Structure Mapping and the Predication of Novel Higher-Order Relations

Structure Mapping and the Predication of Novel Higher-Order Relations Leonidas A. A. Doumas (adoumas@psych.ucla.edu) John E. Hummel (jhummel@psych.ucla.edu) Department of Psychology, University of California, Los Angeles 405 Hilgard Ave. Los Angeles, CA 90095-1563 Abstract one that matches the sample (another red square) and one that does not (e.g., a green square). The animal’s task is to indicate which alternative matches the sample. Many animals, including honeybees (Giurfa et al., 2001), can learn to perform this task with simple stimuli such as colors and shapes (see Holyoak & Thagard, 1995, Thompson & Oden, 2000). The computational requirements for performing this task include the ability to explicitly represent values of the relevant feature dimension (e.g., “red” for the dimension “color”), and the ability to remember the value of that dimension in the sample for the purposes of choosing the correct alternative. Despite initial appearances, the task does not require the animal to explicitly appreciate that the correct choice item is in any way the same as the sample. For example, if color is the relevant dimension, then after the presentation of a red sample, the animal need only maintain a representation of “red” until the choice items appear. The animal need never reflect explicitly on the fact that the sample and the correct choice are the same color (Thompson & Oden, 2000). However, the task can be generalized to require an explicit appreciation of “sameness.” Consider a relational match-to-sample task, in which the sample depicts two triangles, alternative A depicts of circle and a diamond, and alternative B depicts two squares. Choosing B as the correct match to the sample requires the reasoner to represent B and the sample in terms of their shared relation (i.e., same-shape (x , y)). College students find this comparison trivial, yet only humans and symbol-trained chimpanzees are known to be able to perform this task reliably (Thompson & Oden, 2000). (Fagot, Wasserman & Young, 2001, claim to show relational matching to sample in the baboon, Papio papio. However, their data—in particular, the baboons' failure to learn the task when the sample and choice options each contained only two objects—are more consistent with the baboons’ responding to stimulus entropy as a holistic perceptual feature, akin to color, rather than same as an explicit relation; Hummel & Holyoak, 2003.) The assumption that people represent the relation same- shape in the same way for the squares as for the triangles provides an intuitive account of our ability to perform the relational match to sample, but it begs the question of why we see the relation “same shape” in the squares, whereas most other animals only see squares. What are the mental operations that allow us to discover and predicate same- shape as an explicit relation that retains its properties over Relations play a central role in human perception and cognition, but little is known about how relational concepts are acquired and predicated. For example, how do we come to understand that physical force is a higher-order multiplicative relation between mass and acceleration? We report an experiment demonstrating that structure mapping (a.k.a., analogical mapping) plays a key role in the predication of novel higher-order relations. This finding suggests that structure mapping—i.e., the appreciation of analogies—may play a pivotal role in the acquisition and predication of novel relational concepts. Relational Reasoning The processing of relations plays a central role in human perception and thought. It permits us to perceive and understand the spatial relations among an object’s parts (Hummel, 2000; Hummel & Biederman, 1992; Hummel & Stankewicz, 1996), comprehend arrangements of objects in scenes (see Green & Hummel, 2004, for a review), and comprehend abstract analogies between otherwise very different situations or systems of knowledge (e.g., between the structure of the solar system and the structure of the atom; Gentner, 1983; Gick & Holyoak, 1980, 1983; Holyoak & Thagard, 1995). The power of relational thinking resides in its ability to generate inferences and generalizations that are constrained by the roles that elements play, rather than strictly the properties of the elements themselves: The sun is similar to the nucleus of an atom, not because of its literal features, but because of their shared relations to planets and electrons, respectively. Experience can cause profound changes in the way we process relations. The difference between an expert chess player and a novice, for example, lies in the ability to quickly perceive and reason about the meaningful relations among the pieces on the board (and relations among those relations). Relational learning is central to both the most abstract and uniquely human cognitive abilities (including mathematical and scientific reasoning), and the most everyday reasoning using analogies, schemas and rules (Gentner, 1983; Holland, et al., 1986; Hummel & Holyoak, In order to reason explicitly about a relation it is necessary to predicate that relation, that is, to represent it as an explicit predicate that takes arguments. Consider an example. In a match-to-sample task, an animal is shown a sample stimulus (e.g., a red square), and two alternatives,