common. Although the prototypes were logically equivalent, one randomly picked prototype was labeled "Art from a Venusian Colony," and the other two prototypes were labeled "Art from Martian Colony 1" and "Art from Martian Colony 2." It was predicted that the two Martian categories would be more interrelated to each other than they would be to the Venusian category, because the labels make them more likely to be contrasted from each other than they would otherwise be. Consistent with this prediction, for the category labeled "Art from Martian Colony 1," line segments that distinguished the category from art by Martian colony 2 were more influential than were the line segments that distinguished the prototype from art by the Venusian colony. Thus, when labeling caused two categories to be compared and contrasted, features that discriminated between the categories were selectively highlighted.

In addition to the use of nondiagnostic features and caricatures as indicators of concept interrelatedness, a third indicator of interrelatedness concerns the influence of inter- and intra-category similarity on categorization ease. Both types of similarity are expected to influence categorization. As an item becomes more similar to items that belong to its same category, categorization of the item is facilitated. As an item becomes more similar to items that belong in a competing category, categorization of the item is impaired. Inter- and intra-category similarity need not be correlated. Evidence in favor of isolated concepts is obtained if the influence of intra-category similarity is relatively large compared to the influence of inter-category similarity. For categorizing into isolated concepts, the primary consideration is the degree of overlap between an item and the category's independently-derived representation. For interrelated concepts, inter-category similarity is expected to exert a greater influence.

This prediction was tested using the materials shown in Figure 7 (Goldstone, in preparation). Assessments of dissimilarity between every pair of letters were obtained by requiring subjects to move letters on a computer screen such that the distance between letters was proportional to their psychological dissimilarity (Goldstone, 1994d). Thus, dissimilarity was measured in centimeters. These dissimilarity assessments were used to create two categories based upon family-resemblance (Rosch, Simpson, & Miller, 1976) rather than defining features. At first, letters were randomly assigned to two categories. Then, a letter was selected at random. If the letter was more similar on average to the letters of the category that it was currently in, then the letter's category assignment was not changed. However, if the letter was more similar to the letters of the other category, then the category assignment of the letter was switched. This procedure was repeated 500 times. As a result of this procedure, the two categories shown in Figure 7 were generated. In this manner, quite natural categories can be created using materials that are rich, multi-dimensional, and ill-defined.

Subjects were given a category learning task similar to the one used in Experiment 1. The categorization accuracy of each letter was predicted from (linearly regressed on) two factors: the letter's within-category dissimilarity, and between-category dissimilarity. As predicted by the developed framework, the influence of between-category dissimilarity, relative to within-category dissimilarity, increased when task manipulations were given that should bias subjects to create interrelated concepts. In particular, between-category dissimilarity influenced categorization accuracy more when a categorization task rather than a "go/no go" task was used, and when "image" rather than "discriminate" instructions were given to subjects.

One of the main benefits of the isolated/interrelated framework is that it provides an integrated account for results from many different paradigms. For behavioral indicators, the framework links responding to caricatures accurately, being highly influenced by nondiagnostic features, and being highly influenced by inter-category similarities. The framework also links all of the experimental manipulations shown in Table 1. It is possible to explain particular experimental results without hypothesizing a continuum between isolated and interrelated concepts. In fact, a full account of the reported experiments will require the development of particular processing accounts for the experimental manipulations tested. However, the framework is a valuable first step because it predicts the observed commonalities between apparently different tasks and indicators. For many of the manipulations, particularly those that involve labeling, we are a long way from describing adequate process models, but we can still give a general characterization of the tasks as biasing subjects toward isolated or interrelated concept representations.

Similarly, the ramifications of the current experiments for natural semantic categories are not yet clear. While the current experiments have focused on task manipulations that influence concept interrelatedness, there may be systematic differences in the degree of interrelatedness of different classes of natural concepts. The first potential type of group difference is that abstract concepts may be more interrelated than concrete, perceptual objects. The basis for this prediction is that the most readily available methods for representing isolated concepts, including feature detectors and templates, seem to be tied to perceptual features. However, nothing in the current results or discussion requires that interrelated concepts be conceptual or isolated concepts be perceptual. In fact, all of the concepts acquired in Experiments 1-5 are predominantly visual, and one of the sources of evidence for interrelatedness was based on the perceptual caricaturization of concepts.

