The Role of Cross-cutting Systems of Categories in Category-based Induction

The Role of Cross-cutting Systems of Categories in Category-based Induction Neil A. Smith (neil.smith@louisville.edu) Department of Computer Engineering & Computer Science University of Louisville Patrick Shafto (p.shafto@louisville.edu) Department of Psychological & Brain Sciences University of Louisville Abstract Prediction is arguably the most fundamental problem that peo- ple face. Having discovered that some object possesses a par- ticular feature, how is it that people are able to accurately in- fer that another object exhibits the property? Psychologists have actively studied this reasoning process; yet, current mod- els of induction cannot provide an explanation for the entirety of the related phenomena. One reason may be that current models fail to account for people’s ability to assess multiple categories when making an inference. Building on previous research (Shafto et al., 2006), we present a model of induc- tive reasoning based on cross-cutting knowledge representa- tion. We present an experiment that investigates the ability of this model to account for known inductive phenomena. We show that a model which assesses multiple kinds of knowledge explains the flexibility of human inference, better than models relying on a single kind of knowledge. Keywords: Category-based induction; Bayesian model; Cross-categorization. One of the most remarkable features of human reasoning is the ability to predict unobserved aspects of the world. For in- stance, consider learning that mammals have sesamoid bones. Based on this knowledge, people reliably predict that wolves are more likely to have this property than are oxen (Sloman, 1993). What knowledge supports these systematic predic- tions? To understand the underlying knowledge, psychologists have studied people as they reason about novel properties (like “has sesamoid bones”). These efforts have uncovered a variety of systematic patterns, which constrain models de- scribing how knowledge supports inference. For instance, Osherson et al. (1990) describe a “monotonicity” effect, that occurs when people are asked to reason about a novel prop- erty possessed by some object; for instance, consider learn- ing that penguins have a novel property. When people are asked to predict whether another specimen or other speci- mens, such as all birds, will have the property, the strength of their prediction depends on the number of examples that have the property. So, if told that both penguins and finches have the property, people tend to predict that all birds are more likely to have it, than if only told about penguins. Inter- estingly, while this inference may appear to be quite tenable, observe that if the additional exemplar was changed from finches to dolphins, it would seem to temper a willingness to generalize the property to all birds, a phenomenon called “non-monotonicity”. In an attempt to explain this category-based induction, psy- chologists have developed computational models; however, extant models have yet to account for the entirety of the char- acteristic phenomena. One reason may be that previous mod- els rely on a single kind of knowledge, but there is evidence that people use multiple kinds of knowledge to guide predic- tion (e.g. Ross and Murphy, 1999). For example, an attribute possessed by penguins and dolphins seems unlikely to be true of all birds because there is an alternative categorization that would explain the shared property; namely, aquatic creatures. Building off of work by Shafto et al. (2006), we propose a novel model of category-based induction based on cross- cutting categories. We contrast this model with a well-known account of category-based induction, the feature-based induc- tion model (FBIM; Sloman, 1993). We present an experiment comparing the performance of the model in predicting peo- ple’s inferences on a number of known phenomena. Finally, we conclude by discussing implications of the findings for categorization, inductive reasoning, and learning. Category-based Induction Studies in category-based induction typically follow a paradigm introduced by Rips (1975), in which participants are asked to rate the strength of arguments of the form: Zebras have sesamoid bones Hippos have sesamoid bones All mammals have sesamoid bones The statements above the line indicate the premises of the argument, which are assumed to be true. The task is to as- sess the likelihood that the category below the line, the con- clusion, has the property. The most often-cited literature on category-based induction makes use of so-called blank prop- erties, such as “secretes uric acid crystals” or “travels in groups”. The assumption in their use is that blank proper- ties carry minimal a priori knowledge to guide people’s in- ferences. In this paper, we choose an even more generic at- tribute for our stimuli, namely, “Property X”. We use this not simply for convenience, but because evidence has shown that the blank properties may be influential in people’s judge- ment making. For example, when Heit and Rubenstein (1994) asked people to reason about an anatomical or physiologi- cal property of animals (e.g. “secretes uric acid crystals”),