Systematicity as a selection constraint in analogical mapping

Analogy is often viewed as a partial similarity match between domains. But not all partial similarities qualify as analogy: There must be some selection of which commonalities count. Three experiments tested a particular selection constraint in analogical mapping, namely, systematicity. That is, we tested whether a given predicate is more likely to figure in the interpretation of and prediction from an analogy if the predicate participates in a common system of relations. In Experiment 1, subjects judged two matches to be included in an analogy: on isolated match, and a match embedded in a larger matching system. Subjects preferred the embedded match. In Experiments 2 and 3, subjects made analogical predictions about a target domain. Subjects predicted information that followed from a causal system that matched the base domain, rather than information that was equally plausible, but that created an isolated match with the base. Results support Gentner's (1983, 1989) structure-mapping theory in that analogical mapping concerns systems and not individual predicates, and that attention to shared systematic structure constrains the selection of information to include in an analogy.     

Constraints on Analogical Inference

The ability to reason by analogy is particularly important because it permits the extension of knowledge of a target domain by virtue of its similarity to a base domain via a process of analogical inference. The general procedure for analogical inference involves copying structure from the base to the target in which missing information is generated, and substitutions are made for items for which analogical correspondences have already been found. A pure copying with substitution and generation process is too profligate to be useful, and so constraints must be placed on what information is to be carried over. In this paper, the importance of systematicity as a constraint on inference is explored in four studies in which subjects find correspondences between domains and also make inferences. This work suggests that people prefer to make inferences of information connected to systematic correspondences between domains. A second important theme of this paper is that violations of one-to-one mapping can lead to inconsistent object substitutions in inference. The data reveal no such inconsistent substitutions in people's inferences, suggesting that they do respect one-to-one mapping in analogical inference. These findings are discussed relative to four prominent computational models of analogical mapping and inference.     

Intention and outcome: key components of causal structure facilitating mapping in children's analogical transfer.

The consequences of two key features of causal structure in source stories, intention and positive outcome, for analogical transfer were examined in kindergarten and second graders. In Experiment 1, children received either structure-complete, structure-incomplete, or irrelevant source stories. Structure-incomplete stories lacked either the intention to solve a problem (a goal-directed component), evidence of a successful consequence (an outcome-related component), or both as part of the solution activity described in source stories. Evidence for transfer was obtained for second graders when a goal-directed component, and to a lesser extent, an outcome-related component were connected to the solution action in source stories. Differences among conditions for kindergartners were less evident, although they revealed a pattern of performance similar to the second graders. A second experiment was conducted to determine whether memory and an orientation to use the source story information might account for these findings. Efforts to ensure memory for and hints to use information in the source stories, however, did not benefit solution transfer when intention and positive outcome were absent. These results suggest that a complete causal structure, including goal and outcome, in source stories augments transfer in young children by promoting mapping of the analogical relationship between source stories and the target problem.     

Two facets of cognitive control in analogical mapping: The role of semantic interference resolution andgoal-driven structure selection

The study used scene analogies to investigate two component processes of analogical thinking: resolution of semantic interference, which emerges when the proper mapping between analogically matching objects is incoherent with their categorical features (e.g., stereotypical functions), and goal-driven selection of the key relational structure, by directing attention to the most promising objects which constitute that structure among many other candidate objects. We manipulated interference by placing in corresponding scenes the objects from one category in different relational roles. Selection was loaded by including additional, relationally irrelevant objects in a scene. We also manipulated relational complexity and the presence of salient objects (people) in relations. Increased load on both interference resolution and selection decreased the accuracy of analogical mapping, but these factors did not interact. Moreover, the factors yielded opposite patterns of interaction with relational complexity. Finally, salience eased selection, but tended to negatively influence interference resolution. In summary, inference resolution and selection seem to constitute two relatively independent facets of cognitive control involved in analogical thinking. Selection may act before mapping occurs, while interference influences analogy making only if an interfering object takes part in mapping.     

