Toward an Integrated Account of Reflexive and Reflective Reasoning

Some inferences are seemingly automatic (reflexive; Shastri & Ajjanagadde, 1993), whereas others require more effort (i.e., are reflective). We present the beginnings of an integrated account of reflexive and reflective reasoning, based on the LISA model of analogical reasoning (Hummel & Holyoak, 1997). The account holds that reflexive inferences are those that can be generated automatically based on existing knowledge in long-term memory, whereas reflective inferences require explicit structuremapping and therefore demand greater attention and working memory. According to this account, reflexive inferences manifest themselves in the semantic encoding of objects and predicates, whereas reflective inferences manifest themselves as explicit propositions. In contrast to reflexive inferences, which are equally reflexive, reflective inferences may require more or less effort. We present preliminary simulation results demonstrating that both kinds of inference can be modeled in a single architecture for representing propositional knowledge. The most reflexive form of inference is encoding— inferring, for example, that "Mary" in "Bill loves Mary" is an adult human female. It is this most reflexive form of inference that has been most neglected in models of reflective reasoning. One consequence is that these models must be given, in full detail, the representations they are to use for reasoning. For example, the models of Forbus et al. (1995), Holyoak and Thagard (1989) and Hummel and Holyoak (1997) draw analogies between situations whose representations are fully specified for them. In contrast to human reasoners, who can read a sentence such as "Bill loves Mary, but Mary loves Tom" and infer the details for themselves (e.g., that Bill and Tom are adult human males, etc.), these models must be handed all this information for each analogy they are asked to solve.1 One reason for this division between models of reflective and reflexive reasoning may be that the two kinds of reasoning obey different computational constraints, and therefore demand different kinds of algorithms. At the same time, however, both kinds of inference take place within the same cognitive architecture, and must operate on the same mental representations. Reflexive vs. Reflective Reasoning Some inferences are so effortless that we are barely aware of making them. Told that Bill sold Mary his car, you will infer that Mary now owns the car so automatically that Shastri and Ajjanagadde (1993) describe the inference as reflexive. Even more reflexive is the inference that Bill is probably an adult human male, and Mary an adult human female. Other inferences require more effort. Told that Bill loves Mary and Mary loves Tom, it is natural to infer that Bill is likely to be jealous of Tom, but this inference arguably requires a bit more reflection (and is less certain) than the inference that Mary is a woman. More effortful still are many kinds of inferences made in the context of scientific and mathematical reasoning, planning, and so forth. What is the relationship between reflexive inferences, such as Bill is male or Mary owns the car, and more reflective inferences, such as Bill may be jealous of Tom, or matter and energy must be special cases of a common physical principle? And what is the process by which This paper presents the beginnings of an algorithmic account of the relationship between reflexive and reflective reasoning. In broad strokes the account holds that both kinds of reasoning require the capacity to dynamically bind 1One notable exception to this generalization is Hofstadter & Mitchel's (1994) CopyCat model, which solves analogy problems of the form X:Y::Z:? , and uses routines to change its representation of X, Y and Z in order to find the best possible analogy. In contrast to other models of analogy, CopyCat is not "stuck" with fixed representations of the elements of its analogies. At the same time, however, this model cannot simulate the kind of encoding discussed here, or the type of reflexive inferences discussed by Shastri & Ajjanagadde (1993). variables to values (or equivalently, roles to fillers) in order to permit flexible (rule-like) generalization (cf. Shastri & Ajjanagadde, 1993, on the role of variable binding in reflexive reasoning; Holyoak & Hummel, 2000, and Hummel & Holyoak, 1997, on the role of variable binding in reflective reasoning). That is, both reflexive and reflective inferences are operations on symbolic representations. In addition, we propose that what makes reflective reasoning more effortful than reflexive reasoning is, at least in part, that the most reflexive inferences result from a kind of structured memory retrieval (i.e., retrieval that exploits and maintains variable-value bindings), whereas more reflective inferences require explicit structure mapping. That is, as illustrated in the simulations below, we propose that an inference will be fully reflexive when the to-be-inferred information is already available in long-term memory (LTM), and that it becomes progressively more reflective as the to-be-inferred information must be constructed on the basis of mapping large, multiproposition structures. represents the buyer and object roles, respectively, and are connected to the corresponding semantics. Semanticallyrelated predicates share units in corresponding roles (e.g., seller and giver share many units), making the semantic similarity of different predicates explicit. Object units are like predicate units except that they are connected to semantic units describing things rather than roles. For example, Mary might be connected to units for human, adult, female, etc., whereas car might be connected to object, vehicle, etc.