An integrated account of generalization across objects and features

Humans routinely make inductive generalizations about unobserved features of objects. Previous accounts of inductive reasoning often focus on inferences about a single object or feature: accounts of causal reasoning often focus on a single object with one or more unobserved features, and accounts of property induction often focus on a single feature that is unobserved for one or more objects. We explore problems where people must make inferences about multiple objects and features, and propose that people solve these problems by integrating knowledge about features with knowledge about objects. We evaluate three computational methods for integrating multiple systems of knowledge: the output combination approach combines the outputs produced by these systems, the distribution combination approach combines the probability distributions captured by these systems, and the structure combination approach combines a graph structure over features with a graph structure over objects. Three experiments explore problems where participants make inferences that draw on causal relationships between features and taxonomic relationships between animals, and we find that the structure combination approach provides the best account of our data.     

Category and feature identification

This paper considers a family of inductive problems where reasoners must identify familiar categories or features on the basis of limited information. Problems of this kind are encountered, for example, when word learners acquire novel labels for pre-existing concepts. We develop a probabilistic model of identification and evaluate it in three experiments. Our first two experiments explore problems where a single category or feature must be identified, and our third experiment explores cases where participants must combine several pieces of information in order to simultaneously identify a category and a feature. Humans readily solve all of these problems, and we show that our model accounts for human inferences better than several alternative approaches.     

归纳推理的抽样理论

作者提出归纳推理的抽样理论,认为归纳推理实质是根据与归纳特征有关的抽样样本情况来推断结论类别具有归纳特征的可能性,其中的抽样可分为类别抽样和特征抽样两种。以大学生为被试的两个实验结果一致支持抽样理论而不是别的归纳推理理论。对于归纳推理的主要现象,抽样理论比其它的相似性解释具有更大的解释范围,特别是能够解释其它理论严格不能解释的归纳推理非对称性现象     

特征归纳的关联相似性模型

作者提出特征归纳的关联相似性模型,用以描述以归纳特征的关联特征相似性为基础的归纳推理,把归纳推理中相似性和关联知识统一整合起来。该模型认为归纳强度主要取决于归纳特征与关联特征的关联强度和关联特征的相似性程度的乘积,归纳信心主要取决于关联强度,从而分离归纳信心和归纳强度。以大学生为被试的两个实验的主要结果支持关联相似性模型的主要预测。关联相似性模型能够描述解释以关联特征相似性为基础的归纳推理现象,比以往的归纳理论具有更大的解释能力和解释范围     

How causal knowledge affects classification: A generative theory of categorization

Several theories have been proposed regarding how causal relations among features of objects affect how those objects are classified. The assumptions of these theories were tested in 3 experiments that manipulated the causal knowledge associated with novel categories. There were 3 results. The 1st was a multiple cause effect in which a feature's importance increases with its number of causes. The 2nd was a coherence effect in which good category members are those whose features jointly corroborate the category's causal knowledge. These 2 effects can be accounted for by assuming that good category members are those likely to be generated by a category's causal laws. The 3rd result was a primary cause effect, in which primary causes are more important to category membership. This effect can also be explained by a generative account with an additional assumption: that categories often are perceived to have hidden generative causes.     

Describing categories of objects for menu retrieval systems

When searching for information in menu-based retrieval systems, users are given a choice among a set of categories. Successful retrieval of information depends critically on the user’s understanding the system’s division of objects into categories and the system’s labels for these categories. This research compares several different ways of describing ill-defined categories of objects using combinations of names and examples. Examples provide a promising possibility, both as a means of flexibly naming new or difficult menu categories and as a methodological tool for studying certain categorization problems.     