儿童类比推理的影响因素及干预促进

类比推理这一重要认知能力能够帮助儿童在未经历过的复杂情况下进行推断和学习。近年来研究者主要从行为研究、计算机模型和眼动技术的角度探究了儿童抑制控制和工作记忆在类比推理中的交互作用模式及类比推理策略对类比推理的影响。在此基础上,研究者围绕语言标签和物理表征两方面对儿童类比推理进行了干预研究。儿童类比推理的未来研究应着眼于改进研究方法、关注类比推理各加工阶段影响因素及加强儿童类比推理策略的干预应用研究。     

Learning From Fantasy and Real Characters in Preschool and Kindergarten

In three experiments, 3½- to 6-year-old children were presented with analogical problems in which the protagonists were either real people or fantasy characters. Children were more likely to transfer solutions from the stories about real people rather than the stories about fantasy characters. These results suggest that the use of a fantasy character might not be an effective strategy for teaching children information that is meant to be applied to the real world.     

On Adaptation in Analogy: Tests of Pragmatic Importance and Adaptability in Analogical Problem Solving

When people use analogies to solve problems, they form an analogical mapping between two domains of knowledge. This mapping may support inferences by analogy that suggest a novel solution to a problem. Several factors have been proposed to be important in selecting this mapping from among several alternative mappings: structural factors (systematicity and structural consistency) and pragmatic factors (the exploitation of higher-order planning categories). We suggest another set of factors plays a role in selecting mappings: adaptability. Specifically, if a mapped solution can be adapted easily to a problem, then it will be preferred over an alternative mapping that is less adaptable. Two experiments are reported which test the effects of pragmatic and adaptation factors, using a novel technique in which the story analogue has two alternative plans, either of which can be used to solve an insight problem. In Experiment 1, these plans were varied in terms of their pragmatic importance (success or failure) and their adaptability. In Experiment 2, the relative adaptability of plans was manipulated. The results suggest that there is little evidence for these specific pragmatic factors, but that adaptability plays a definite role in selecting an analogous plan. The findings suggest that most models need to be extended to include adaptation constraints.     

Structural constraints and object similarity in analogical mapping and inference

Theories of analogical reasoning have viewed relational structure as the dominant determinant of analogical mapping and inference, while assigning lesser importance to similarity between individual objects. An experiment is reported in which these two sources of constraints on analogy are placed in competition under conditions of high relational complexity. Results demonstrate equal importance for relational structure and object similarity, both in analogical mapping and in inference generation. The human data were successfully simulated using a computational analogy model (LISA) that treats both relational correspondences and object similarity as soft constraints that operate within a limited-capacity working memory; but not with a model (SME) that treats relational structure as pre-eminent.     

Mathematical problem solving by analogy.

We report the results of 2 experiments and a verbal protocol study examining the component processes of solving mathematical word problems by analogy. College students first studied a problem and its solution, which provided a potential source for analogical transfer. Then they attempted to solve several analogous problems. For some problems, subjects received one of a variety of hints designed to reduce or eliminate the difficulty of some of the major processes hypothesized to be involved in analogical transfer. Our studies yielded 4 major findings. First, the process of mapping the features of the source and target problems and the process of adapting the source solution procedure for use in solving the target problem were clearly distinguished: (a) Successful mapping was found to be insufficient for successful transfer and (b) adaptation was found to be a major source of transfer difficulty. Second, we obtained direct evidence that schema induction is a natural consequence of analogical transfer. The schema was found to co-exist with the problems from which it was induced, and both the schema and the individual problems facilitated later transfer. Third, for our multiple-solution problems, the relation between analogical transfer and solution accuracy was mediated by the degree of time pressure exerted for the test problems. Finally, mathematical expertise was a significant predictor of analogical transfer, but general analogical reasoning ability was not. The implications of the results for models of analogical transfer and for instruction were considered.     

More evidence for a relational shift in the development of analogy: Children's performance on a causal-mapping task

Gentner (1988) has proposed a relational shift whereby children interpret analogy and metaphor first in terms of object similarity and then in terms of relational similarity. Goswami (1996) argues against the relational shift hypothesis, citing as evidence a study performed by Goswami and Brown (1989) in which 3-, 4-, and 6-year-old children were able to correctly complete pictorial A:B::C:? analogies based on familiar causal relations, and, contrary to the predictions of the relational shift hypothesis, made very few object-similarity errors despite the presence of an object-similarity choice. In the present experiment we obtained similarity ratings of Goswami and Brown's stimuli and found that the materials did not contain a true object similarity choice and therefore that study was not an adequate test of the relational shift hypothesis. After appropriate modifications to their methodology, we found that 4- and 5-year-old children's performance was consistent with the relational shift hypothesis: First, object-similarity errors were highly frequent initially and decreased with age; second, the rate of relational (correct) responding increased with age; and third, performance on the analogues was positively related to children's knowledge about the participating causal relations. We conclude by proposing an explanation for the relational shift based on an alignment view of similarity comparison and, further, suggest a new role for object similarity in children's analogical development.     

