Context-Sensitive Induction

Sensitive Induction Patrick Shafto 1 , Charles Kemp 1 , Elizabeth Baraff 1 , John D. Coley 2 , & Joshua B. Tenenbaum 1 Department of Brain and Cognitive Sciences, Massachusetts Institute of Technology Department of Psychology, Northeastern University Abstract Different kinds of knowledge are relevant in different inductive contexts. Previous models of category-based induction have focused on judgments about taxonomic properties, but other kinds of models are needed for other kinds of properties. We present a new model of reasoning about causally transmitted properties. Our first experiment shows that the model predicts judg- ments about a disease-related property when only causal information is available. Our second experiment uses a disease-related property and a genetic property in a set- ting where both causal and taxonomic information are available. Our new model accounts only for judgments about the disease property, and a taxonomic model ac- counts only for judgments about the genetic property. This double dissociation suggests that qualitatively dif- ferent models are needed to account for property induc- tion. Any familiar thing can be thought about in a multi- tude of ways. A cat is a creature that climbs trees, eats mice, has whiskers, belongs to the category of felines, and was revered by the ancient Egyptians. Knowledge of all of these kinds plays an important role in inductive inference. If we learn that cats suffer from a recently dis- covered disease, we might think that mice also have the disease — perhaps the cats picked up the disease from something they ate. Yet if we learn that cats carry a recently discovered gene, lions and leopards seem more likely to carry the gene than mice. Flexible inferences like these are a hallmark of human reasoning, which is notable for the selective application of different kinds of knowledge to different kinds of problems. Psychologists have confirmed experimentally that in- ductive generalizations vary depending on the property involved. When told about genes or other internal anatomical properties, people generalize to taxonomi- cally related categories (Osherson, Smith, Wilke, L´ opez, and Safir, 1990). When told about novel diseases, how- ever, people generalize to categories related by the causal mechanism of disease transmission (Shafto and Coley, 2003). Psychologists have also suggested, at least in principle, how complex inferences like these might work. Flexible inductive inferences are supported by intuitive theories, or “causal relations that collectively generate or explain the phenomena in a domain” (Murphy, 1993). Many theories may apply within a single domain, and very different patterns of inference will be observed de- pending on which theory is triggered. Although a theory-based approach is attractive in principle, formalizing the approach is a difficult chal- lenge. Previous work describes a theory-based taxo- nomic model (Kemp and Tenenbaum, 2003), and here we use the same Bayesian framework to develop a theory- based model for induction about causally transmitted properties like diseases. The models differ in the causal knowledge used to generate probability distributions over potential hypotheses, resulting in qualitatively dif- ferent patterns of generalization for different theories. These are but two of the many models that may be needed to explain the full set of inductive contexts, and extending our framework to deal with a broader range of contexts is an ongoing project. Our work goes beyond previous formal models, which find it difficult to capture the insight that different kinds of knowledge are needed in different inductive contexts. In the similarity-coverage model, a representative and often-cited example, the domain-specific knowledge that drives generalization is represented by a similarity metric (Osherson et al., 1990). Even if we allow a context- specific notion of similarity, a similarity metric is too limited a representation to carry the richly structured knowledge that is needed in some contexts. In contrast, the knowledge that drives generalization in our Bayesian framework can be as complex and as structured as a given context demands. We begin by introducing our new model of reasoning about causally transmitted properties. We then present experiments showing that our new model predicts human generalizations about diseases, but not about genetic properties. The theory-based taxonomic model has com- plementary strengths, and predicts generalizations about genetic properties, but not diseases. We finish by com- paring our model to previous approaches, and describing some of the challenges to be surmounted in developing a truly comprehensive theory of context-sensitive induc- tion. Theory-based induction Our theory-based framework includes two components: an engine for Bayesian inference and a theory-based prior. The inference engine implements rational statis- tical inference, and remains the same regardless of the inductive context. We model these theories using proba- bilistic processes over structured represenations of causal knowledge.