A second potential difference is that artifact categories may be more interrelated than natural kind categories. Barr and Caplan (1987) find that artifacts have many extrinsic features associated with them (a feature of hammer is that it is used to hit nails), while natural kinds have a preponderance of internal, intrinsic features (a feature of robin is that it has wings). Third, real-world concepts may be more interrelated than fictional concepts. Potts, St. John, & Kirson's (1989) subjects read a story about a novel bird and were told that the bird was fictional or truly existed. Subjects' concept of the bird was more isolated from the rest of subjects' knowledge (as measured by the time required to answer questions about the bird that are presented in a context not related to the story) when they believed the story to be fictional than real. Fourth, verbs may be more interrelated than nouns. Gentner (1981) argues that interpretations of nouns are typically independent of the other elements of a sentence, whereas interpretations of verbs depend on the sentence context.

Potential Categorization Models

The primary implication of the results for psychological models is that a full model of categorization should be able to have categories exert varying degrees of influence on each other. In order to account for the empirical results, models should be able to predict both main effects (diagnostic features are more influential than nondiagnostic features, nondiagnostic features exert some influence, and caricatures are categorized faster than prototypes), and the interactions between these effects and task manipulations. In this section, the ability of existing categorization models to account for the main effects and interactions is assessed.

Due to their processing principles, prototype (Posner & Keele, 1968; Reed, 1972; Rosch, 1975) and exemplar (Medin & Schaffer, 1978; Nosofsky, 1986) models can accommodate results that have been taken to indicate relatively interrelated concepts such as a caricature advantage (Nosofsky, 1991) and selective influence of diagnostic features (Rosch, Simpson, & Miller, 1976). Even in situations where the representation of a concept is not influenced by other concepts, the extension of the concept may be influenced by competition with other concepts. The Hull-Spence model (Hull, 1943; Spence, 1936) provides a classic demonstration of a model that is able to explain a caricature advantage such as is found in Experiments 4 and 5. In a phenomenon known as "peak-shift," when an animal is rewarded for responding in the presence of a stimulus with dimension value X, and is not rewarded when shown a stimulus with a dimension value noticeably greater than X, then the animal responds maximally to a stimulus with a dimension value less than X. The rewarded stimulus, S+, may be a light with a wavelength of 550 nm (the details are taken from Hanson, 1959), and the unrewarded stimulus, S-, may have a wavelength of 560 nm. After this discrimination training, subjects respond maximally not to 550 nm, the stimulus originally rewarded, but to a value displaced from 550 nm, in the direction opposite to the unrewarded stimulus.

According to the Hull-Spence model, responses to the rewarded and unrewarded stimuli generalize to similar stimuli. Sample generalization curves with a Gaussian distribution are shown in Figure 8. Furthermore, it is assumed that the tendency to respond is obtained by subtracting the strength of the unrewarded stimulus response from the strength of the rewarded stimulus response. Thus, to determine how great the response is to a stimulus, one would compare the difference between the S+ and S- curves at the wavelength corresponding to the stimulus. When this is done, it is apparent that the maximal responding occurs for a stimulus with a lower value than the trained value of 550 nm. Even though the internal representation of the rewarded stimulus is veridical and is not influenced by the unrewarded stimulus (it remains centered on 550 nm), a caricature advantage emerges, because of the process by which representations are integrated in order to make a response.

Categorization models can accommodate a differential influence of nondiagnostic and diagnostic features on categorization accuracy, even if concept representations in the models are not influenced by other concepts. For example, in the Context Model of Medin and Schaffer (1978), the probability of an item i being placed in a category n is equal to

,

where Sij is the similarity of items j and i. Thus, the probability of placing an item in a category is equal to the summed similarity of the item to every example in the category n divided by the summed similarity of the item to all examples from all categories. If we further assume, as Medin and Schaffer do, that Sij is determined by multiplying dimensional proximities (if two items have the same value on a dimension, then a value of 1 is assigned; otherwise, a value between 0 and 1 is assigned), then it is evident that nondiagnostic features are not expected to influence categorization accuracy. For example, consider two categories, with Category A consisting of {red square, red circle, red diamond} and Category B consisting of {red hexagon, red triangle, red pentagon}. Assume that a color mismatch results in a dimensional proximity of d, and any shape mismatch results in a dimensional proximity of e. Presenting a red square results in

,

whereas presenting a blue square results in

.

