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.     

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.     

Relations, objects, and the composition of analogies

This research addresses the kinds of matching elements that determine analogical relatedness and literal similarity. Despite theoretical agreement on the importance of relational match, the empirical evidence is neither systematic nor definitive. In 3 studies, participants performed online evaluations of relatedness of sentence pairs that varied in either the object or relational match. Results show a consistent focus on relational matches as the main determinant of analogical acceptance. In addition, analogy does not require strict overall identity of relational concepts. Semantically overlapping but nonsynonymous relations were commonly accepted, but required more processing time. Finally, performance in a similarity rating task partly paralleled analogical acceptance; however, relatively more weight was given to object matches. Implications for psychological theories of analogy and similarity are addressed.     

Finding similarity in a model of relational reasoning

Similarity plays a central role in the study of perception and cognition. Previous attempts to model similarity have captured effects of either featural or structural similarity, but typically not both. We simulated both by fitting similarity data with the LISA model of relational reasoning [Hummel, J. E., & Holyoak, K. J. (1997). Distributed representations of structure: A theory of analogical access and mapping. Psychological Review, 104, 427–466, Hummel, J. E., & Holyoak, K. J. (2003a). A symbolic-connectionist theory of relational inference and generalization. Psychological Review, 110, 220–264]. The same mechanisms LISA uses to simulate analogy also provide a natural account of feature-based similarity effects (e.g., violations of symmetry), structural effects (e.g., the advantage of alignable over non-alignable differences), and the combined effects of featural and structured information (i.e., MIPs and MOPs; “Matches In/Out of Place”) on similarity judgments. Our approach differs from most models of similarity in that LISA was not originally designed to simulate similarity judgments, but rather analogical reasoning. LISA’s incidental ability to simulate diverse similarity effects speaks to the plausibility of the model’s account of human knowledge representation.     

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。     

An Eye-tracking Analysis of the Effect of Prior Comparison on Analogical Mapping

The present research examined the effect of prior experience on the distribution of attention during judgments of analogical similarity. Identifying analogical similarity requires mapping a set of relations in one situation onto a matching set of relations in an analogous situation. Analogical mapping is difficult when the common relational structure is embedded in contexts with dissimilar surface features and irrelevant surface similarities. Prior comparison of analogs may help subjects find future relational correspondences and ignore surface similarity (Markman and Gentner 1993). In the present study, attention was measured with eye tracking, which was monitored while subjects rated the similarity of analogous scenes. Experimental but not control subjects had previously compared scenes with the same structure. Eye fixation data indicated that prior comparison did not affect attention to structure-relevant objects, but significantly reduced attention to irrelevant surface-similar objects. Scanning data showing that both groups scanned within scenes more than between scenes were consistent with structure-mapping models of analogy.     

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。     

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。     

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.     

Integrating structure and meaning: a distributed model of analogical mapping

In this paper we present Drama , a distributed model of analogical mapping that integrates semantic and structural constraints on constructing analogies. Specifically, Drama uses holographic reduced representations (Plate, 1994), a distributed representation scheme, to model the effects of structure and meaning on human performance of analogical mapping. Drama is compared to three symbolic models of analogy (SME, Copycat, and ACME) and one partially distributed model (LISA). We describe Drama's performance on a number of example analogies and assess the model in terms of neurological and psychological plausibility. We argue that Drama's successes are due largely to integrating structural and semantic constraints throughout the mapping process. We also claim that Drama is an existence proof of using distributed representations to model high-level cognitive phenomena.     

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。     

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.     

Analogical Mapping by Constraint Satisfaction

A theory of analogical mapping between source and target analogs based upon interacting structural, semantic, and pragmatic constraints is proposed here. The structural constraint of isomorphism encourages mappings that maximize the consistency of relational corresondences between the elements of the two analogs. The constraint of semantic similarity supports mapping hypotheses to the degree that mapped predicates have similar meanings. The constraint of pragmatic centrality favors mappings involving elements the analogist believes to be important in order to achieve the purpose for which the analogy is being used. The theory is implemented in a computer program called ACME (Analogical Constraint Mapping Engine), which represents constraints by means of a network of supporting and competing hypotheses regarding what elements to map. A cooperative algorithm for parallel constraint satisfaction identities mapping hypotheses that collectively represent the overall mapping that best fits the interacting constraints. ACME has been applied to a wide range of examples that include problem analogies, analogical arguments, explanatory analogies, story analogies, formal analogies, and metaphors. ACME is sensitive to semantic and pragmatic information if it is available, and yet able to compute mappings between formally isomorphic analogs without any similar or identical elements. The theory is able to account for empirical findings regarding the impact of consistency and similarity on human processing of analogies.     

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.     

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.     

