Roles of Shared Relations in Induction

Two experiments examined the roles of shared relations between representations in induction. Lassaline (1996) found that shared attributes contribute to the inductive strength, but shared relations do not, whereas both shared attributes and shared relations contribute to similarity judgment. A structural alignment view of induction was generalized to account for these phenomena. According to the structural alignment view proposed in this paper, (1) insufficiency of the number of shared relations caused the dissociation between shared relations and inductive strength, and (2) structural alignment during similarity judgment made shared relations so salient as to increase similarity. Experiment 1 examined the first hypothesis. Participants judged inductive strength of arguments that had a crossing number of shared attributes and shared relations. The results showed that shared relations contribute to the inductive strength if a sufficient number of relations are shared. Experiment 2 examined the second hypothesis. The participants who rated similarity between categories of arguments prior to judgment of inductive strength judged arguments having a shared relation to be stronger, whereas the participants who only judged inductive strength did not judge so. The results support the proposed structural alignment view of induction. Category-based Induction People frequently make inferences and expand their knowledge in uncertainty. This type of inference is generally referred to as induction. One form of induction where the premises and the conclusion are of the form “All members of a category C have property P” is referred to as category-based induction. In category-based induction, a categorical argument is said to be strong when the premises increase the degree of belief in the conclusion. Osherson, Smith, Wilkie, Lopez, and Shafir (1990) proposed that the strength of an inductive argument increases with (a) the degree to which the premise categories are similar to the conclusion category, and (b) the degree to which the premise categories are similar to members of the lowest-level category that includes both the premise and the conclusion categories. They implemented their idea as a mathematical model that is called similarity-coverage model. The similarity-coverage model provides a comprehensive explanation to a variety of phenomena in category-based induction. As an alternative to the similarity-coverage model, Sloman (1993) proposed a connectionist, feature-based, model of induction. According to the feature-based model, an argument whose conclusion claims a relation between category C (e.g., Zebras) and property P (e.g., love onions) is judged strong to the extent that the features of C have already been associated with P in the premises. Structural Alignment According to the similarity-coverage model, strength of induction is based on similarities between categories. Recent studies on similarity have revealed flexible and dynamical properties of similarity (Goldstone, 1994; Goldstone, Medin, & Gentner, 1991; Markman & Gentner, 1993; Medin, Goldstone, & Gentner, 1993). One of the most important findings is that similarity judgment involves a process of alignment of structured relational representations (Markman & Gentner, 1993). In structural alignment, the correspondences between pairs of representations are computed by seeking matches that are structurally consistent. A structurally consistent match means that each attribute or relation in one representation is placed in correspondence with, at most, one attribute or relation in the other representation. The structural alignment view accounts for important empirical results of similarity and analogy. An important result that is relevant to induction is that attributes and relations in representations are distinguished. This result suggests the possibility that attributes and relations are also distinguished in induction. Roles of Attributes and Relations in Induction and Similarity Structural Alignment in Induction Lassaline (1996) proposed a structural alignment view of induction based on structural alignment of similarity and analogy, and examined roles of attributes and relations in induction and similarity. She hypothesized that (1) shared attributes and shared relation between categories contribute to increasing similarity, whereas (2) nonshared binding relations that connect the target attribute (the attribute being mapped from one category to the other in an inductive judgment) to an attribute shared by the two categories contribute to increasing the strength of inductive arguments. Inductive arguments related to Hypothesis 1 are illustrated in Figure 1. The four arguments have crossing numbers of shared attributes (2 and 3) and shared relations (0 and 1). In argument (a), two attributes “X and Z” are shared by two animals. Argument (c) is formed by adding a common causal relation to argument (a). Therefore arguments (a) and (c) have two shared attributes, and zero and one shared relation, respectively. Argument (b) and (d) are formed by adding a common attribute to (a) and (c), respectively. Therefore argument (b) and (d) have three shared attributes, and zero and one shared relation, respectively. According to Hypothesis 1, animal A and B in arguments (c) and (d) are respectively judged more similar than those in arguments (a) and (b) because arguments (c) and (d) have more shared attributes. Similarly, animal A and B in arguments (b) and (d) are respectively judged more similar than those in arguments (a) and (c) because arguments (b) and (d) have a shared relation. Note that shared relations in argument (c) and (d) do not connect the target attribute “Y” and a shared attribute. Therefore these shared relations are not binding relations. Her hypotheses do not make any specific prediction about the contribution of nonbinding shared relations to inductive strength. (a) Animal A has X and Z. Animal B has X, Z and Y. Animal A also has Y? (2A-0R) (b) Animal A has W, X and Z. Animal B has W, X, Z and Y. Animal A also has Y? (3A-0R) (c) Animal A has X and Z. Animal B has X, Z and Y. For both animals, X causes Z. Animal A also has Y? (2A-1R) (d) Animal A has W, X and Z. Animal B has W, X, Z and Y. For both animals, X causes Z. Animal A also has Y? (3A-1R) Figure 1: Abstract structure of stimuli used in Lassaline (1996)’s Experiment 1. xA-yR indicates that the number of shared attributes is x, and the number of shared relations is y. W, X, Z, and Y represent attributes of the