Integrating analogical mapping and general problem solving: the path-mapping theory

This article describes the path-mapping theory of how humans integrate analogical mapping and general problem solving. The theory posits that humans represent analogs with declarative roles, map analogs by lower-level retrieval of analogous role paths, and coordinate mappings with higher-level organizational knowledge. Implemented in the ACT-R cognitive architecture, the path-mapping theory enables models of analogical mapping behavior to incorporate and interface with other problem-solving knowledge. Path-mapping models thus can include task-specific skills such as encoding analogs or generating responses, and can make behavioral predictions at the level of real-world metrics such as latency or correctness. We show that the path-mapping theory can successfully account for the major phenomena addressed by previous theories of analogy. We also describe a path-mapping model that can account for subjects' incremental eye-movement and typing behavior in a story-mapping task. We discuss extensions and implications of this work to other areas of analogy and problem-solving research.     

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.     

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.     

Domain transfer via cross-domain analogy

Analogical learning has long been seen as a powerful way of extending the reach of one’s knowledge. We present the domain transfer via analogy (DTA) method for learning new domain theories via cross-domain analogy. Our model uses analogies between pairs of textbook example problems, or worked solutions, to create a domain mapping between a familiar and a new domain. This mapping allows us to initialize a new domain theory. After this initialization, another analogy is made between the domain theories themselves, providing additional conjectures about the new domain. We present two experiments in which our model learns rotational kinematics by an analogy with translational kinematics, and vice versa. These learning rates outperform those from a version of the system that is incrementally given the correct domain theory.     

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。     

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.     

儿童问题解决中的类比迁移

儿童问题解决中的类比迁移是儿童认知发展中的一个基本问题,但在儿童发展研究中却一直没有得到足够的重视。在对儿童问题解决中的类比迁移研究进行回顾和总结的基础上,特别是仔细分析最近十年里的类比迁移研究,该文总结出了儿童问题解决中类比迁移研究的发展趋势,主要包括从探讨迁移是否存在到验证迁移是一种早期能力、从关注迁移的年龄差异到关注促进迁移的有关因素、从关注迁移是否是基本能力到关注迁移的加工机制、从描述迁移技能到领域概化、从关注近迁移到关注远迁移。最后,该文对未来儿童问题解决中的类比迁移研究进行了展望     

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.     

Constraints on Analogical Mapping: A Comparison of Three Models

Three theories of analogy have been proposed that are supported by computational models and data from experiments on human analogical abilities. In this article we show how these theories can be unified within a common metatheoretical framework that distinguishes among levels of informational, behavioral, and hardware constraints. This framework clarifies the distinctions among three computational models in the literature: the Analogical Constraint Mapping Engine (ACME), the Structure-Mapping Engine (SME), and the Incremental Analogy Machine (IAM). We then go on to develop a methodology for the comparative testing of these models. In two different manipulations of an analogical mapping task we compare the results of computational experiments with these models against the results of psychological experiments. In the first experiment we show that increasing the number of similar elements in two analogical domains decreases the response time taken to reach the correct mapping for an analogy problem. In the second psychological experiment we find that the order in which the elements of the two domains are presented has significant facilitative effects on the ease of analogical mapping. Of the three models, only IAM embodies behavioral constraints and predicts both of these results. Finally, the immediate implications of these results for analogy research are discussed, along with the wider implications the research has for cognitive science methodology.     

A computational model of visual analogies in design

We present an analysis of the work of human participants in addressing design problems by analogy. We describe a computer program, called Galatea, that simulates the visual input and output of four experimental participants. Since Galatea is an operational computer program, it makes specific commitments about the visual representations and reasoning it uses for analogical transfer. In particular, Galatea provides a computational model of how human designers might be generating new designs by incremental transfer of the problem-solving procedure used in previous design cases.     

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.     