The ‘living dead’ — Survivors of torture and psychosis

Regardless of all differences between patients who have suffered from psychotic breakdowns and those with the sequelae of torture, our experience have shown that some common features can be recognized. We can attempt to understand patients' experience of being ‘living dead’ in terms of regression to the ‘psychotic core’ in the personality, and in terms of actualisation and enactment of archaic relations to primary objects. The major difference between thee two categories of patients deals with a located, limited, and concrete traumatic event in the life of the torture-survivor, whilst in the schizophrenic individual the trauma also emanates from within through own destructiveness and rage. Regressive forms of relations toward distorted, aggressively cathected and persecutory primary objects are reestablished in both cases, leading to a more or less stable reorganisation of the ego. Difficulties in psychotherapy with schizophrenic patients and torture-survivors are here discussed as a consequence of the patients' persistently holding onto the distorted and regressive forms of relating to primary objects, when the projections of the patients' own destructiveness and hate is followed by a strong tendency to symbiotic merging.     

Hierarchies, similarity, and interactivity in object recognition: "category-specific" neuropsychological deficits.

Category-specific impairments of object recognition and naming are among the most intriguing disorders in neuropsychology, affecting the retrieval of knowledge about either living or nonliving things. They can give us insight into the nature of our representations of objects: Have we evolved different neural systems for recognizing different categories of object? What kinds of knowledge are important for recognizing particular objects? How does visual similarity within a category influence object recognition and representation? What is the nature of our semantic knowledge about different objects? We review the evidence on category-specific impairments, arguing that deficits even for one class of object (e.g., living things) cannot be accounted for in terms of a single information processing disorder across all patients; problems arise at contrasting loci in different patients. The same apparent pattern of impairment can be produced by damage to different loci. According to a new processing framework for object recognition and naming, the hierarchical interactive theory (HIT), we have a hierarchy of highly interactive stored representations. HIT explains the variety of patients in terms of (1) lesions at different levels of processing and (2) different forms of stored knowledge used both for particular tasks and for particular categories of object.     

Relational properties and memory-based category construction.

Although many experiments have investigated factors that constrain perceptual category construction, there have been no investigations of factors that constrain memory-based (MB) category construction. Six experiments examined the extent to which perceptual and MB sorting were influenced by correlated dimensions, family resemblance principles, and conceptual knowledge. Sensitivity to many types of relational information (e.g., correlated features, causal relations, interactive properties of objects, and family resemblance relations) was observed with perceptual sorting, but these properties were rarely used to organize information in MB sorting conditions. Instead, there was a clear preference to organize categories around single dimensions. Even when perfectly correlated features were causally related, Ss in memory conditions did not use correlations to construct categories. The strengths and limitations of MB analyses and categorizations are discussed.     

The reasoning skills and thinking dispositions of problem gamblers: a dual‐process taxonomy

We present a taxonomy that categorizes the types of cognitive failure that might result in persistent gambling. The taxonomy subsumes most previous theories of gambling behavior, and it defines three categories of cognitive difficulties that might lead to gambling problems: The autonomous set of systems (TASS) override failure, missing TASS output, and mindware problems. TASS refers to the autonomous set of systems in the brain (which are executed rapidly and without volition, are not under conscious control, and are not dependent on analytic system output). Mindware consists of rules, procedures, and strategies available for explicit retrieval. Seven of the eight tasks administered to pathological gamblers, gamblers with subclinical symptoms, and control participants were associated with problem gambling, and five of the eight were significant predictors in analyses that statistically controlled for age and cognitive competence. In a commonality analysis, an indicator from each of the three categories of cognitive difficulties explained significant unique variance in problem gambling, indicating that each of the categories had some degree of predictive specificity. Copyright © 2006 John Wiley & Sons, Ltd.     

A probabilistic model of theory formation

Concept learning is challenging in part because the meanings of many concepts depend on their relationships to other concepts. Learning these concepts in isolation can be difficult, but we present a model that discovers entire systems of related concepts. These systems can be viewed as simple theories that specify the concepts that exist in a domain, and the laws or principles that relate these concepts. We apply our model to several real-world problems, including learning the structure of kinship systems and learning ontologies. We also compare its predictions to data collected in two behavioral experiments. Experiment 1 shows that our model helps to explain how simple theories are acquired and used for inductive inference. Experiment 2 suggests that our model provides a better account of theory discovery than a more traditional alternative that focuses on features rather than relations.     