Thus, whether the item to be categorized possesses the nondiagnostic feature (red) that is characteristic of both categories should not influence categorization. Appendix A contains a demonstration of this conclusion for the particular materials and the methods used in Experiment 1.

The Context Model and the Hull-Spence model show that it is possible to develop models that account for evidence of interrelated concepts without positing that concepts influence each other's representations. Instead, these model predict advantages for caricatures and diagnostic features by decisional rules that use evidence for one response relative to evidence for another response. In the case of the Context Model, the nondiagnostic and diagnostic features have different influences because of the inherently relative categorization rule (a ratio rule). The results from Experiments 1-5 suggest two problems for this purely decisional approach. First, results from tasks where subjects provide depictions of their category knowledge are not naturally accommodated. In all five experiments, subjects were asked to draw their best possible representation of the acquired concepts. Results showed that diagnostic features were generally more likely to be correctly drawn than nondiagnostic features, and that there was a bias to draw caricatured, as opposed to prototypical, dimension values. Importantly, the draw-a-concept task requires an absolute, not relative, judgment (Busemeyer & Myung, 1988). Deciding what category to place an object in involves consideration of all of the learned categories; the judgment is an inherently relative one. By contrast, there is nothing in the instructions to draw an accurate representation of a typical concept member that should dispose subjects to consider other concepts. The task can be accomplished by considering the concept alone. The empirical result that caricatures and diagnostic features dominate drawings suggests that the characterization of an acquired concept is influenced by other concepts, even when the concept's characterization is probed with tasks that are not relational.

The second difficulty for these particular models is in accommodating the influences of the task manipulations. It is not sufficient to develop a model that can predict a caricature or prototype advantage, or predict that nondiagnostic features either will or will not influence categorization accuracy. An account is also needed that describes the conditions under which each of the results is likely to be found. For example, nondiagnostic features are more likely to exert an influence under conditions that have been grouped together under the label "relatively isolated." These conditions include: imagery instructions, infrequent category alternation, and unrelated labeling. If we assume that the degree of concept interrelatedness is variable, and we make reasonable assumptions about how particular tasks affect interrelatedness, then the observed influences of the task manipulations are predicted. If we assume only isolated representations, then no systematic explanation is given for the task manipulations' effects. Thus, we gain confidence in the isolated/interrelated continuum because its task manipulation predictions are borne out empirically. While there may be alternative explanations to account for the effect of some of the task manipulations separately, the isolated/interrelated framework provides a single coherent account for the entire set of manipulations.

There are ways of manipulating parameters in exemplar models that shift the categorization advantage of caricatures and prototypes, or vary the influence of nondiagnostic features. However, the necessary parameter manipulations map less naturally onto the particular task manipulations used than does the isolated/interrelated continuum. For example, Medin (personal communication, May 1993) suggests that a "junk category" could be included as a possible category response when a presented item is not sufficiently similar to the items in existing categories. This junk category would be used more frequently as nondiagnostic features are removed, thus capturing responses that would otherwise fall into correct categories. Nosofsky (1991) suggests including a constant amount of noise into the category decision rule. When nondiagnostic features are present, the noise will be relatively unimportant because the item-to-category similarities (S values) will be large. When nondiagnostic features are removed, noise will have more of an influence on decreasing categorization accuracy. Although these modifications do allow nondiagnostic features to influence categorization, their relation to the actual task manipulations is not compelling. For example, Nosofsky's noise parameter could accommodate the results from Experiment 1 for both Imagery and Discriminate groups, but only if the amount of noise were greater for the Imagery than for the Discriminate group. There is little reason to think that system noise or the likelihood of categorizing items into a "junk" category increases when image instructions are used, when categories are alternated infrequently, or when unrelated category labels are given. In fact, categorization accuracy is greater when categories are alternated infrequently rather than frequently, in opposition to the assumption of high noise for infrequent alternation that would be needed to account for the results of Experiments 2 and 5 (see also Whitman & Garner, 1963). Thus, the natural mechanisms of these models for increasing the influence of nondiagnostic features do not seem to correspond closely to the experimental manipulations used.

