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.     

The neural, evolutionary, developmental, and bodily basis of metaphor

We propose that there are four fundamental kinds of metaphor that are uniquely mapped onto specific brain “networks” and present preliterate (i.e., evolutionary, including before the appearance of written language in the historical record), prelinguistic (i.e., developmental, before the appearance of speech in human development), and extralinguistic (i.e., neuropsychological, cognitive) evidence supportive of this view. We contend that these basic metaphors are largely nonconceptual and entail (a) perceptual-perceptual, (b) cross-modal, (c) movement-movement, and (d) perceptual-affective mappings that, at least, in the initial stages of processing may operate largely outside of conscious awareness. In opposition to our basic metaphor theory (B_mT), the standard theory (S_mT) maintains that metaphor is a conceptual mapping from some base domain to some target domain and/or represents class-inclusion (categorical) assertions. The S_mT captures aspects of secondary or conceptual metaphoric relations but not primary or basic metaphoric relations in our view. We believe our theory (B_mT) explains more about how people actually recognize or create metaphoric associations across disparate domains of experience partly because they are “pre-wired” to make these links.     

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.     

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。     

Approximate Semantic Transference: A Computational Theory of Metaphors and Analogies

In this paper we start from the assumption that in a metaphor, or an analogy, some terms belonging to one domain (source domain) are used to refer to objects other than their conventional referents belonging to a possibly different domain (target domain). We describe a formalism, which is based on the First Order Predicate Calculus, for representing the knowledge structure associated with a domain and then develop a theory of Constrained Semantic Transference [CST] which allows the terms and the structural relationships of the source domain to be transferred coherently across to the target domain. We show how metaphors and analogies can be characterized in CST in such a way that many of their cognitive properties con be explained. We then propose a theory of Approximate Semantic Transference [AST] which is a computational version of CST and is derived from it by replacing the coherency requirement with approximate coherency. We show how AST can be used as a basis for designing models of cognitive processes involved in comprehending metaphors and analogies.     

Similarity and causality in the use of social analogies

The present paper examines whether causal relations are necessary for the use of social analogies. Although causal relations increase the use of social analogies, it is not known whether they are necessary. Establishing this is important for understanding both analogical reasoning and learning in novel situations where people lack knowledge of the causal relations. Study 1 demonstrated that, in the absence of an explicit causal relation, as the similarity between a target individual and a previously encountered individual (the base) increased, people thought the target was increasingly likely to perform the same behavior as the base. Thus, a causal relation is not necessary. Two additional studies used asymmetries in similarity judgments to provide additional evidence that when reasoning analogically people relied on similarity. Manipulating whether subjects focused primarily on the target or the base completely reversed asymmetries both in judgments of how similar the target was to the base and in predictions of how likely the target was to perform the same behavior as the base. The asymmetries for similarity and prediction were completely parallel. Thus, in the absence of an explicit causal relation, use of the analogy was based on judgments of global similarity. The implications of these asymmetries in similarity judgments and predictions for other judgments, such as stereotyping, are also discussed.     

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.     

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.     

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.     

The effects of relational structure on analogical learning

Relational structure is important for various cognitive tasks, such as analogical transfer, but its role in learning of new relational concepts is poorly understood. This article reports two experiments testing people’s ability to learn new relational categories as a function of their relational structure. In Experiment 1, each stimulus consisted of 4 objects varying on 2 dimensions. Each category was defined by two binary relations between pairs of objects. The manner in which the relations were linked (i.e., by operating on shared objects) varied between subjects, producing 3 logically different conditions. In Experiment 2, each stimulus consisted of 4 objects varying on 3 dimensions. Categories were defined by three binary relations, leading to six logically different conditions. Various learning models were compared to the behavioral data, based on the theory of schema refinement. The results highlight several shortcomings of schema refinement as a model of relational learning: (1) it can make unreasonable demands on working memory, (2) it does not allow schemas to grow in complexity, and (3) it incorrectly predicts learning is insensitive to relational structure. We propose schema elaboration as an additional mechanism that provides a more complete account, and we relate this mechanism to previous proposals regarding interactions between analogy and representation construction. The current findings may advance understanding of the cognitive mechanisms involved in learning and representing relational concepts.     

Productivity and Schematicity in Metaphors

The theory of metaphor proposed by Lakoff and Johnson (1980a, 1980b) and Lakoff (1993) involves a mapping of conceptual structure from one semantic domain to another. We investigate properties of these conceptual domain mappings by comparing them to morphological derivational relations. Schematicity and productivity are properties that Bybee (1985) and Langacker (1987) propose for characterizing morphological derivational relations, which we apply to our analysis of metaphor. Metaphors are argued to vary in their degree of semantic schematicity: Domain relations function as generalizations over specific metaphorical expressions. We also demonstrate three points on a continuum of productivity: Conventional metaphors are highly productive, metaphorically motivated transparent idioms are semiproductive, and opaque idioms are unproductive. Each point is compared with an example of morphological productivity having a corresponding conceptual organization. The results demonstrate that semantic productivity can be characterized in the same way as morphological productivity, suggesting that form and meaning are organized by the same principles.     

