Running head: Causal-Model Theory A Causal-Model Theory of Conceptual Representation and Categorization

This article presents a theory of categorization that accounts for the effects of causal knowledge that interrelates or links the features of categories. According to causal-model theory, people explicitly represent the probabilistic causal mechanisms that link category features, and classify objects by evaluating whether they were likely to have been generated by those mechanisms. Participants were taught causal knowledge that linked features of a novel category into a causal chain. In three experiments causal-model theory provided a good quantitative account of the effect of this causal knowledge on the importance of both individual features and inter-feature correlations to classification, and did so without postulating explicit weights on features or pairs of features. By enabling precise model fits and interpretable parameter estimates causal-model theory helps place the "theory-based" approach to conceptual representation on equal footing with the well-known similarity-based approaches. Causal-Model Theory 3 A Causal-Model Theory of Conceptual Representation and Categorization For several decades research on the topic of categorization has focused on the problem of learning new categories given examples of category members, that is, from empirical observations. The result has been a host of categorization models based on representational ideas such as central prototypes, stored exemplars, and variabilized rules, and processing principles such as similarity, that have considerable explanatory power and experimental support. More recently, the influence of the prior "theoretical" knowledge that learners often contribute to their representations of categories has also been a topic of study (Carey, 1985; Keil, 1989; Murphy & Medin, 1985; Schank, Collins, & Hunter, 1986). For example, adults and even many children not only believe that birds have features such as wings, flying, and building nests in trees, they also believe that birds have nests in trees because they can fly, and they fly because they have wings. Many even believe that morphological features of birds such as wings are ultimately caused by the kind of DNA that birds possess. However, in comparison to the development of models accounting for the effects of empirical observations, there has been relatively little development of formal models to account for the effects of such prior knowledge (although see Heit, 1994; Heit & Bott, 2000; Pazzani, 1991b; Rehder & Murphy, in press; Sloman, Love, & Ahn, 1998). The purpose of this article is to present a theory of categorization that accounts for the effects of theoretical knowledge, particularly causal knowledge, that interrelates or links the features of many categories that people possess. According to causal-model theory people’s knowledge of many categories includes not just a representation of a category’s features but also an explicit representation of the causal mechanisms that people believe link those features (Rehder, 1999; Waldmann, Holyoak, & Fratianne, 1995). Further, according to this theory people employ causal models to determine a new object’s category membership. In this work causal-model theory is applied to two outstanding problems in the domain of categorization research. The first concerns determining the importance, or weight, that individual features have on establishing category membership. Since the popularization of the notion of probabilistic categories in the 1970’s it has usually been assumed that features of a category vary Causal-Model Theory 4 regarding their influence on category membership (Hampton, 1979; Rosch, 1973; Rosch & Mervis, 1975; Smith & Medin, 1981). Indeed, formal models of categorization have formalized the manner in which a feature s weight is influenced by its perceptual saliency (Lamberts, 1995; 1998) and by the frequency with which it appears in category members and non-members (Nosofsky, 1986; Reed, 1972; Rosch & Mervis, 1975; Shepard, Hovland, & Jenkins, 1961). However, these models do not account for the fact that feature weights are also determined by categorizers’ domain theories. For instance, Medin and Shoben (1988) have found that straight bananas are rated as better members of the category bananas than straight boomerangs are of the category boomerangs, a result they attribute to the default feature curved occupying a more theoretically central position in the conceptual representation of boomerang as compared to banana (also see Kaplan & Murphy, 2000; Murphy & Allopenna, 1994; Pazzani, 1991b; Wattenmaker, Dewey, Murphy, & Medin, 1986). Keil (1989) found that second and fourthgraders judged that animals with transformed perceptual features retained their category membership (e.g., a raccoon made skunk-like by being dyed black, painted with a white stripe, and given a "sac of super smelly yucky stuff" is still a raccoon), a result Keil attributed to their belief that the theoretically central (albeit hidden) features of the kind important for category membership had been left unaltered (also see Gelman & Wellman, 1991; Rips, 1989). Rehder and Hastie (2001) showed that category features involved in many causal relationships have more influence on category judgments than other features (for related results see Ahn, 1998; Ahn, Kim, Lassaline, & Dennis, 2000; Sloman et al., 1998). The second outstanding problem concerns the effect of specific configurations of features on category