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.     

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.     

Generating Relations Elicits a Relational Mindset in Children

Relational reasoning is a hallmark of human higher cognition and creativity, yet it is notoriously difficult to encourage in abstract tasks, even in adults. Generally, young children initially focus more on objects, but with age become more focused on relations. While prerequisite knowledge and cognitive resource maturation partially explains this pattern, here we propose a new facet important for children's relational reasoning development: a general orientation to relational information, or a relational mindset. We demonstrate that a relational mindset can be elicited, even in 4‐year‐old children, yielding greater than expected spontaneous attention to relations. Children either generated or listened to an experimenter state the relationships between objects in a set of formal analogy problems, and then in a second task, selected object or relational matches according to their preference. Children tended to make object mappings, but those who generated relations on the first task selected relational matches more often on the second task, signaling that relational attention is malleable even in young children.     

Physical and cognitive dimensions in stimulus comparison

Two experiments were carried out using a same-different task with sets of four stimuli varying orthogonally in three dimensions. Sameness was defined by each of the three dimensions in turn, as well as by physical identity. Two types of dimensions, physical and cognitive, were studied. In Experiment 1, the numerals 6, 10, VI, and X, which vary in Length, System, and Name, were used. With simultaneous presentation, order of difficulty was from the physical dimension of Length to the cognitive dimension of Name. While overall difficulty was related to dimensional discriminability, internal evidence suggested that Name was not a dimension in the same sense as Length is, and that some stimulus pairs were simply easier to process than others, regardless of the response required (e.g., short stimulus pairs and Arabic numerals). With sequential presentation, Name was processed as fast as System, due largely to the fact that much faster responding occurred when an Arabic numeral was the second stimulus. Thus, with sequential presentation, Name provides a processing mechanism not provided by physical dimensions. In Experiment 2, the numerals 3, 4, 6, and 7, which vary in Magnitude, Oddness, and Curvilinearity, were used. The cognitive dimension of Magnitude was pro cessed most rapidly, and numerical distance between pairs of numbers dominated the results for “same” responses, regardless of the sameness rule used. Again, evidence was found for fast processing of some stimulus pairs (e.g., 3 4), regardless of the response required. Overall, these experiments are interpreted as indicating that cognitive factors such as stimulus familiarity may override aspects of physical discriminability with many dimensions and stimuli, that, even though a cognitive dimension can be used to generate a logically proper set of stimuli, it does not necessarily act as other, more physical dimensions do, and that clarification of the functional role of a dimension is more important than attempts to locate stages.     

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。     

The impact of arbitrarily applicable relational responding on evaluative learning about hypothetical money and shock outcomes

Evaluative learning comprises changes in preferences after co-occurrences between conditioned stimuli (CSs) and an unconditioned stimulus (US) of affective value. Co-occurrences may involve relational responding. Two experiments examined the impact of arbitrary relational responding on evaluative preferences for hypothetical money and shock outcomes. In Experiment 1, participants were trained to make arbitrary relational responses by placing CSs of the same size but different colours into boxes and were then instructed that these CSs represented different intensities of hypothetical USs (money or shock). Liking ratings of the CSs were altered in accordance with the underlying bigger/smaller than relations. A reversal of preference was also observed: the CS associated with the smallest hypothetical shock was rated more positively than the CS associated with the smallest amount of hypothetical money. In Experiment 2, procedures from Relational Frame Theory (RFT) established a relational network of more than/less than relations consisting of five CSs (A-B-C-D-E). Overall, evaluative preferences were altered, but not reversed, depending on (a) how stimuli had been related to one another during the learning phase and (b) whether those stimuli referred to money or shocks. The contribution of RFT to evaluative learning research is discussed.     