Structural Alignment during Similarity Comparisons

Similarity comparisons are a basic component of cognition, and there are many elegant models of this process. None of these models describe comparisons of structured representations, although mounting evidence suggests that mental representations are well characterized by structured hierarchical systems of relations. We propose that structured representations can be compared via structural alignment, a process derived from models of analogical reasoning. The general prediction of structural alignment is that similarity comparisons lead subjects to attend to the matching relational structure in a pair of items. This prediction is illustrated with a computational simulation that also suggests that the strength of the relational focus is diminished when the relational match is impoverished, or when competing interpretations lead to rich object matches. These claims are tested in four experiments using the one-shot mapping paradigm, which places object similarity and relational similarity in opposition. The results support the hypothesis that similarity involves the alignment of structured representations.     

The impact of anxiety on analogical reasoning

The effect of state anxiety on analogical reasoning was investigated by examining qualitative differences in mapping performance between anxious and non-anxious individuals reasoning about pictorial analogies. The working-memory restriction theory of anxiety, coupled with theories of analogy that link complexity of mapping with working-memory capacity, predicts that high anxiety will impair the ability to find correspondences based on relations between multiple objects relative to correspondences based on overlap of attributes between individual objects. Anxiety was induced in one condition by a stressful speeded subtraction task administered prior to the analogy task. Anxious participants produced fewer relational responses and more attribute responses than did non-anxious participants, both in the absence of explicit instructions to find relational mappings (Experiment 1) and after receiving such instructions (Experiment 2). The findings support the postulated links among anxiety, working memory, and the ability to perform complex analogical mapping.     

Children's development of analogical reasoning: insights from scene analogy problems

We explored how relational complexity and featural distraction, as varied in scene analogy problems, affect children's analogical reasoning performance. Results with 3- and 4-year-olds, 6- and 7-year-olds, 9- to 11-year-olds, and 13- and 14-year-olds indicate that when children can identify the critical structural relations in a scene analogy problem, development of their ability to reason analogically interacts with both relational complexity and featural distraction. Error patterns suggest that children are more likely to select a distracting object than to make a relational error for problems that present both possibilities. This tendency decreases with age, and older children make fewer errors overall. The results suggest that changes in analogical reasoning with age depend on the interplay among increases in relational knowledge, the capacity to integrate multiple relations, and inhibitory control over featural distraction.     

Bayesian analogy with relational transformations

How can humans acquire relational representations that enable analogical inference and other forms of high-level reasoning? Using comparative relations as a model domain, we explore the possibility that bottom-up learning mechanisms applied to objects coded as feature vectors can yield representations of relations sufficient to solve analogy problems. We introduce Bayesian analogy with relational transformations (BART) and apply the model to the task of learning first-order comparative relations (e.g., larger, smaller, fiercer, meeker) from a set of animal pairs. Inputs are coded by vectors of continuous-valued features, based either on human magnitude ratings, normed feature ratings (De Deyne et al., 2008), or outputs of the topics model (Griffiths, Steyvers, & Tenenbaum, 2007). Bootstrapping from empirical priors, the model is able to induce first-order relations represented as probabilistic weight distributions, even when given positive examples only. These learned representations allow classification of novel instantiations of the relations and yield a symbolic distance effect of the sort obtained with both humans and other primates. BART then transforms its learned weight distributions by importance-guided mapping, thereby placing distinct dimensions into correspondence. These transformed representations allow BART to reliably solve 4-term analogies (e.g., larger:smaller::fiercer:meeker), a type of reasoning that is arguably specific to humans. Our results provide a proof-of-concept that structured analogies can be solved with representations induced from unstructured feature vectors by mechanisms that operate in a largely bottom-up fashion. We discuss potential implications for algorithmic and neural models of relational thinking, as well as for the evolution of abstract thought.     

Analogy as relational priming: a developmental and computational perspective on the origins of a complex cognitive skill

The development of analogical reasoning has traditionally been understood in terms of theories of adult competence. This approach emphasizes structured representations and structure mapping. In contrast, we argue that by taking a developmental perspective, analogical reasoning can be viewed as the product of a substantially different cognitive ability - relational priming. To illustrate this, we present a computational (here connectionist) account where analogy arises gradually as a by-product of pattern completion in a recurrent network. Initial exposure to a situation primes a relation that can then be applied to a novel situation to make an analogy. Relations are represented as transformations between states. The network exhibits behaviors consistent with a broad range of key phenomena from the developmental literature, lending support to the appropriateness of this approach (using low-level cognitive mechanisms) for investigating a domain that has normally been the preserve of high-level models. Furthermore, we present an additional simulation that integrates the relational priming mechanism with deliberative controlled use of inhibition to demonstrate how the framework can be extended to complex analogical reasoning, such as the data from explicit mapping studies in the literature on adults. This account highlights how taking a developmental perspective constrains the theory construction and cognitive modeling processes in a way that differs substantially from that based purely on adult studies, and illustrates how a putative complex cognitive skill can emerge out of a simple mechanism.