Impact of intuitive theories on feature recruitment throughout the continuum of expertise

Expertise in object domains involves both the perceptual learning of the differentiating and higher order features that are indicative of concepts and the elaboration of intuitive theories. Triad-similarity judgments, feature-salience ratings, and verbal protocols were used to investigate the effects of theories on the recruitment of features across different categorization contexts, as well as the degree to which expert categorization skills transferred to less familiar domains. Whereas novices considered features that indicated overall similarity to be more perceptually salient than were modified parts that indicated taxonomic relations, experts found them equally salient. Experts’ theories were instrumental in directing feature recruitment in contexts involving identification, image generation, and similarity decisions. Experts’ theories also supported the transfer of categorization skills to related, less familiar domains. The relation of mutual dependence between perceptual learning and theory development throughout the continuum of expertise is considered.     

Solving geometric analogy problems through two-stage analogical mapping

Evans' 1968 ANALOGY system was the first computer model of analogy. This paper demonstrates that the structure mapping model of analogy, when combined with high-level visual processing and qualitative representations, can solve the same kinds of geometric analogy problems as were solved by ANALOGY. Importantly, the bulk of the computations are not particular to the model of this task but are general purpose: We use our existing sketch understanding system, CogSketch, to compute visual structure that is used by our existing analogical matcher, Structure Mapping Engine (SME). We show how SME can be used to facilitate high-level visual matching, proposing a role for structural alignment in mental rotation. We show how second-order analogies over differences computed via analogies between pictures provide a more elegant model of the geometric analogy task. We compare our model against human data on a set of problems, showing that the model aligns well with both the answers chosen by people and the reaction times required to choose the answers.     

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.     

几何图形类比推理的ERP研究

该研究以几何图形作为实验材料,测定14名硕士研究生在完成两种类比推理任务（大小变化和颜色变化）和其基线任务时的事件相关电位（ERP）,探讨类比推理过程的脑内时程动态变化。研究发现,两种推理任务所诱发的波形基本一致,而推理任务与其基线任务之间的ERP波形存在显著差异,两种基线任务之间的ERP波形也存在显著差异;类比推理的加工过程是有阶段性的,即编码潍断、映射、得出结论,研究结果进一步支持了Sternberg的成分理论;推断和映射这两个类比推理所特有的加工阶段都有其对应的脑机制,图式推断阶段主要激活的是前额皮层和双侧的顶叶皮层,类比映射和调整阶段主要激活的是左半球的颞叶、额叶和中央顶。     

语言类比推理的神经机制：来自ERP研究的证据

实验通过“A:B::C:D”范式, 采用事件相关电位技术, 考察了语言类比推理的神经机制。实验结果显示：图式生成阶段诱发出N400和P300成分, 反映了类比源域的词对概念通达和词对关系抽取的加工过程; 类比映射阶段诱发出N400和晚期负成分LNC, 反映了类比目标域前项词汇概念意义的激活, 以及将已获取的图式关系类比映射于目标域, 并进行推理的加工过程。研究结果表明, 语言类比推理的神经机制复杂, 牵涉到一系列认知加工步骤; LNC成分与类比映射阶段的加工关系密切, 其波幅和头皮分布的广泛性情况与类比映射关系的复杂程度成正比。     

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.     

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.     

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.     

The Micro-Category account of analogy

Here, we investigate how activation of mental representations of categories during analogical reasoning influences subsequent cognitive processing. Specifically, we present and test the central predictions of the "Micro-Category" account of analogy. This account emphasizes the role of categories in aligning terms for analogical mapping. In a semantic priming paradigm, a four-word analogy task was compared to two other four-word tasks. Stimuli were identical in all tasks; only the instructions given to participants differed. Participants were instructed to identify analogy relations, category relations, or conventionalized semantic relations in the four-word sets. After each four-word set, a single target word appeared and participants named this word aloud. Target words that referred to category relations in the preceding four-word sets were primed as strongly when participants identified analogies as when participants identified categories, suggesting that activation of category concepts plays an important role in analogical thinking. In addition, priming of category-referent words in the analogy and category tasks was significantly greater than priming of these words when participants identified conventionalized semantic relations. Since identical stimuli were used in all conditions, this finding indicates that it is the activation of category relations, distinct from any effect of basic semantic association, that causes analogical reasoning to prime category-referent words. We delineate how the "Micro-Category" account of analogy predicts these phenomena and unifies findings from diverse areas of research concerning analogical reasoning.