Establishing arbitrary comparative relations and referential transformations of stimulus function in individuals with autism

Relational Frame Theory posits that complex language develops through arbitrarily applicable relational networks, with potential implications for individuals with autism. Responding relationally based on comparison occurs when participants respond to any number of comparative properties, such as “bigger” or “faster.” Experiment 1 established two 3-member comparative networks, in which a stimulus A was conditioned as “bigger” or “faster” than a stimulus B, and the stimulus B was conditioned as “bigger” or “faster” than a stimulus C in 2 children with autism. Both participants met the mastery criterion for the trained relations and demonstrated the emergence of the untrained combinatorially entailed A–C and C–A relations. The participants could also match the arbitrary A stimuli with larger or faster objects and the C stimuli with smaller or slower objects. The results were replicated in Experiment 2 with the same participants, where a 5-member relational network was established for the bigger/smaller relation.     

Producing and Recognizing Analogical Relations

Analogical reasoning is an important component of intelligent behavior, and a key test of any approach to human language and cognition. Only a limited amount of empirical work has been conducted from a behavior analytic point of view, most of that within Relational Frame Theory (RFT), which views analogy as a matter of deriving relations among relations. The present series of four studies expands previous work by exploring the applicability of this model of analogy to topography-based rather than merely selection-based responses and by extending the work into additional relations, including nonsymmetrical ones. In each of the four studies participants pretrained in contextual control over nonarbitrary stimulus relations of sameness and opposition, or of sameness, smaller than, and larger than, learned arbitrary stimulus relations in the presence of these relational cues and derived analogies involving directly trained relations and derived relations of mutual and combinatorial entailment, measured using a variety of productive and selection-based measures. In Experiment 1 participants successfully recognized analogies among stimulus networks containing same and opposite relations; in Experiment 2 analogy was successfully used to extend derived relations to pairs of novel stimuli; in Experiment 3 the procedure used in Experiment 1 was extended to nonsymmetrical comparative relations; in Experiment 4 the procedure used in Experiment 2 was extended to nonsymmetrical comparative relations. Although not every participant showed the effects predicted, overall the procedures occasioned relational responses consistent with an RFT account that have not yet been demonstrated in a behavior-analytic laboratory setting, including productive responding on the basis of analogies.     

Patterns, chunks, and hierarchies in serial reaction-time tasks

The impact of relational structures (i.e., the systematicity of relations between successive items) on incidental sequence learning was investigated in a serial reaction-time (SRT) task while keeping constant the statistical structure. In order to assess the influence of relational structures in stimulus and response sequences separately, the strength of relational patterns in sequences of digits as stimuli and of keystrokes as responses was orthogonally varied. In Exps. 1 and 2, the variation of relational patterns was mainly effective in the keystroke sequence. In Exp. 2, in addition to the variation of relational patterns, the presentation of stimuli was delayed at serial positions that were incongruent with the relational structure. The results show that these incongruent pauses reduced the learning of strongly structured sequences of keystrokes but improved the learning of weakly structured sequences. Experiment 3 suggests that even higher-order relations between elementary patterns are utilized to accelerate responses. The data are interpreted as evidence for the impact of relational patterns, in addition to statistical redundancies, on the formation of chunks. Reasons are discussed for the finding that relational chunking was more pronounced in the keystroke than in the digit sequences. Received: 25 June 1998 / Accepted: 3 December 1998     

Free-flying honeybees extrapolate relational size rules to sort successively visited artificial flowers in a realistic foraging situation

Learning and applying relational concepts to solve novel tasks is considered an indicator of cognitive-like ability. It requires the abstraction of relational concepts to different objects independent to the physical nature of the individual objects. Recent research has revealed the honeybee’s ability to rapidly learn and manipulate relations between visual stimuli such as ‘same/different’, ‘above/below’, or ‘larger/smaller’ despite having a miniature-sized brain. While honeybees can solve problems using rule-based relative size comparison, it remains unresolved as to whether bees can apply size rules when stimuli are encountered successively, which requires reliance on working memory for stimuli comparison. Additionally, the potential ability of bees to extrapolate acquired information to novel sizes beyond training sets remains to be investigated. We tested whether individual free-flying honeybees could learn ‘larger/smaller’ size rules when visual stimuli were presented successively, and whether such rules could then be extrapolated to novel stimulus sizes. Honeybees were individually trained to a set of four sizes such that individual elements might be correct, or incorrect, depending upon the alternative stimulus. In a learning test, bees preferred the correct size relation for their respective learning group. Bees were also able to successfully extrapolate the learnt relation during transfer tests by maintaining the correct size relationships when considering either two smaller, or two larger, novel stimulus sizes. This performance demonstrates that an insect operating in a complex environment has sufficient cognitive capacity to learn rules that can be abstracted to novel problems. We discuss the possible learning mechanisms which allow their success.     