Future research with exemplar or prototype models may generate parameters that are naturally associated with the task manipulations used in Experiments 1-5 and that correctly predict when caricatures are well categorized and nondiagnostic features are influential. Until this happens, it seems that the most parsimonious synthesis of the results is that experimental manipulations differentially affected how interrelated concepts were. This interpretation naturally captures commonalities of the experimental manipulations, captures commonalities between the two experimental measures (prototype/caricatures categorizations and nondiagnostic/diagnostic feature influence), and predicts the results from measures of interrelatedness that involve category reconstructions rather than categorization judgments. The results suggest that complete models of categorization should incorporate concept characterizations, through representation and process, that can vary in their degree of interrelatedness.

A connectionist approach to isolated/interrelated concepts

A connectionist model, RECON, has been developed to provide a qualitative account of the experiments' results. The purpose of the model is to provide a demonstration of how a single mechanism can yield both isolated and interrelated concepts, rather than to provide detailed quantitative fits (such as those provided by Kruschke, 1992; Nosofsky, 1986). Essentially, RECON is a two-layer recurrent network. One layer of units represents the input dimensions, and one layer represents the categories being learned. All units in RECON are connected to each other by variable strength connections. The most important elements of RECON are its recurrent connections between category units, and from category units to input units. These connections provide a mechanism for categories to influence each other and for a featural description to be produced when a category label is given. By varying a single parameter, the degree of influence of category units on each other, varying degrees of concept interrelatedness are obtained.

In feed-forward connectionist systems, activation flows from input to hidden to output units, and the weights that are learned regulate this uni-directional flow. Typically, input units encode the featural or dimensional representation of the object to be categorized, and each output unit signifies a category. In RECON, activation flows between output/category units, from output to input units, and between input units, in addition to the standard feed-forward flow. Recurrent activation passing is a feature of several connectionist models, including McClelland and Rumelhart's Interactive Activation Model (1981) and Grossberg's ART system (Carpenter and Grossberg, 1991).

Learning in RECON consists of two stages: recurrent activation passing, followed by a weight adjustment procedure similar to that proposed by Hebb (1949). In the first stage, units that represent input dimensions and categories spread activation between each other. The spread of activation is modulated by learned connection weights. Activation is spread for a number of cycles determined by the parameter cycles (arbitrarily set to 15 for all of the simulations). In the second stage, weights are adjusted so that the units that have similar activations after the allotted number of activation-passing cycles become more strongly connected. When RECON is tested after training, the recurrent flow of activation between units occurs when a pattern is presented, and in this way, concepts are influenced by each other, and influence input representations. The concept-to-input influence provides a way to account for results that suggest that categorization training can change low-level perceptual sensitivity to objects (Goldstone, 1994a).

Activation for both input dimensions and categories are in the range -1 to +1. All connections weights are initially set to zero. When processing a new trial, activation is first spread between all units (units are not connected to themselves). The input activation to a unit j, netj, is

,

where ej is the externally provided activation of unit j, wji is the weight of the connection from unit i to j, the internal and external strengths (extr and intr) are both set to 0.15, and ai is the current activation of unit i (0.15 was selected because of its use in simulations by McClelland and Rumelhart, 1986). The change of activation of unit j can now be expressed as

,

where max=1 and min=-1. These two formulae are taken from McClelland and Rumelhart (1986). After a set number of cycles have passed, weights are adjusted via

,

where the activation values ai and aj have been influenced by the preceding recurrent spread of activation, and a is the learning rate (set at 0.1). Via this learning rule, connection weights between nodes will increase to the extent that the nodes have similar activation values, but are constrained not to fall below min or above max. Following Kruschke (1992), categorization decisions are made by

,

where P(c) is the probability of placing the item in category c, f =1.0, K is the set of units representing categories, and ac is the activation of the node designating category c. Output activation are determined by the same recurrent spread of activation that occurs during training.

Although specific process models for task manipulations are desirable (Goldstone, 1994b; Goldstone & Medin, 1994), the current modeling focuses on the underlying commonalities between the different task manipulations. As such, a single parameter is changed to model all task manipulations that vary the interrelatedness of concepts. The advantages of this abstract modeling of the experimental results are that significant similarities between dissimilar tasks are highlighted, and specific processing accounts with numerous additional assumptions are not required. For example, although an account could describe the different processes involved in traditional categorization tasks and "Go/no go" tasks (or different labeling conditions), such an account would probably need to involve elaborate assumptions about subject's comprehension and interpretation of instructions. Process accounts for other experimental manipulations, such as category alternation frequency, are more easily tackled, but are beyond the scope of the current modeling.

