A Theory of Reflexive Relational Generalization

A Theory of Reflexive Relational Generalization Leonidas A. A. Doumas (adoumas@indiana.edu) Department of Psychological and Brain Science, 1101 E. Tenth Street Bloomington, IN 47405 Miriam Bassok & Amy Guthormson (mbassok@u.washington.edu) Department of Psychology, Box 351525 Seattle, WA 98195-1525 John E. Hummel (jehummel@cyrus.psych.uiuc.edu) Department of Psychology, 603 E. Daniel Street Champaign, IL 61820 While relational reasoning is reflective, in that it is effortful and deliberate, many of the inferences we routinely make are so effortless that we are hardly even aware of the fact that we are making them. For example, if you are told that Susan went to the movie theater you might infer that Susan saw a movie. Moreover, you probably assume that Susan is human and a female (as opposed to, say, a male raccoon). This kind of inference is made so automatically that it is often referred to as reflexive (e.g., Shastri and Ajjanagadde, 1993). In the study of human cognition, reflexive and reflective inference have, for the most part, been examined separately. For example, reflexive inference is often studied in the context of reading and story comprehension (e.g., Kintsch & van Dijk, 1978; Shastri & Ajjanagadde, 1993; St. John, 1992; St. John & McClelland, 1990), while reflective inference is emphasized in studies of problem solving and higher level reasoning (e.g., Anderson & Lebiere, 1998; Byrne & Johnson-Laird, 1989; Forbus, Gentner, & Law, 1995; Gentner, 1983, 2003; Holyoak & Thagard, 1989, 1995; Newell, 1990). Consequently, most computational models of reflexive reasoning are not suited to account for reflective processes (e.g., Shastri & Ajjanagadde, 1993; St. John, 1992), and models of reflective reasoning are not suited to account for more reflexive inferences (e.g., Falkenhainer et al., 1989; Forbus et al., 1995; Holyoak & Thagard, 1989). While reflexive and reflective processes do seem to follow different kinds of computational constraints (Shastri & Ajjanagadde, 1993), in many cases, these two types of processes interact and need to be integrated in the performance of a single task. For example, a mathematical solution that requires a reflective rule-based reasoning often involves retrieval of arithmetic facts (e.g., 3 + 5 = 8). The activation of such facts is highly reflexive (e.g., LeFevre, Bisanz, & Mrkonjic, 1988; Niedeggen & Rosler, 1999) . For this reason, it might be limiting to view reflective and reflexive reasoning as isolated phenomena. After all, both occur within the same cognitive architecture, and both processes should operate on the same set of mental representations (Hummel & Choplin, 2000). Abstract We present the beginnings of an account of how representations and processes developed for the purposes of reflective reasoning provide a basis for reflexive reasoning as well. Specifically, we show how the symbolic-connectionist representations that underlie the DORA model (Doumas & Hummel, 2005), and the comparison based routines that DORA exploits in the service of addressing reflective problems, such as analogy making and the discovery of novel relations, can be extended to address reflexive reasoning phenomena. We use the reflexive reasoning routines developed in DORA to simulate findings demonstrating that reflexive processes operate when subjects solve real-world mathematics problems. Keywords: Reflexive reasoning, reflective reasoning, relational reasoning, representation. Reflective and Reflexive Reasoning Relational processing 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). Relational thinking is powerful because it allows us to generate inferences and generalizations that are constrained by the roles that elements play, rather than strictly the properties of the elements themselves. For example, in the analogy between the an atom and a solar system the sun is similar to the nucleus of the atom, not because of its literal features, but because of their shared relations to planets and electrons, respectively. Moreover, given that gravity causes the earth to revolve around the sun, you can infer that some force might also cause electrons to revolve around atoms. This kind of inference is effortful and requires reflective thought (Hummel & Choplin, 2000; Hummel & Holyoak, 2003).