Relations Relating Relations

The aim of the current work is to incorporate structural information in judgments of similarity . According to the assumption of feature independence, how one feature affects similarity is independent of the values of the other features present. We present three violations of this assumption, all arising from the influence of relations between features and of relations between relations . A shared relation is more important for similarity judgments if it cooccurs with (A) relations that augment the first relation by "pointing in the same direction' as the first relation, (B) relations which are themselves salient, and (C) salient relations that involve the same objects as the first relation . We interpret these results as suggesting that relations do not have separately determined weights or saliences; the weight of a relation depends the relational structure in which it exists . Relations influence each other by creating higherorder relational structures, and also by affecting prncessing . Introduction Our current interest in structural similarity stems from two sources . First, similarity has been a pivotal, if under-explored, agent in many theories . Problems are said to be easier to solve if similar problems have been previously solved . The transfer of one skill to another is said to be proportional to their degree of gimilarity. One . event reminds us another if they are simil . An object belongs to a category if it is similar to the category's examples or prototype. An account of what makes things similar is essential to our understanding of cognition . Second, it has long been argued, particularly in artificial intelligence, that simple, independent feature representations, inadequately capture most of our knowledge .pr positional representations, explanation based learning, and pattern recognition all point to the need for systems that represent how the units of analysis are related and interconnected in structural descriptions. Thus, separate fields have argued for the importance of structure and for the importance of similarity ; at the most general level, our research goal is to consolidate structure and similarity into a single framework . One of the most important and common assumptions associated with a wide variety of psychological models is that there exists a set of features that are i entof one another. Features are independent if the effect of the value on any one feature does not depend on the value of any other feature . A selection of prominent examples illustrates the prevalence of the feature independence assumption. Tversky's influential contrast model (1977) makes the explicit assumption that the joint effect of two components in determining similarity is independent of the fixed level of the third component Posner and Keele (1968) assume that the psychological distance of a dot from its prototypical location is inde of the locations of other dots . Independent-cue prototype models propose that categorization of an example into a group is a function of the feature matches between the example and the group, additively combined in an independent manner. The assumption of feature independence is a powerful simplifying assumption , permitting analyses which would otherwise be unwieldy or impossible . Without the independence assumption, any single feature of a system with ten binary-valued features could produce 1024 different effects; with the independence assumption, the same feature can produce only two effects. Unfortunately, it is not always true that what makes for a simple and powerful model also makes for an accurate model of human behavior. Theme is ood reason to suppose that cognitive processes are often based on highly interactive features. The feature "gray" does not mean the same thing in "gray hair" as it does in "gray cloud" (Medin & Shoben, 1988). Pomerantz (1986) has shown that in displays such as X the two parentheses are not independently perceived although they are physically detached, they are psy~logr~y fused,~gemergent propertiea Gad and Tversky (1984) present examples in which monotonicity and feature 'independence are violated because adding certain features causes interactions with the features alma present. Indeed all context effects can be construed as cases of non-independence. In , there is reason to think that feature independence is the exception rather than the rule object features of mutually constrain and modulate each other . It might be thought that admitting feature dependencies into a model would yield an overwhelming number of degrees of freedom and a loss of important constraints. Contrary to this position, we will argue that feature dependence need not be a "counsel of despair ." The similarity judgments that this p investigates are not constrained by feature independence, but they are constrained by specific principles . central claim will be that the importance of a relation in a scene depends on the quality, quantity, and location of the other relations present. The general representational system outlined in Dedre Gentner's Structure-mapping Theory (SMT) (Gentner,1983,1989) will be used . In Gentner's terminology, a first-order relation is any relation that takes two or more objects as arguments. The relation "DARKER-T " is first-order because it takes two objects, two wings for example, and establishes a relation between them . The relation can be propositionally represented as DARKERGREATER (DOTS(trtangle), DOTS(circle)) AUGMENTS (GREATER, GREATER) GREATER (SIZE(triangle), SIZE(ctrc)e)) Goldstone, Gentner, Medin