Induction of Relational Schemas: Common Processes in Reasoning and Complex Learning

Five experiments were performed to test whether participants induced a coherent representation of the structure of a task, called a relational schema, from specific instances. Properties of a relational schema include: An explicit symbol for a relation, a binding that preserves the truth of a relation, potential for higher-order relations, omnidirectional access, potential for transfer between isomorphs, and ability to predict unseen items in isomorphic problems. However relational schemas are not necessarily coded in abstract form. Predictions from relational schema theory were contrasted with predictions from configural learning and other nonstructural theories in five experiments in which participants were taught a structure comprised of a set of initial-state,operator → end-state instances. The initial-state,operator pairs were presented and participants had to predict the correct end-state. Induction of a relational schema was achieved efficiently by adult participants as indicated by ability to predict items of a new isomorphic problem. The relational schemas induced showed the omnidirectional access property, there was efficient transfer to isomorphs, and structural coherence had a powerful effect on learning. The “learning to learn” effect traditionally associated with the learning set literature was observed, and the long-standing enigma of learning set acquisition is explained by a model composed of relational schema induction and structure mapping. Performance was better after reversal of operators than after shift to an alternate structure, even though the latter entailed more overlap with previously learned tasks in terms of the number of configural associations that were preserved. An explanation for the reversal shift phenomenon in terms of induction and mapping of a relational schema is proposed. The five experiments provided evidence supporting predictions from relational schema theory, and no evidence was found for configural or nonstructural learning theories.     

Making Probabilistic Relational Categories Learnable

Theories of relational concept acquisition (e.g., schema induction) based on structured intersection discovery predict that relational concepts with a probabilistic (i.e., family resemblance) structure ought to be extremely difficult to learn. We report four experiments testing this prediction by investigating conditions hypothesized to facilitate the learning of such categories. Experiment 1 showed that changing the task from a category‐learning task to choosing the “winning” object in each stimulus greatly facilitated participants' ability to learn probabilistic relational categories. Experiments 2 and 3 further investigated the mechanisms underlying this “who's winning” effect. Experiment 4 replicated and generalized the “who's winning” effect with more natural stimuli. Together, our findings suggest that people learn relational concepts by a process of intersection discovery akin to schema induction, and that any task that encourages people to discover a higher order relation that remains invariant over members of a category will facilitate the learning of putatively probabilistic relational concepts.     

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.     

Implicit learning: An analysis of the form and structure of a body of tacit knowledge

Subjects learned implicitly the underlying structure of an artificial language by memorizing a set of representative exemplars from the language. The form and structure of their resulting knowledge of the language was evaluated and analyzed over a four day period by several procedures: (a) solving anagrams from the language, (b) determining the well-formedness of novel letter strings, and (c) providing detailed introspective reports. Several important implications about implicit acquisition of a novel complex system emerged. First, the memorial representation of a structured system is acquired through the dual operations of a differentiation-like process based upon relational invariances and a configurational process based upon overall structure. Second, the form of tacit knowledge is an abstract representation of the intrinsic structure of the stimulus field. Third, while the ability to make explicit what is known implicitly increases with performance levels, the conscious apprehension of structure always lags behind what is known unconsciously.     

上下级之间应该存在何种关系?上下级关系图式

以往上下级关系研究大多聚焦于关系的实然特征, 缺乏对关系应有特征或模式的探讨。上下级关系图式是个体对上下级之间关系应有模式或特征的内隐认知, 这种内隐认知有助于揭示上级与下属之间的互动过程, 并为促进上级和下属的积极心理与行为提供理论启示。经过对文献的系统梳理, 将上下级关系图式与内隐关系理论、追随力认知图式、关系自我和关系认同等概念进行区分。个体传统性和现代性、依恋风格、领导行为以及文化因素能够预测上下级关系图式; 上下级关系图式能影响领导的态度与行为、下属忠诚、下属工作绩效、角色外行为、领导评价(道德领导)以及上下级关系评价; 移情的社会认知模型、泛家族主义、社会学习理论、信息加工理论解释了上下级关系图式的前因后果。未来可以从识别预测因素、拓展后果研究以及挖掘作用机制等方面推动上下级关系图式的研究。     

A comparison of simple correction and functional feedback in schema learning

The role of knowledge of results (KR) in a schematic concept formation task was clarified by manipulating the specificity of information provided during feedback. Ss learned to discriminate between pairs of random forms from two schema families. Verbal correction was compared with a functional KR procedure in which the schema prototypes were superimposed over test stimuli. In no case did verbal correction improve learning in comparison with functional KR. Differences in acquisition persisted in a retention test.     

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.     

