Feature- vs. Relation-Defined Categories: Probab(alistic)ly Not the Same

Feature- vs. Relation-Defined Categories: Probab(alistic)ly Not the Same Aniket Kittur (nkittur@ucla.edu) John E. Hummel (jhummel@lifesci.ucla.edu) Keith J. Holyoak (holyoak@lifesci.ucla.edu) Department of Psychology, 1285 Franz Hall University of California, Los Angeles Los Angeles, CA 90095 known about how people learn relational categories. Relational category learning is important because rela- tional concepts (i.e., mental representations of relational categories) play an essential role in virtually all aspects of human thinking, including our ability to make and use analogies, problem solving, scientific discovery, and even aspects of perception (see, e.g., Gentner, 1983; Gentner et al., 1997; Green, 2004; Hesse, 1966; Holyoak & Thagard, 1995; Hummel, 2000). The utility of relational representa- tions is that they permit generalization from a small (often as few as one or two) number of examples to a large (poten- tially infinite) number of new cases (as in the case of inferences generated through the use of analogies, schemas and rules; Gick & Holyoak, 1983; Pirolli & Anderson, 1985; Ross, 1987). Relational concepts cannot be adequately represented as lists of features (as assumed by most current models of category learning), but instead must be mentally represented as relational structures such as schemas or theories (Gentner, 1983; Holland, Holyoak, Nisbett, & Thagard, 1986; Hummel & Holyoak, 2003; Keil, 1989; Murphy & Medin, 1985). This observation suggests that the operations governing relational schema induction may also underlie the acquisition of relational categories (see, e.g., Kuehne et al., At least one theory of schema induction, Hummel and Holyoak’s, 2003, LISA model, predicts that a schema in- duced from two or more examples retains (roughly) the structured intersection of what the examples have in com- mon. For example, consider two analogous stories about love triangles. In the first, Abe loves Betty, but Betty loves Chad, so Abe is jealous of Chad; in the second Alice loves Bill, but Bill loves Cathy, so Alice is jealous of Cathy. Drawing an analogy between these stories maps Abe to Al- ice, Betty to Bill, and Chad to Cathy (along with the roles of the loves and jealous-of relations). The schema LISA in- duces from this analogy retains what the examples have in common, and de-emphasizes the ways in which they differ. For example, since the analogy maps males to females and vice versa, the resulting schema effectively discards the actors’ genders, stating (roughly) “person1 loves person2 but person2 loves person3, so person1 is jealous of per- son3,” where persons1…3 are generic people, rather than being specifically males or females (see Hummel & Holyoak, 2003). Importantly, this intersection discovery process also takes place at the level of whole propositions. For example, if the second story contained a proposition stating that, as a Abstract Relational categories underlie many uniquely human cogni- tive processes including analogy, problem solving, and scientific discovery. Despite their ubiquity and importance, the field of category learning has focused almost exclusively on categories based on features. Classification of feature- based categories is typically modeled by calculating similarity to stored representations, an approach that successfully mod- els the learning of both probabilistic and deterministic category structures. In contrast, we hypothesize that rela- tional category learning is analogous to schema induction, and relies on finding common relational structures. This hypothe- sis predicts that relational category acquisition should function well for deterministic categories but suffer catastro- phically when faced with probabilistic categories, which contain no constant relations. We report support for this pre- diction, along with evidence that the schemas induced in the deterministic condition drive categorization of novel and even category-ambiguous exemplars. Relational and Feature-Based Categorization Most mathematical models of human category learning start with the assumption that people represent categories as lists of features, and assign instances to categories by comparing the features of an instance to the features stored with the mental representation of the category (either a prototype or stored exemplars; e.g., Bruner, Goodnow, & Austin, 1956; Kruschke, 1992; Kruschke & Johansen, 1999; Nosofsky, 1992; Rosch & Mervis, 1975; Shiffrin & Styvers, 1997). Accordingly, most studies of human category learning in the laboratory investigate how people learn categories with ex- emplars consisting of well-defined (to the experimenter, at least) features. In the real world, as some researchers have forcefully pointed out (e.g., Barsalou, 1993; Keil, 1989; Murphy & Medin, 1985; Rips, 1989; Ross & Spalding, 1994) catego- ries are less often defined in terms of lists of features than in terms of relations between things: either relations between the features or parts of an exemplar (e.g., the legs need to be in a particular kind of relation to the seat in order for an object to serve as a chair), or relations between the exemplar and the user’s goals (e.g., any object that affords sitting can, in some circumstances, be considered a chair), or relations between the exemplar and other objects in the world (e.g., what makes an object a “conduit” is a relation between that object and whatever thing flows through it, whether it be water, light, electricity, information, or karma). In spite of their importance in human cognition, comparatively little is