Explanatory Reasoning for Inductive Confidence

Explanatory Reasoning for Inductive Confidence David Landy (dlandy@richmond.edu) Department of Psychology, M03B Richmond Hall University of Richmond, VA, 23173 USA John E. Hummel (jehummel@illinois.edu) Department of Psychology, 603 E. Daniel St. Champaign, IL 61820 USA Abstract We present Explanatory Reasoning for Inductive Confidence (ERIC), a computational model of explanation generation and evaluation. ERIC combines analogical hypothesis generation and justification with normative probabilistic theory over statement confidences. It successfully captures a broad range of empirical phenomena, and represents a promising approach toward the application of explanatory knowledge in new situations. Keywords: induction; analogy; probabilistic reasoning Introduction We are constantly making guesses. When we come across something new, we know about it in part from its relations to other things and we attribute to the novel the properties of the familiar. For instance, when Apple announced the iPad, technology reporters alternately compared it to tablet PCs, which are similar in size and function, and the iPhone, which is similar in appearance and operating system. In each case, the game was to predict the features of the new object on the basis of the old ones. Property inductions of this kind—extending known properties of one category to other categories—have been heavily studied in experimental psychology (see Heit, 2000, for a review). Such inductions seem to take advantage of taxonomic knowledge about category structures as well as specific knowledge about particular categories (Shafto, Kemp, Bonawitz, Coley, & Tenenbaum, 2008). One intuition, pursued here, is that people make inductions by adapting explanations for known properties to novel categories. People are habitual generators of explanations: Scientists explain natural phenomena; engineers explain why structures will or will not support various loads; mathematicians explain why a formal property does or does not hold of a particular situation or object; and everyone routinely explains much more mundane things such as why the doorbell rang, why we smell gas in the kitchen and why a child has a fever. Explanations serve many cognitive functions, but perhaps none is more important than their ability to support inductive inferences: A person who can explain a novel observation can have much greater confidence in their inferences about the circumstances under which that observation is likely to be repeated than a person who cannot explain it—which is why, for example, your auto mechanic is better than you are at knowing whether that strange noise you car is making is likely to be dangerous. In order to apply explanations of past experiences to novel situations, a cognitive architecture must solve several problems. First, it must be able to generate and retain explanations in the first place. Second, it must have a way to generate novel hypotheses about a current situation from its beliefs about past circumstances. Finally, it must be able to distinguish when a novel explanation is plausible in the current situation, and when it is not. Bayesian models, and particularly hierarchical Bayesian models, are adept at the last of these goals. For example, the model of Kemp and Tennenbaum (2009) carves known situations into disjoint domains, and applies to novel situations the domain assumptions that appear most appropriate. However, human reasoners also adapt explanation patterns across multiple, dissimilar domains (Medin, Coley, Storms, & Hayes, 2003). Although such cross-domain reasoning is the sine qua non of analogical approaches to reasoning (Falkenhainer, Forbus, & Gentner, 1989; Hummel & Holyoak, 1997), models of analogy generally provide no basis for generating probabilistic estimates of confidence in their inferences. In this paper, we present the model ERIC, Explanatory Reasoning for Inductive Confidence (see also Landy & Hummel, 2009). ERIC uses a combination of analogical and probabilistic reasoning to (a) generate explanations for newly learned facts, (b) evaluate the plausibility of those explanations in light of its existing knowledge, (c) use those explanations to update its confidence in its existing knowledge and (d) make judgments about the plausibility of new inferences. The resulting model accounts for a large body of empirical findings from the literature on inductive confidence (e.g., Heit, 2000; Shafto et al., 2008). A central tenet of the model is that the mind uses analogy to adapt old explanations to new situations and then uses those new explanations both to determine its confidence in the new observation and to update its confidence in its existing knowledge—both existing basic facts and existing explanations. The knowledge updated includes both the source analogs (i.e., the old explanations used to generate the new ones) and the analogies themselves (i.e., the mappings from the old [source] explanations to the new [target] explanations). As a result, if an analogy results in a good explanation, then the model becomes more convinced both that the source was true and that the analogy was good.