The Role of Abstract and Specific Knowledge in the Formation of Product Judgments: An Analogical Learning Perspective

Prior research has assumed that existing knowledge exerts its influence on consumer judgments primarily through abstract knowledge structures. Consequently, little attention has been given to the possibility that judgments may, under certain circumstances, be influenced by knowledge associated with more specific knowledge structures. This article examines the factors responsible for determining the impact of abstract versus specific knowledge on consumer judgments. Based on the Consumer Learning by Analogy model (CLA model; Gregan‐Paxton & John, 1997), it is argued that the relative influence of abstract and specific knowledge is a function of (a) the relation between the new product and existing knowledge and (b) the nature of consumer's knowledge. These ideas were tested in a series of experiments in which participants were required to judge a new product that varied in its relation to an existing product or brand. In this context, the influence of specific knowledge was most evident when participants were able to construct an attribute mapping, but not a relational mapping, to link the novel product to a familiar brand exemplar. When it was possible to construct a relational mapping, a more abstract knowledge structure, such as a schema, was retrieved and used as the basis of product judgments.     

The use of schemata in the acquisition and transfer of knowledge

A learning model based on “memory schemata” is presented. The model assumes that knowledge substructures in memory are shared by multiple representations of information from diverse contexts. These substructures, or schemata, are collections of concepts and associations that occur together repeatedly and act as unitary, higher-order concepts. When knowledge is represented in terms of a schema, associations from the schema to additional concepts specify the detailed information for that context. This organization of knowledge entails both costs and benefits for the acquisition and retention of new information that utilizes a schema. The use of a familiar encoding structure facilitates memory access at storage and retrieval time. Multiple uses of the shared structure produce interference among concepts from the various contexts. The predictions of the model were tested in two transfer experiments in prose learning. Experiment l demonstrated the simultaneous effects of both facilitation and interference in the learning of diverse information conforming to a single schema. Recall of information from the schema was a non-monotonic function of schema strength. In Experiment 2 facilitation was preserved while interference was eliminated by increasing the discriminability among competing contexts. Results from both experiments confirmed the predictions of the model.     

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。     

基于熟悉性的项目间语义关系再认

在项目间语义关系的熟悉性研究中, 一个关键问题是熟悉性效应依赖于哪种信息的加工, 关系概念还是抽象结构?研究通过两个实验, 借助无线索回忆再认范式(the recognition without cued recall paradigm, 简称RWCR范式)和四词类比材料, 采用混合设计, 直接分离与比较关系概念和抽象结构的加工对RWCR效应的影响。结果发现, 关系概念作为测验线索能够引发显著RWCR效应, 但仅仅学习关系概念却不能;只有学习关系概念的结构化材料时, 才能引发显著RWCR效应。该结果表明, 项目间语义关系的熟悉性过程与结构信息有关。     

Analogical encoding facilitates knowledge transfer in negotiation

Information learned in one situation often fails to transfer to a similarly structured situation. However, prior findings suggest that comparing two or more instances that embody the same principle can promote abstraction of a schema that can be transferred to new situations. In two lines of research, we examined the effects of analogical encoding on knowledge transfer in negotiation situations. In Experiment 1, undergraduates were more likely to propose optimal negotiation strategies and less likely to propose compromises (a suboptimal strategy) when they received analogy training. In Experiment 2, graduate management students who drew an analogy from two cases were nearly three times more likely to incorporate the strategy from the training cases into their negotiations than were students given the same cases separately. For both novices and experienced participants, the comparison process can be an efficient means of abstracting principles for later application.     

Pitch distribution,melodic contour or both? Modeling makam schema with multidimensional scaling and self-organizing maps

Experienced listeners internalize musical tonal knowledge via statistical learning of pitch distributions as a result of exposure to musical environment. Cross-cultural studies of music cognition offer new perspectives to investigate the acquisition of tonal schema. Makam music is a rich musical system characterized by modal structures defined by micro-tonal pitch sets, and melodic progression patterns (aka seyir features). Makam schema is possibly acquired by internalizing the seyir in addition to pitch features. In the current study, we examined whether an ideal model of makam schema is built with multidimensional scaling analysis and with self-organizing maps (SOMs). We were interested in whether statistical information about seyir features, in addition to pitch distributions, would form an acceptable makam schema model. We qualitatively analyzed topographical organizations in the models to understand whether they reflect complex relations between makams. Multidimensional scaling analyses did not produce an acceptable model for makam schema. The SOM trained with pitch distributions provided an adequate model for makam schema. However, the SOM trained with both pitch distributions and seyir features was better in capturing the complex relations between makams. Further behavioral research is necessary to understand whether melodic progression patterns are intrinsic features of the tonal knowledge of the experienced listeners of makam music.     

