Causal Models Guide Analogical Inference

Causal Models Guide Analogical Inference Hee Seung Lee (heeseung@ucla.edu) Keith J. Holyoak (holyoak@lifesci.ucla.edu) Department of Psychology, University of California, Los Angeles Los Angeles, CA 90095 USA objects as arguments (e.g., “The dog is bigger than the cat”) and higher-order relations, which include propositions as arguments (e.g., “Because the dog is bigger than the cat, the cat ran away from the dog”). Gentner argued that higher- order relations, such as “cause”, are more important for analogical inference than first-order relations. The priority of higher-order relations is due to what she termed the systematicity principle, which hypothesizes a preference for inferences based on predicates having many mutually interconnecting relationships. An entity embedded within corresponding higher-order relations has more matched structures, and hence will receive a higher “match” score in SME, than would an entity embedded in first-order relations, or an isolated entity. SME therefore predicts that deeply hierarchical information is especially likely to be transferred to the target. Lassaline (1996) demonstrated that when a causal relation in the source is unmapped, and the cause property is shared by the source and target, then people are likely to infer the corresponding effect in the target. For example: Abstract Computational models of analogical inference have assumed that inferences about the target are generated solely by “copying with substitution and generation” from the source, guided by a mapping based on similarity and parallel structure. In contrast, work in philosophy of science has stressed that analogical inference is based on causal models of the source and target. In two experiments, we showed that reducing analogical overlap by eliminating a matching higher-order relation (a preventive cause) from the target increased inductive strength even though it decreased similarity of the analogs. Analogical inference appears to be mediated by building and then “running” a causal model. Keywords: analogical inference; causal model; similarity; inductive strength; preventive cause; generative cause. Introduction In everyday life, people often face uncertainty, which permeates such situations as meeting a new person, solving a novel math problem, or resolving a foreign policy crisis. To reduce uncertainty about a novel target situation, people frequently make analogical inferences based on similar source situations they experienced in the past. When a source includes properties that the target initially lacks, any of these missing properties in the target can become a candidate for analogical inference. Yet people do not draw all possible inferences. How, then, do people make analogical inferences selectively? Similarity and structure as inductive constraints People are more likely to draw strong analogical inferences when they perceive a source and a target to be similar. According to the contrast model of similarity (Tversky, 1977), common properties tend to increase perceived similarity of two concepts whereas differences tend to reduce the perceived similarity. By manipulating the number of shared properties of the source and target, Lassaline (1996) demonstrated that both similarity and inductive strength increased with addition of shared properties. Although overlap of properties influences analogical inference, formal models have placed major emphasis on the role of structural parallels between relations in the source and target. The importance of relations in analogical inference provided the basis for Gentner’s (1983) structure mapping theory, which has been implemented in a computational model, SME (Structure Mapping Engine; Falkenhainer, Forbus, & Gentner, 1989). Gentner distinguished between first-order relations, which take Animal A has properties X, W, and Z. For Animal A, X causes Z. Animal B has X, W, and Y. Therefore, Animal B also has Z. Here property X is the cause property shared by Animal A and Animal B, leading to the inference that effect Z found in Animal A will also be present in the target, Animal B. Using a similar paradigm, Rehder (2006) showed that category-based generalizations are preferentially guided by causal relations, such that standard effects of typicality, diversity, and of similarity itself are eliminated when a causal relation is present. However, in Rehder’s experiments the single causal relation, when present, was also the sole higher-order relation. Given this confounding, his findings are consistent with Gentner’s (1983) systematicity principle. In addition to SME, other computational models of analogical inference, such as ACME (Analogical Constraint Mapping Engine; Holyoak & Thagard, 1989) and LISA (Learning and Inference with Schemas and Analogies; Hummel & Holyoak, 1997, 2003) incorporate similar relation-based constraints. All these models generate candidate inferences using variants of a procedure termed “copy with substitution and generation”, or CWSG (Holyoak, Novick, & Melz, 1994), in which inferences about the target are constructed directly from the mapping between source and target relations.