membership decisions. That is, above and beyond the influence of individual features, particular combinations of features displayed by an object may be seen as good evidence for or against category membership. For example, previous research has found that sensitivity to inter-feature correlations can emerge when people categorize by analogy to previously-observed category members (Medin & Schaffer, 1978; Nosofsky, 1986; also see Anderson & Fincham, 1996 and Thomas, 1998). However, current categorization theories do not Causal-Model Theory 5 account for how domain theories also influence which feature configurations make for acceptable category members. For example, Wattenmaker et al. (1986) elicited sensitivity to particular correlations of features (between working indoors versus outdoors and working all year versus working in the non-winter months) by reminding participants of the existence of both indoor and outdoor painters. Murphy and Wisniewski (1989) found that whether categorization judgments were affected by feature combinations depended on whether those combinations were expected on the basis of prior knowledge rather than on whether they had been previously observed in category exemplars (also see Chapman & Chapman, 1967; 1969). Wisniewski (1995) found that certain objects were better examples of the category "captures animals" when they possessed novel combinations of features that were useful (e.g., "contains peanuts" and "caught a squirrel") versus when they did not ("contains acorns" and "caught an elephant") (also see Malt & Smith, 1984; Rehder & Ross, 2001). The central claim of causal-model theory is that sensitivity to features and specific configurations of features can often be attributed to the presence of causal knowledge about a category. According to causal-model theory, features and configurations of features influence judgments of category membership to the extent they are likely to be produced, or generated, by a category’s causal laws. For example, assuming that people believe that Bird DNA causes wings which causes flying which causes nests in trees, they will also believe (all things being equal) that features that are more directly caused by bird DNA (e.g., having wings) are more reliably generated than those that are more indirectly caused (e.g., building nests in trees). As a result, directly-caused features will be viewed as occurring more frequently among category members (and hence will be weighed more heavily in judgments of category membership). In addition, causal-model theory also claims that combinations of features are important pieces of evidence for category membership to the extent that they are jointly consistent or inconsistent with the category’s causal knowledge. For example, an animal that doesn’t fly and yet still builds nests in trees might be considered a less plausible bird (how did the nest get into the tree?) than an animal that doesn’t fly and builds nests on the ground (e.g., an ostrich), even though the former animal Causal-Model Theory 6 has more features that are typical of birds. This article presents causal-model theory s formal account of how causal knowledge influences the importance of features and specific configurations of features in judgments of category membership. Previous investigators have suggested that the theoretical knowledge that people possess about categories may be conceived of as "constraining or even generating properties" that we observe in category members (Medin & Ortony, 1989, p. 185). Causal-model theory formalizes this proposal by specifying the feature weights that can be expected given a category’s causal laws, and also extends it by additionally specifying the pattern of expected inter-feature correlations. As will be demonstrated, causal-model theory yields a precise, quantitative account of both the differences in feature weights and the importance of feature configurations induced by knowledge of a category’s causal laws that emerges when categorization decisions are being made. Because the theoretical knowledge that people possess of many natural categories is likely to be complex and to vary considerably from person to person, this study employed novel categories to provide experimental control over the knowledge associated with a category. Table 1 presents an example of the features and causal relationships for one of the novel categories, Lake Victoria Shrimp. Lake Victoria Shrimp were described to participants as possessing four binary features and three causal relationships among those features. The causal links were arranged in a chain pattern such that the first feature causes the second feature, which causes the third feature, which causes the fourth. The knowledge associated with categories such as Lake Victoria Shrimp was intended to be a simplified analog of real-world category knowledge, such as that bird DNA causes wings, which causes flying, which causes nests in trees. In the section that follows I present causal-model theory, which includes proposals regarding the representation of causal knowledge and a method for computing evidence that an object is a category member in light of that knowledge. The predictions of causal-model theory regarding feature weights and inter-feature correlations will be shown to be based on the structure of causal knowledge rather than its content (i.e., the details of the causal mechanisms), Causal-Model Theory 7 an assumption tested by the use of five novel categories in addition to Lake Victoria Shrimp.