Experimental manipulations of interrelatedness are modeled by manipulating category-to-category weights. Category-to-category weights are clamped to particular values. The assumption is that tasks that yield highly interrelated concepts are modeled with category-to-category weights with relatively large absolute values. If category-to-category weights are small, then the activation of one category will not depend on the other categories' activations very much. Increasing the strength of connection weights between categories is expected to produce performance that is similar to subjects who were given task manipulations that yielded interrelated concepts.

Nondiagnostic and Diagnostic Features. Increasing the strength of category-to-category weights (by making the weights increasingly negative) yields a larger disparity between the influence of diagnostic and nondiagnostic features. One of the simplest tests of the influence of nondiagnostic and diagnostic features is to provide RECON with the two patterns: 1 0 1 0 1 0, and 1 0 0 1 0 1, as shown in Figure 9. These two patterns are presented to RECON 100 times each, in random order. In these patterns, the first two values code for one binary dimension ("1 0" can be interpreted as "red =yes, blue = no"), the third and fourth values code for a second binary dimension ("1 0" = large, "0 1" = small), and the last two values code the category ("1 0" can be interpreted as "category A = yes, category B = no"). By using two units to code dimensions and categories, conceptual problems with +1/-1 units are avoided (e.g. how are absent features represented - as -1 or 0?) and several potential relations between concepts can be modeled (categories A and B may be negatively connected if mutually exclusive, or positively connected if hierarchically or associatively related).

The pattern "1 0" on the first two units is nondiagnostic for categorization. Both the A and B category items have the same values for this dimension. This pattern has high category validity though, because all items possess this pattern. The second dimension is diagnostic. If the pattern for the second dimension is "1 0," then the category pattern is "1 0." If the pattern is "0 1" then the category pattern is "0 1."

Figure 9 shows RECON's architecture for the problem, and the learned weights under two values of category-to-category weights. All weights are directional, with solid and dashed lines indicating positive and negative weights, respectively. The thickness of a connection reflects the magnitude of the weight. Only some of the connections are shown; the actual network is fully connected. Three sources of evidence point to an influence of category-to-category weights on the importance of diagnostic/nondiagnostic features.

First, the difference between the dimension-to-category weights for nondiagnostic and diagnostic features is greater as category-to-category weights become increasingly negative. When category-to-category weights are -1, the connection strength from nondiagnostic and diagnostic features to the categories is roughly equal after training on the two patterns. When categories exert more influence on each other, achieved by increasing category-to-category weights to -10, then the connection from diagnostic features to categories is much stronger than the connection from nondiagnostic features to categories.

Second, nondiagnostic features have decreasing influence on categorization accuracy with increasingly negative category-to-category weights. Test trials consist of the patterns "0 0 1 0 0 0" (nondiagnostic feature removed) and "1 0 1 0 0 0" (nondiagnostic feature present). During testing, RECON is given one of the patterns, learning is disabled, and 5 cycles (this value was used in all simulations of post-training behavior) of recurrent activation spread are executed. The likelihood of giving the correct "1 0" category response is substantially reduced when the nondiagnostic feature is removed, but only when the categories do not have strongly negative connecting weights. If category-to-category weights are strongly negative, then the two patterns result in almost identical categorization accuracies.

Third, relative to diagnostic features, nondiagnostic features are less prominently figured in concept representations when category-to-category weights are strongly negative. Because of the category-to-dimensions connections in RECON, we can observe the resulting spread of activation from the pattern "0 0 0 0 1 0." This is tantamount to telling RECON that an item belongs to Category A, and asking RECON what it looks like. As such, it provides a method for modeling the draw-a-concept tasks of Experiments 1-5. Although both nondiagnostic and diagnostic units are activated by activating a category node, diagnostic units become much more activated with increasingly negative category-to-category weights. If category-to-category weights are only -1, then nondiagnostic and diagnostic features are almost equally strongly activated by "0 0 0 0 1 0."