Processing of tactile spatial information with crossed fingers

The erroneous perception of two objects when one object is touched with crossed fingers has been explained as an inability of the brain to correctly perceive the crossed fingers' positions. This account is examined in Experiment 1, in which the perceived position of stimuli touching the crossed fingers is mapped. Crossing the third finger over the fourth displaced the perceived stimulus position counter-clockwise; crossing the third under the fourth displaced perceptions clockwise. In Experiment 2, perceived positions were found to fit a model of tactile saturation past the point of the functional range of action of the fingers. Two major conclusions are drawn: (a) Tactile stimuli are always perceived as if fingers were uncrossed, and (b) spatial mapping is present only within the functional range of finger excursion.     

The Structural Metaphysics of Quantum Theory and General Relativity

The paper compares ontic structural realism in quantum physics with ontic structural realism about space–time. We contend that both quantum theory and general relativity theory support a common, contentful metaphysics of ontic structural realism. After recalling the main claim of ontic structural realism and its physical support, we point out that both in the domain of quantum theory and in the domain of general relativity theory, there are objects whose essential ways of being are certain relations so that these objects do not possess an intrinsic identity. Nonetheless, the qualitative, physical nature of these relations is in the quantum case (entanglement) fundamentally different from the classical, metrical relations treated in general relativity theory.     

Linguistic and conceptual influences on adjective acquisition in 24- and 36-month-olds

Two hundred forty English-speaking toddlers (24- and 36-month-olds) heard novel adjectives applied to familiar objects (Experiment 1) and novel objects (Experiment 2). Children were successful in mapping adjectives to target properties only when information provided by the noun, in conjunction with participants' knowledge of the objects, provided coherent category information: when basic-level nouns or superordinate-level nouns were used with familiar objects, when novel basic-level nouns were used with novel objects, and--for 36-month-olds--when the nouns were underspecified with respect to category (thing or one) but participants could nonetheless infer a category from pragmatic and conceptual knowledge. These results provide evidence concerning how nouns influence adjective learning, and they support the notion that toddlers consider pragmatic factors when learning new words.     

Does analogical transfer involve a term-to-term alignment?

According to dominant models of reasoning by analogy, analogical transfer requires subjects to first define a full one-to-one correspondence between the base and the target problems. Accordingly, these models predict that if there is a cross-mapping between the base and the target (cross-mapping exists when similar or identical elements in the base and the target play different roles), the time spent transferring a property from the base to the target will be greater. The present results are inconsistent with this prediction. Indeed, if the mapping task is more difficult in the cross-mapping condition than in the control condition, the time needed to make the transfer is not affected by the presence of a cross-mapping. Consequently, we conclude that the mapping phase is not a necessary condition for transfer.     

Modeling Children's Understanding of Quantitative Relations in Texts: A Developmental Perspective

This article describes developmental models of word problem solving that are grounded in the notion of general developmental constraints of the mind. These models were constructed based on the assumption that differences in children's word problem-solving performance are due, at least in part, to developmental differences in their conceptual structures in the quantitative domain. Three levels of knowledge were identified and modeled. The simplest model represents quantitative relations as an ordered array of mental objects. The next level of the model represents numbers as objects of manipulations open two mental number lines that are coordinated in a tentative fashion. The most complex model represents numerical operations as objects of manipulations on two mental number lines that are well-coordinated with explicit, functional rules. These models were implemented as production systems. The accuracy of the predictions resulting from the simulations of the models was tested in an empirical study. Global tests of the models found a good fit of the data to the models. The results wee consistent with the theoretical analysis that the three levels of knowledge were internally coherent and qualitatively different from each other, and that the models could predict children's performance differences to a satisfactory degree.     

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.     

Melting chocolate and melting snowmen: analogical reasoning and causal relations

Children's performance in the classical a:b::c:d analogy task is traditionally very poor prior to the Piagetian stage of formal operations. The interpretation has been that the ability to reason about higher-order relations (the relations between the a:b and c:d parts of the analogy) is late-developing. However, an alternative possibility is that the relations used to date in the analogies are too difficult for younger children. Two experiments presented children aged 3, 4 and 6 years with a:b::c:d analogies which were based on relations of physical causality such as melting and cutting, for example chocolate bar:melted chocolate::snowman:melted snowman. Understanding of these particular causal relations is known to develop between the ages of 3 and 4 years. It was found that even 3-year-olds could solve the classical analogies if they understood the causal relations on which they were based.     

Spatial problem solving and functional relations

Three experiments investigated the role of object knowledge on participants' ability to solve a spatial arrangement problem. The task was to rearrange six real-world three-dimensional objects so that their relative locations agreed with a given set of rules. The aim of the experiments was to tease out the relative extent to which object association, orientation, and object-specific functional relations affect performance on arrangement tasks. When the problem was presented vertically (objects arranged in piles), participants solved functional canonical versions of the problem significantly quicker than functional non-canonical versions both between (Experiments 1a and 2), and within subjects (Experiment 3). When the arrangement problem was presented horizontally (objects arranged flat in two rows), no significant differences in solution times were found between conditions (Experiments 1b and 2). Overall the results provide evidence for the importance of object-specific functional relations as a predictor of the solution time of spatial arrangement problems, although some differences were noted between single and multiple presentation of problems when specific rules within problems were rotated. The importance of functional information in memory as a constraint on the building of mental models and problem spaces is discussed.