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.     

Testing the actual equivalence of automatically generated items

If the automatic item generation is used for generating test items, the question of how the equivalence among different instances may be tested is fundamental to assure an accurate assessment. In the present research, the question was dealt by using the knowledge space theory framework. Two different ways of considering the equivalence among instances are proposed: The former is at a deterministic level and it requires that all the instances of an item template must belong to exactly the same knowledge states; the latter adds a probabilistic level to the deterministic one. The former type of equivalence can be modeled by using the BLIM with a knowledge structure assuming equally informative instances; the latter can be modeled by a constrained BLIM. This model assumes equality constraints among the error parameters of the equivalent instances. An approach is proposed for testing the equivalence among instances, which is based on a series of model comparisons. A simulation study and an empirical application show the viability of the approach.     

Connecting instances to promote children's relational reasoning

The practice of learning from multiple instances seems to allow children to learn about relational structure. The experiments reported here focused on two issues regarding relational learning from multiple instances: (a) what kind of perceptual situations foster such learning and (b) how particular object properties, such as complexity and similarity, interact with relational learning. Two kinds of perceptual situations were of interest here: simultaneous view, where instances are viewed at once, and sequential view, where instances are viewed one at a time (one right after the other). We examined the influence of particular perceptual situations and object properties using two tests of relational reasoning: a common match-to-sample task, where new instances are compared with a common sample, and a variable match-to-sample task, where new instances are compared with a sample that varies on each trial. Experiments 1 and 2 indicate that simultaneous presentation of even highly dissimilar instances, one simple and one complex, effectively connects them together and improves relational generalization in both match-to-sample tasks. Experiment 3 shows that simple samples are more effective than complex ones in the common match-to-sample task. However, when one instance is not used a common sample and various pairs of instances are simply compared, as in Experiment 4, simple and rich instances are equally effective at promoting relational learning. These results bear on our understanding of how children connect instances and how those initial connections affect learning and generalization.     

A Piagetian perspective on mathematical construction

In this paper, we offer a Piagetian perspective on the construction of the logico-mathematical schemas which embody our knowledge of logic and mathematics. Logico-mathematical entities are tied to the subject's activities, yet are so constructed by reflective abstraction that they result from sensorimotor experience only via the construction of intermediate schemas of increasing abstraction. The ‘axiom set’ does not exhaust the cognitive structure (schema network) which the mathematician thus acquires. We thus view ‘truth’ not as something to be defined within the closed ‘world’ of a formal system but rather in terms of the schema network within which the formal system is embedded. We differ from Piaget in that we see mathematical knowledge as based on social processes of mutual verification which provide an external drive to any ‘necessary dynamic’ of reflective abstraction within the individual. From this perspective, we argue that axiom schemas tied to a preferred interpretation may provide a necessary intermediate stage of reflective abstraction en route to acquisition of the ability to use formal systems in abstracto.     

Relational knowledge: the foundation of higher cognition

Accumulating evidence on the nature, function and acquisition of relational knowledge indicates a crucial role of such knowledge in higher cognitive processes. In this review, we specify the essential properties of relational knowledge, together with the role it plays in reasoning, categorisation, planning, quantification and language. Furthermore, we discuss the processes involved in its acquisition and how these processes have been implemented in contemporary neural network models. We present evidence demonstrating that relational knowledge integrates heuristic and analytic cognition, is important for symbolic processes and the creation of novelty, activates specific regions of the prefrontal cortex, and is the most recently evolved and slowest-developing cognitive process. Arguably, relational knowledge represents the core of higher cognition.     

On teaching articulatory phonetics via an orthography

In six experiments, the ability of university students to obtain generalizable knowledge about subphonemic distinctive features through learning to read an orthography based on these features was explored. In the reference experiment, it was found that learning four grapheme-phoneme pairs did not generate “feature awareness,” as tested by generalization to new instances of the orthography. In a second experiment, it was demonstrated that this failure was not due to inherent limitations in the testing technique, and a third experiment indicated that a considerable increase in exposure to the orthography and its principles did not help. In the last three experiments, instruction in articulatory phonetics was given prior to subjects’ learning the orthography, but reliable generalization to new instances emerged only when the instruction was based directly on the phonemes used in acquisition. Also, successful generalization was found to go hand in hand with verbalizable awareness of phonetic structure. A high level of performance was achieved only when the orthography/speech isomorphism was pointed out clearly. The results indicate that usable knowledge about an implicitly known property of speech is relatively resistant to instruction via an orthography, and that direct instruction in the property is necessary. An analogy is drawn with the acquisition of reading by nonreaders, with the results of the study lending weight to the use of curricula that emphasize phonemic awareness.