All three of these effects are attributable to a single cause. If the connection between categories is strongly negative (the concepts are relatively interrelated), then when one category unit begins to be activated by the input it will inhibit the other category unit. If the inhibition is sufficiently strong, the less activated unit will develop a negative activation. If this occurs during the recurrent activation passing stage, then during the learning stage there will be a negative correlation between the present nondiagnostic features' activation and the inhibited category's activation. According to the Hebbian learning rule, this negative correlation will result in a decrease in the input-to-category connection weight. This learned weight change will counteract the increase in the weight that occurs when one category dominates over the other category. As a result, the nondiagnostic feature will not be strongly associated with either category.

If the connection between categories is not strong (the concepts are relatively isolated), then no category unit will be strongly inhibited by other categories, and there will be positive correlations between the present nondiagnostic features and both category units. As a result, the association between the nondiagnostic features and both categories will increase.

In short, when category units strongly inhibit each other, then diagnostic features become much more important for categorization than do nondiagnostic features. Strongly negative category-to-category weights result in competition between the categories. After activation has been passed for several cycles, only one category will have a strong positive activation. In these circumstances, features that do not distinguish between categories will not be highly associated with either category. This effect has been replicated in a simulation that involved 20 input nodes, and 600 randomly generated distortions of two category prototypes constructed in the same manner that they were constructed in Experiments 1-3.

Prototype and Caricature Categorizations. The categorization advantage of caricatures over prototypes is increased by making category-to-category weights increasingly negative. This is apparent from an analysis of categorization performance, concept production, and connection strengths. One of the simplest sets of materials for exploring caricature/prototype categorizations is shown at the top of Figure 10. Six patterns are placed in two categories. Six units are used to represent a single underlying dimension, and each example is unidimensional. The six patterns shown in Figure 10 are randomly presented to RECON 100 times each during learning. The dimension value of an item is represented by the heightened activity of units that are linearly ordered (for another example of "place coding" in connectionist architectures, see McClelland & Jenkins, 1991). The three input patterns to Category A can be thought of as coding for 2, 3 , and 4 inches, whereas the three input patterns to Category B are 5, 4, and 3 inches. The prototype for Category A is 3 inches, and its caricature is 2 inches. As before, Category A is represented by "0 1" on two additional units, and Category B is represented by "1 0."

As evident in Figure 10, the connection weights between input and category units depends on the strength of category-to-category weights. When category-to-category weights are -1 the input unit with the strongest connection to Category A is the one that codes for 3 inches. When category-to-category weights are -10, the input that codes for 1 inch is most strongly connected to Category A, and the unit that codes for 4 inches is negatively connected to category A. Thus, as categories increasingly inhibit each other, the category becomes increasingly associated with its caricature rather than its prototype.

A similar trend from strong prototype to strong caricature connections exists for the weights that connect categories to inputs. Because of these reciprocal connections, the draw-a-concept results are accommodated. When category-to-category weights are -1 and the representation "0 0 0 0 0 0 1 0" is given as input (i.e. only the category name is provided), then the inputs attain values in which the prototype is much more active than the caricature (0.14 versus 0.01). When category-category weights are -10, the caricature is more active than the prototype (0.19 and 0.13 respectively)

Finally, when categorization judgments are requested, the expected interaction between cycles and prototype/caricature advantage is found. When category-to-category weights are -1, Category A is more likely evoked by "0 0 1 0 0 0 0 0" (i.e. only the prototype unit activated) than by "0 1 0 0 0 0 0 0" (caricature). When category-to-category weights are -10, there is a categorization advantage for the caricature.

RECON, rather than being a competitor to current connectionist models of categorization (Gluck & Bower, 1988; Kruschke, 1992), is properly viewed as a method for augmenting these models. Architectural aspects of these models, such as learned selective attention to diagnostic dimensions (Kruschke, 1992), would have to be incorporated into RECON for it to be a full model of categorization. RECON's value is that it furnishes possible methods for accommodating task manipulations, yielding concepts that occupy various positions along the isolated/interrelated continuum. RECON cannot model all of the specific results from the experiments, but it does show how a single model can develop varying degrees of inter-category influence. Furthermore, it provides an account for the empirical correlation found between dependent measures. In RECON, the same parameter manipulation that produces a caricature advantage also produces a relatively strong influence of diagnostic features.