Protagonist,theme, and goal object: Effects of surface features on analogical transfer

This study examined the effects of the similarity of protagonist, thematic context, and goal object on choice of solution principles in analogical transfer. Kindergartners and second-graders listened to five stories before solving a problem. In the experimental condition, four stories included workable solution principles, and one of each of these included the same protagonist, the same goal object, and the same thematic context as the target problem. Children in the experimental condition at both ages produced more solutions than children in a control group. Kindergartners, but not second-graders, were particularly likely to transfer a solution associated with the same goal object, and to a lesser extent, same protagonist and story theme, compared to a solution in a source story sharing no surface feature with the target problem. The results indicate that younger children are more likely to rely on salient surface features whereas older children flexibly map underlying structure independently of these features.     

3～5岁儿童表面与结构相似性类比推理的实验研究

采用经典类比推理问题对3~5岁儿童表面相似性与结构相似性类比推理能力进行了实验研究。结果发现:(1)表面相似性与结构相似性对儿童解决类比问题的影响不同。一般来说,前者更有利于3~5岁儿童类比问题的解决;(2)儿童解决表面相似性与结构相似性类比问题的能力随年龄增长而发展,但发展趋势不同。在表面相似性问题方面,4岁以前发展较慢,而4岁以后的发展较快;在结构相似性问题方面,4岁以前发展较快,而4岁以后的发展较慢。4岁是儿童解决类比推理问题能力的转折点;(3)在本实验条件下,工作记忆负荷对儿童解决表面相似性类比问题与结构相似性类比问题的影响不显著;(4)类比映射关系提示能促进儿童解决两类类比问题,但对不同年龄儿童的作用是非线性的。     

空间行为关系类比匹配中客体相似性的作用

客体相似性在类比匹配中的作用,是一直存在着争论的问题。该研究通过交叉匹配结合与分离的材料设计,控制类比源和类比目标之间不同相似性,探讨了客体相似性在儿童和成人空间行为关系类比匹配中的作用。实验一通过让儿童和成人完成单目标匹配任务,检验客体相似性对儿童和成人类比匹配影响的不同。实验二采用眼动技术对客体相似性在成人类比匹配过程中的作用进行分区域探讨。结果发现,客体相似性影响儿童空间行为关系类比匹配的成绩,但不影响成人的成绩。成人类比匹配的过程受到结合在关系结构之内的客体相似性的影响。我们提出优先-限制调整观点解释客体相似性在类比匹配中的作用。     

因果模型在类比推理中的作用

通过操纵因果模型的特征维度及推理方向, 探讨因果模型在类比推理中的作用。实验一探讨了当结果特征未知时进行类比推理的情况, 发现在一果多因时, 被试采用因果模型进行类比推理, 而在一因多果时, 被试同时采用因果模型和计算模型进行类比推理。实验二探讨当原因特征未知时进行类比推理的情况, 发现在一果多因和一因多果时, 被试均采用因果模型进行类比推理。结果表明：(1)当结果特征未知时, 人们会建构因果模型进行类比推理。且当因果模型和计算模型处于冲突情境时, 人们会采用因果模型进行类比推理; 但当因果模型和计算模型处于非冲突情境时, 人们会同时采用因果模型和计算模型。(2)当原因特征未知时, 即按照因果模型推理的难度增加时, 人们仍会建构因果模型进行类比推理。     

A computational account of children's analogical reasoning: balancing inhibitory control in working memory and relational representation

Theories accounting for the development of analogical reasoning tend to emphasize either the centrality of relational knowledge accretion or changes in information processing capability. Simulations in LISA (Hummel & Holyoak, 1997, 2003), a neurally inspired computer model of analogical reasoning, allow us to explore how these factors may collaboratively contribute to the development of analogy in young children. Simulations explain systematic variations in United States and Hong Kong children's performance on analogies between familiar scenes (Richland, Morrison & Holyoak, 2006; Richland, Chang, Morrison & Au, 2010). Specifically, changes in inhibition levels in the model's working-memory system explain the developmental progression in US children's ability to handle increases in relational complexity and distraction from object similarity during analogical reasoning. In contrast, changes in how relations are represented in the model best capture cross-cultural differences in performance between children of the same ages (3-4 years) in the United States and Hong Kong. We use these results and simulations to argue that the development of analogical reasoning in children may best be conceptualized as an equilibrium between knowledge accretion and the maturation of information processing capability.     