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.     

Qualities, Relations, and Property Exemplification

The question whether qualities are metaphysically more fundamental than or mere limiting cases of relations can be addressed in an applied symbolic logic. There exists a logical equivalence between qualitative and relational predications, in which qualities are represented as one-argument-place property predicates, and relations as more-than-one-argument-place predicates. An interpretation is first considered, according to which the logical equivalence of qualitative and relational predications logically permits us ontically to eliminate qualities in favor of relations, or relations in favor of qualities. If metaphysics is understood at least in part as an exercise in ontic economy, then we may be encouraged to adopt a property ontology of qualities without quality-irreducible relations, or relations without relation-irreducible qualities. If either strategy is followed, the choice of reducing qualities to relations or relations to qualities will need to be justified on extra-logical grounds. These might include a perceived greater intuitiveness, explanatory fecundity, compatibility with cognitive ontogeny or developmental psychology, expressive or explanatory elegance or cumbersomeness, and an open-ended list of philosophical motivations that could reasonably favor the ontic prioritization of qualities over relations or relations over qualities. Despite its intuitive appeal, the thesis that logical equivalence together with extra-logical preferences justifies unidirectional ontic reduction of relations to qualities or qualities to relations is rejected in light of the more defensible proposition that the logical equivalence of qualitative and relational predications actually supports the opposite conclusion, that both qualities and relations are logically indispensable to a complete ontology of properties. The logical equivalence of qualitative and relational predications, insofar as we continue to observe the distinction, makes it logically necessary ontically for both qualities and relations to exist whenever either one exists. That logically equivalent qualitative and relational predications have as their truth-makers the exemplification by objects of both qualities and relations as equi-foundational properties further suggests that there is no deeper logical distinction between qualities and relations, but only two convenient lexical-grammatical designations for property predications involving one- versus more-than-one-argument-place.     

Relational Priming Based on a Multiplicative Schema for Whole Numbers and Fractions

Why might it be (at least sometimes) beneficial for adults to process fractions componentially? Recent research has shown that college‐educated adults can capitalize on the bipartite structure of the fraction notation, performing more successfully with fractions than with decimals in relational tasks, notably analogical reasoning. This study examined patterns of relational priming for problems with fractions in a task that required arithmetic computations. College students were asked to judge whether or not multiplication equations involving fractions were correct. Some equations served as structurally inverse primes for the equation that immediately followed it (e.g., 4 × 3/4 = 3 followed by 3 × 8/6 = 4). Students with relatively high math ability showed relational priming (speeded solution times to the second of two successive relationally related fraction equations) both with and without high perceptual similarity (Experiment 2). Students with relatively low math ability also showed priming, but only when the structurally inverse equation pairs were supported by high perceptual similarity between numbers (e.g., 4 × 3/4 = 3 followed by 3 × 4/3 = 4). Several additional experiments established boundary conditions on relational priming with fractions. These findings are interpreted in terms of componential processing of fractions in a relational multiplication context that takes advantage of their inherent connections to a multiplicative schema for whole numbers.     

Learning to Align Relations: The Effects of Feedback and Self-Explanation

Relational similarity connects superficially dissimilar objects and events. In 2 experiments, the ability to recognize and respond to similar relations was studied in children ages 3 to 5 with 2 comparison tasks. Children interpreted illustrated pictures that shared perceptual or relational aspects and then made 2 comparison choices and explanations of these choices. Results of Experiment 1 demonstrated that when given explicit feedback regarding the relations depicted in the pictures, children learned to respond quickly to this type of similarity in subsequent trials, which involved novel relations. In Experiment 2, the effect of re- explanation on relational understanding was examined. Children age 4.5 to 5 years, but not 3- to 4-year-olds, showed relational learning when asked to explain the experimenter's relational choice.     