Conclusion

The five experiments support the postulation of a continuum between completely isolated and completely interrelated concepts. It is possible to experimentally manipulate the degree of isolation of a concept, as measured by a variety of converging operations. A connectionist framework accounts for the results by assuming recurrent connections among concept units, and from concept units to input units. Interrelated concepts are modeled by allowing concept units to exert a relatively large influence on each other. This line of work offers the promise of providing a bridge between two communities that study concepts. On the one hand, as many psychologists who study language argue, concepts are intricately connected to each other, and these connections influence the internal representations of concepts. On the other hand, as exemplified by models of object recognition, concepts also seem to be directly accessed for the purpose of recognition, using representations that are partially independent of other concepts. In fact, concepts may typically be located at intermediate positions along a continuum of interrelatedness such that they gain their meaning in part from relations to other concepts and in part from external grounding.

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Assuming that the individual line segments of the materials from Experiments 1-3 are the psychologically relevant features, the Context Model (Medin & Schaffer, 1978) predicts that the presence of nondiagnostic line segments will not alter categorization accuracy, even if the nondiagnostic line segments have high category validity [e.g. P(line segment|category)>0.5]. To simplify the demonstration, all dimensional proximities between differing values are assumed equal, and assigned the parameter p and all identical values are given a dimensional proximity of 1.0. According to the Context Model,

,

where Sij is the similarity between i and j, and is determined by

,

where pijf=p is the dimensional proximity between i and j on dimension f.

To demonstrate the lack of influence of nondiagnostic features, we will assign separate terms for nondiagnostic and diagnostic feature matches, and will observe that the term for nondiagnostic features drops out of the equation for categorization probability. Let n be the number of nondiagnostic features that an item has in common with Category 1, d be the number of diagnostic features that an item has in common with Category 1, and Tn and Td be the total numbers of nondiagnostic and diagnostic features that category 1 has (the numbers are 12 and 8 respectively for Experiments 1-3). Let a be the probability of preserving a line segment in generating a category instance as opposed to switching it from on to off or from off to on - equal to 0.8 in Experiments 1-3. Now, the probability of a test item from a category possessing n nondiagnostic and d diagnostic feature matches in common with a previously stored item from the same category is

,

where

.

This is because there are two occasions when a feature match occurs - when neither instance alters the category's prototypical features [probability = a2], or when both do [probability = (1-a)2]. The probability of an item possessing n nondiagnostic and d diagnostic feature matches in common with an item from the other category is

,

where

.

That is, the two items will tend to agree on nondiagnostic features, because nondiagnostic features, by definition, tend to be associated with both categories. On the other hand, the only time instances from different categories will agree on a diagnostic feature will be when one and only one of the instances has altered the feature from its category prototype.

Given these probabilities, we can now define the probability of correctly categorizing an item into category 1 with n nondiagnostic and d diagnostic category 1 features as

,

which algebraically reduces to

.

As such, the determination of the correct category for an item depends on the number of diagnostic features it shares with a category's prototype, but does not depend on the number of nondiagnostic features. A similar demonstration can be provided for Nosofsky's (1986) generalization of the context model.

Experiments 1 and 2 were presented at the Thirteenth Annual Conference of the Cognitive Science Society, University of Chicago, August 1991. Experiment 4 was presented at the Fifteenth Annual Conference of the Cognitive Science Society, University of Colorado, June 1993. The author wishes to express thanks to Dorrit Billman, Michael Gasser, John Kruschke, James Hampton, Ben Martin, Douglas Medin, Robert Nosofsky, Steven Ryner, Richard Shiffrin, Edward Smith, and Linda Smith for their criticisms and suggestions, and to Paula Niedenthal for extensive help with editing and ideas. The research was supported by National Science Foundation Grant SBR-9409232.

Requests for reprints should be sent to Robert Goldstone, Psychology Department, Indiana University, Bloomington, Indiana 47405.

Table 1

Overview of Manipulations and Diagnostics

Manipulation	Prediction	Diagnostic	Indicators
Instructions Experiments 1, 4	imagery = isolated discriminate = interrelated	influence of non-diagnostic features on accuracy Experiments 1, 2, 3	large influence = isolated little influence = interrelated
Category alternation Experiments 2, 5	seldom = isolated often = interrelated	Presence of non-diagnostic features in drawings Experiments 1, 2, 3	frequent appearance = isolated rare appearance = interrelated
Category labels Experiment 3	standard = isolated negation = interrelated	categorization speed of caricature and prototype Experiments 4, 5	prototype advantage = isolated caricature advantage = interrelated
Practice Experiments 2, 3, 4, 5	early = isolated late = interrelated	Degree of caricaturization in subject-made drawings Experiments 4, 5	low degree = isolated high degree = interrelated
Degree of distortion Experiments 1, 2, 4, 5	low = isolated high = interrelated	influence of within and between category similarity	large w/i influence = isolated large b/w influence = interrelated
Category frequency	frequent = isolated rare = interrelated	dissemination of information to new concepts	restricted = isolated disseminated = interrelated
Presentation order	first category = isolated second category = interrelated
Classification task	Go/No-go = isolated classification = interrelated

