The Influence of Structural Support on the Evaluation of Analogical Inferences

The Influence of Structural Support on the Evaluation of Analogical Inferences Jeffrey P. Laux (laux@mail.utexas.edu) Department of Psychology, University of Texas, 1University Station A8000 Austin, TX 78712-0187 USA Arthur B. Markman (markman@psy.utexas.edu) Department of Psychology, University of Texas, 1University Station A8000 Austin, TX 78712-0187 USA Abstract Analogical inferences occur when knowledge about one domain is extended by virtue of its similarity to a second. How such inferences are evaluated is not yet known, but two factors (support and extrapolation) were suggested by Forbus, Gentner, Everett and Wu in 1997. We report an initial test of the role of support in inference evaluation. Subjects were asked to provide a confidence rating for an inference that had more or less structural support. The results yielded evidence that support influences the evaluation of inferences. This paper is discussed within the framework of the Structure-Mapping Theory of analogy. Introduction Analogy is a central cognitive process involved in representation, learning, categorization, and reasoning. An important use of analogies is to extend knowledge of one domain based on the analogy to a second domain. While some research has explored factors that govern how these inferences are made, little research has examined how they are evaluated. An important question that needs to be addressed is how people make judgments about the strength of an inference that is based on an analogy. Specifically, what factors make people think that an inference is more or less likely to be true? These questions will be addressed within the framework of Gentner’s (1983) Structure- Mapping theory of analogy. There are other theories of analogy in cognitive psychology, but the general description used in the Structure-Mapping theory is compatible with the consensus of many researchers in the field (see, for example, Gentner, Holyoak, & Kokinov, 2001; Hummel, & Holyoak, 1997; Keane, Ledgeway, & Duff, 1994). Review of Structure-Mapping Theory Structure-Mapping Theory posits that concepts are represented “as propositional networks of nodes and predicates” (Gentner, 1983, p. 157). A predicate is a statement that is asserted of a subject or subjects; arguments are the subjects of which predicates are asserted. These predicates are partitioned into attributes (defined as taking single arguments) and relations (which take two or more arguments). For example, in the statement ‘the boot is brown’, brown is an attribute, and can be written using the one argument predicate Brown(boot). In the form ‘Brown(boot)’, ‘Brown’ is a predicate and ‘boot’ is its argument. The boot itself, outside of its role in the predicate, is an object. In the statement ‘the boot is larger than the shoe’, larger-than is a relation, which would be written with the two argument predicate Larger_than(boot,shoe). Relations can connect other relations as well as objects. The most common example of this is the relation cause, as in ‘Bob is taller than Sam, causing Bob to jump higher than Sam’, written Cause(Taller_than(Bob,Sam), Can_jump_higher_than(Bob, Sam)). Such a relation is known as a higher order relation (in the preceding example cause is a second order relation). In general, the order of a predicate is one higher than the order of its highest ordered argument; objects are always zero order (for a fuller account, see Falkenhainer, Forbus, & Gentner, 1989). Using these definitions, the Structure-Mapping Theory of analogy holds that analogies are a special case of comparisons between two domains, where primarily the relational predicates, but not the attributes or objects, match (Gentner, 1983; see also Gentner & Markman, 1997). The two domains are called the base and the target. Usually the base domain is the one the analogizer knows more about, although it is possible that both are known equally well. In the Structure-Mapping theory, analogical comparison and inference generation take place via a process of mapping. Mapping occurs when the predicates of the base domain are placed in correspondence with the target domain. The theory places several constraints on the mapping process including parallel connectivity and one-to- one mapping. Parallel connectivity ensures that once a correspondence between two predicates has been made, their arguments are placed in correspondence also. One-to- one mapping means that once an element of the target has been swapped out for an element of the base, that same correspondence must be honored for the rest of the mapping process. In this manner, an element in one of the domains cannot correspond to more than one element in the other domain. Review of Analogical Inference Analogies would be of limited use if they only found similarities between domains. Analogies can also help people extend their knowledge of a topic by virtue of its similarity to another, better known topic. An analogical