Skill transfer through goal-driven representation mapping

In this paper, we present an approach to transfer that involves analogical mapping of symbols across different domains. We relate this mechanism to Icarus, a theory of the human cognitive architecture. Our system can transfer skills across domains hypothesizing maps between representations, improving performance in novel domains. Unlike previous approaches to analogical transfer, our method uses an explanatory analysis that compares how well a new domain theory explains previous solutions under different mapping hypotheses. We present experimental evidence that the new mechanism improves transfer over Icarus’ basic learning processes. Moreover, we argue that the same features which distinguish Icarus from other architectures support representation mapping in a natural way and operate synergistically with it. These features enable our analogy system to translate a map among concepts into a map between skills, and to support transfer even if two domains are only partially analogous. We also discuss our system’s relation to other work on analogy and outline directions for future research.     

Enabling spontaneous analogy through heuristic change

Despite analogy playing a central role in theories of problem solving, learning and education, demonstrations of spontaneous analogical transfer are rare. Here, we present a theory of heuristic change for spontaneous analogical transfer, tested in four experiments that manipulated the experience of failure to solve a source problem prior to attempting a target problem. In Experiment 1, participants solved more source problems that contained an additional financial constraint designed to signal the inappropriateness of moves that maximized progress towards the goal. This constraint also led to higher rates of spontaneous analogical transfer to a superficially similar problem. Experiments 2 and 3 showed that the effects of this constraint extend to superficially and structurally different analogs. Experiment 4 generalized the finding to a non-analogous target problem that also benefitted from inhibiting maximizing moves. The results indicate that spontaneous transfer can arise through experience during the solution of a source problem that alters the heuristic chosen for solving both analogical and non-analogical target problems.     

Structural priming as structure-mapping: children use analogies from previous utterances to guide sentence production

What mechanisms underlie children’s language production? Structural priming—the repetition of sentence structure across utterances—is an important measure of the developing production system. We propose its mechanism in children is the same as may underlie analogical reasoning: structure‐mapping. Under this view, structural priming is the result of making an analogy between utterances, such that children map semantic and syntactic structure from previous to future utterances. Because the ability to map relationally complex structures develops with age, younger children are less successful than older children at mapping both semantic and syntactic relations. Consistent with this account, 4‐year‐old children showed priming only of semantic relations when surface similarity across utterances was limited, whereas 5‐year‐olds showed priming of both semantic and syntactic structure regardless of shared surface similarity. The priming of semantic structure without syntactic structure is uniquely predicted by the structure‐mapping account because others have interpreted structural priming as a reflection of developing syntactic knowledge.     

The role of causal models in analogical inference

Computational models of analogy have assumed that the strength of an inductive inference about the target is based directly on similarity of the analogs and in particular on shared higher order relations. In contrast, work in philosophy of science suggests that analogical inference is also guided by causal models of the source and target. In 3 experiments, the authors explored the possibility that people may use causal models to assess the strength of analogical inferences. Experiments 1-2 showed that reducing analogical overlap by eliminating a shared causal relation (a preventive cause present in the source) from the target increased inductive strength even though it decreased similarity of the analogs. These findings were extended in Experiment 3 to cross-domain analogical inferences based on correspondences between higher order causal relations. Analogical inference appears to be mediated by building and then running a causal model. The implications of the present findings for theories of both analogy and causal inference are discussed.     

Analogical and category-based inference: a theoretical integration with Bayesian causal models

A fundamental issue for theories of human induction is to specify constraints on potential inferences. For inferences based on shared category membership, an analogy, and/or a relational schema, it appears that the basic goal of induction is to make accurate and goal-relevant inferences that are sensitive to uncertainty. People can use source information at various levels of abstraction (including both specific instances and more general categories), coupled with prior causal knowledge, to build a causal model for a target situation, which in turn constrains inferences about the target. We propose a computational theory in the framework of Bayesian inference and test its predictions (parameter-free for the cases we consider) in a series of experiments in which people were asked to assess the probabilities of various causal predictions and attributions about a target on the basis of source knowledge about generative and preventive causes. The theory proved successful in accounting for systematic patterns of judgments about interrelated types of causal inferences, including evidence that analogical inferences are partially dissociable from overall mapping quality.