Table 2

Results from Experiment 3

Experimental Condition	Categorization Accuracy when 0 nondiagnostic Features were Altered	Categorization Accuracy when 4 nondiagnostic Features were Altered	Categorization Accuracy when 0 diagnostic Features were Altered	Categorization Accuracy when 4 diagnostic Features were Altered
Symmetric labels	72%	65	82	51
Asymmetric labels "Yarpleaux" "Not Yarpleaux"	79 65	66 61	82 72	51 48
Early Trials (1-300)	71	58	76	52
Late Trials (301-600)	73	68	84	49

Figure 1. Sample stimuli from Experiment 1. Nondiagnostic line segments were included in both categories' prototypes. Diagnostic line segments were included in only one category's prototype. Distortions of categories were produced by randomly altering line segments with a probability of 0.2. In the actual materials shown to subjects, only the line segments and not the dots were displayed.

Figure 2. Results from Experiment 1, showing an interaction between instructions and type of features changed on categorization accuracy. The influence of a type of feature is given by the slope of its line.

Figure 3. Results from Experiment 2, showing an interaction between frequency of category alternation and type of features changed on categorization accuracy. The influence of a type of feature is given by the slope of its line.

Figure 4. Sample stimuli from Experiment 4. Each of the four diagnostic bars, if lengthened, provides evidence in favor of one of the four categories. For example, Category 1 is suggested if the rightmost bar is lengthened. The standard heights of the nondiagnostic bars are the same for each of the four categories. Caricatures are created by further lengthening the height of a category's diagnostic bar.

Figure 5. Results from Experiment 4. "Standard" = the nondiagnostic bars of the displayed item were given the standard values of the concept's prototype. "Random" = the nondiagnostic bars of the displayed item were assigned random values. Categorizing caricatures is generally faster than categorizing prototypes. This speed advantage is particularly pronounced when nondiagnostic bars are assigned random heights, and when subjects are told to search for discriminating features.

Figure 6. Results from Experiment 5. "Standard" = the nondiagnostic bars of the displayed item were given the standard values of the concept's prototype. "Random" = the nondiagnostic bars of the displayed item were assigned random values. A strong caricature advantage is found when nondiagnostic bars are assigned random heights, and when the categories are alternated frequently.

Figure 7. Materials used to test the prediction that between-category similarity is more influential for interrelated than isolated concepts (Goldstone, in preparation). Each of the two categories had 32 letters in it. The two numbers below each letter are distances (in centimeters) that reflect dissimilarity. The top number below each letter shows the average distance/dissimilarity between the letter and the other letters within the

Figure 8. An illustration of peak shift. A stimulus of 550 nm is rewarded, while a stimulus of 560 nm is not rewarded. Maximal response strength now occurs to a stimulus with a value less than 550 nm. This result is accommodated by the assumption that response strength to a stimulus is a function of the difference between the generalization curves for rewarded and non-rewarded responses. Greater response strength to a stimulus of 540 nm is predicted because the difference D2 is greater than the difference D1.

Figure 9. RECON networks that model the influence of nondiagnostic and diagnostic features on categorization under two different values for cycles. Dashed and solid lines represent negative and positive connection weights respectively. The thickness of a line represents the absolute magnitude of a connection. Diagnostic units (e.g. input unit 3) are relatively more influential than nondiagnostic units (e.g. input unit 1) as cycles or category-to-category learning increases.

Figure 10. A simulation of caricature/prototype advantages in RECON. The top of the figure depicts the 6 training trials presented to RECON. Category A consists of inputs representing values of 2, 3, and 4 on a dimension. Category B consists of inputs representing values of 3, 4, and 5. If few cycles of recurrent activation passing are allowed, then the prototypical values are most strongly associated with the categories. If more cycles are allowed, then the caricature values are associated with categories almost as strongly as are prototypical values.