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.     

Categorization by schema relations and perceptual similarity in 5-year-olds and adults: A study in vision and in audition

This research explores the way in which young children (5 years of age) and adults use perceptual and conceptual cues for categorizing objects processed by vision or by audition. Three experiments were carried out using forced-choice categorization tasks that allowed responses based on taxonomic relations (e.g., vehicles) or on schema category relations (e.g., vehicles that can be seen on the road). In Experiment 1 (visual modality), prominent responses based on conceptually close objects (e.g., objects included in a schema category) were observed. These responses were also favored when within-category objects were perceptually similar. In Experiment 2 (auditory modality), schema category responses depended on age and were influenced by both within- and between-category perceptual similarity relations. Experiment 3 examined whether these results could be explained in terms of sensory modality specializations or rather in terms of information processing constraints (sequential vs. simultaneous processing).     

Learning of event sequences is based on response-effect learning: further evidence from a serial reaction task

Four experiments provide converging evidence that serial learning in a serial reaction task is based on response-effect learning, mediated by the learning of the relations between a response and the stimulus that follows it. In Experiment 1, the authors varied the stimulus sequence and the response-stimulus relations while holding the response sequence constant. Learning effects depended on the complexity of the response-stimulus relations but not on the stimulus-stimulus relations. In Experiment 2, transfer of serial learning from 1 stimulus sequence to another was only found when both sequences had identical response-stimulus relations. In Experiment 3, a variation of the stimulus sequence alone had no effect on serial learning, whereas in Experiment 4 learning effects increased when the response-stimulus relations but not the stimulus-stimulus relations were simplified. These findings suggest that serial learning is based on mechanisms of voluntary action control.     

Mapping relational structure in spatial reasoning

Three experiments investigated whether the similarity of relational structures influences the interpretation of spatial representations. Adults were shown diagrams of hand gestures paired with simple statements and asked to judge the meaning of new gestures. In Experiment 1 the gestures were paired with active declarative statements. In Experiment 2, the gestures were paired with conjunctive and disjunctive relations. Experiment 3 used statements similar to those used in Experiment 1, but eliminated the initial object-to-object mapping provided in Experiments 1 and 2. In all three experiments, most participants chose an interpretation that set up a parallel relational structure between the gesture and its meaning: spatial elements were paired with conceptual elements and spatial relations were paired with conceptual relations. These results are consistent with the hypothesis that similarity of relational structures influences spatial reasoning, and have implications for analogical reasoning, diagrammatic reasoning, and language processing.     

The role of multiple-exemplar training and naming in establishing derived equivalence in an infant

The conditions under which symmetry and equivalence relations develop are still controversial. This paper reports three experiments that attempt to analyze the impact of multiple-exemplar training (MET) in receptive symmetry on the emergence of visual-visual equivalence relations with a very young child, Gloria. At the age of 15 months 24 days (15m24d), Gloria was tested for receptive symmetry and naming and showed no evidence of either repertoire. In the first experiment, MET in immediate and delayed receptive symmetrical responding or listener behavior (from object-sound to immediate and delayed sound-object selection) proceeded for one month with 10 different objects. This was followed, at 16m25d, by a second test conducted with six new objects. Gloria showed generalized receptive symmetry with a 3-hr delay; however no evidence of naming with new objects was found. Experiment 2 began at 17m with the aim of establishing derived visual-visual equivalence relations using a matching-to-sample format with two comparisons. Visual-visual equivalence responding emerged at 19m, although Gloria still had not shown evidence of naming. Experiment 3 (22m to 23m25d) used a three-comparison matching-to-sample procedure to establish visual-visual equivalence. Equivalence responding emerged as in Experiment 2, and naming emerged by the end of Experiment 3. Results are discussed in terms of the history of training in bidirectional relations responsible for the emergence of visual-visual equivalence relations and of their implications for current theories of stimulus equivalence.     

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.