Progressive Alignment Facilitates Learning of Deterministic But Not Probabilistic Relational Categories

Progressive Alignment Facilitates Learning of Deterministic But Not Probabilistic Relational Categories Wookyoung Jung (jung43@illinois.edu) Department of Psychology, 603 E. Daniel Street Champaign, IL 61820 USA John E. Hummel (jehummel@illinois.edu) Department of Psychology, 603 E. Daniel Street Champaign, IL 61820 USA Abstract Kotovsky and Gentner (1996) showed that presenting progressively aligned examples helped children discover relational similarities: Comparisons based on initially concrete and highly similar, but progressively more abstract exemplars helped the discovery of higher-order relational similarities. We investigated whether progressive alignment can aid learning of relational categories with either a deterministic (in which one relation reliably predicts category membership) or a probabilistic structure (in which each relation predicts category membership with 75% reliability). Progressive alignment helped participants learn relational categories with the deterministic structure. However, progressive alignment did not help participants learn the probabilistic relational categories. The results show that learning relational categories with a deterministic structure can be improved by progressive alignment, consistent with previous findings (e.g., Kotovsky & Gentner, 1996), but also support previous findings suggesting that relational categories are represented as a schemas, which are learned by a process of intersection discovery that fails catastrophically with probabilistic category structures (Jung & Hummel, 2009; Kittur et al., 2004, 2006). Key words: Relational category learning; relational invariants; probabilistic category structure; deterministic category structure; progressive alignment One of the most generally accepted assumptions in the study of concepts, categories and category learning is that we represent categories in terms of their exemplars’ features and that the process of category learning is a process of learning which features are diagnostic of category membership. Likewise, the process of assigning an exemplar to a category is a process of comparing the exemplars’ features to those of the category (represented either in terms of a prototype or as a collection of known exemplars). This account of category learning provides a natural basis for understanding the family resemblance structure of our concepts and categories: The idea, first proposed by Wittgenstein (1956) and subsequently supported by numerous experiments in cognitive psychology (for a review see Murphy, 2002), that, like the members of a family, the various members of a category tend to have many features in common with one another, but that there need not be any necessary or sufficient features for category membership. Feature-based theories of categorization also provide a natural account of the well- known prototype effects in categorization (e.g., the fact that an exemplar is judged to be a “good” member of a category to the extent that it shares many features with the prototype of the category; see Murphy, 2002). Another widely held view is that this feature-based account of concepts and categories, for all its successes as an account of prototype effects, fails to provide a complete account of the richness and power of our conceptual structures. As pointed out by Gentner (1983), Barsalou (1993), Murphy and Medin (1985) and others, our knowledge of the interrelations among an object’s “features” (e.g., that birds tend to fly and tend to nest in trees, but that not all do, and that only those that fly also nest in trees) and our ability to reason flexibly with our concepts (e.g., inferring that a man who jumps fully-clothed into a pool at a party is probably drunk; Murphy & Medin, 1985) seem to demand explanation in terms of more sophisticated conceptual structures, such as schemas and theories. The primary factor distinguishing schemas and theories from lists of features is that the former, but not the latter, represent relations explicitly: Whereas a feature list can specify that a bird “can fly” or “lives in trees”, relational representations are required to specify that the ability to fly enables a bird to nest in trees. More generally, the schema/theory based view of concepts fares better as an account of the relations between our concepts and the larger theoretical structures in which they are embedded: We understand the relations, not just between the properties of various objects (e.g., the fact that a bird flies is what allows it to nest in trees), but between concepts and other concepts (e.g., that an interaction is when the effect of one variable depends on the value of another). Moreover, some concepts and categories appear to be largely if not entirely relational in nature. For example, the category conduit is defined by a relation between the conduit and the thing it carries; barrier is defined by the relation between the barrier, the thing to which it blocks access and the thing deprived of that access; and even the category mother is defined by a relation between the mother and her child. Relational categories may be more the rule than the exception: As reported by Asmuth and Gentner (2005), informal ratings of the 100 highest-frequency nouns in the British National Corpus revealed that about half refer