The mereology of thermodynamic equilibrium

The special composition question (SCQ), which asks under which conditions objects compose a further object, establishes a central debate in modern metaphysics. Recent successes of inductive metaphysics, which studies the implications of the natural sciences for metaphysical problems, suggest that insights into the SCQ can be gained by investigating the physics of composite systems. In this work, I show that the minus first law of thermodynamics, which is concerned with the approach to equilibrium, leads to a new approach to the SCQ, the thermodynamic composition principle (TCP): Multiple systems in (generalized) thermal contact compose a single system. This principle, which is justified based on a systematic classification of possible mereological models for thermodynamic systems, might form the basis of an inductive argument for universalism. A formal analysis of the TCP is provided on the basis of mereotopology, which is a combination of mereology and topology. Here, “thermal contact” can be analyzed using the mereotopological predicate “self-connectedness”. Self-connectedness has to be defined in terms of mereological sums to ensure that scattered objects cannot be self-connected.

     

Learning to learn causal models

Learning to understand a single causal system can be an achievement, but humans must learn about multiple causal systems over the course of a lifetime. We present a hierarchical Bayesian framework that helps to explain how learning about several causal systems can accelerate learning about systems that are subsequently encountered. Given experience with a set of objects, our framework learns a causal model for each object and a causal schema that captures commonalities among these causal models. The schema organizes the objects into categories and specifies the causal powers and characteristic features of these categories and the characteristic causal interactions between categories. A schema of this kind allows causal models for subsequent objects to be rapidly learned, and we explore this accelerated learning in four experiments. Our results confirm that humans learn rapidly about the causal powers of novel objects, and we show that our framework accounts better for our data than alternative models of causal learning.     

Effects of semantic cues on mathematical modeling: Evidence from word-problem solving and equation construction tasks

Mathematical solutions to textbook word problems are correlated with semantic relations between the objects described in the problem texts. In particular, division problems usually involve functionally related objects (e.g., tulips-vases) and rarely involve categorically related objects (e.g., tulips-daisies). We examined whether middle school, high school, and college students use object relations when they solve division word problems (WP) or perform the less familiar task of representing verbal statements with algebraic equations (EQ). Both tasks involved multiplicative comparison statements with either categorically or functionally related objects (e.g., "four times as many cupcakes [commuters] as brownies [automobiles]"). Object relations affected the frequency of correct solutions in the WP task but not in the EQ task. In the latter task, object relations did affect the structure of nonalgebraic equation errors. We argue that students use object relations as "semantic cues" when they engage in the sense-making activity of mathematical modeling.     

Induction, overhypothesis, and the origin of abstract knowledge. Evidence from 9-month-old infants

Human cognition relies on the ability to extract generalizable knowledge from limited evidence. One type of inductive learning, overhypothesis formation, allows learners to make inferences that take them beyond the limits of direct experience, leading to the creation of abstract knowledge. The developmental roots of this ability have yet to be investigated. We report three experiments examining whether 9-month-old infants are capable of forming overhypotheses. Our results show that when given evidence about a few objects in some category, infants formed a second-order generalization about categories in general. These findings provide evidence that infants possess a powerful mechanism for inductive learning-a mechanism that may be applied to many domains and that can account for the development of many inductive biases later on.     

Visual attention and the semantics of space: beyond central and peripheral cues

The distinction between central and peripheral cues has played an important role in understanding the functional nature of visual attention for the past 30 years. In the present article, we propose a new taxonomy that is based on linguistic categories of spatial relations. Within this framework, spatial cues are categorized as either "projective" or "deictic." Using an empirical diagnostic, we demonstrate that the word cues above, below, left, and right express projective spatial relations, whereas arrow cues, eye-gaze cues, and abrupt-onset cues express deictic spatial relations. Thus, the projective-versus-deictic distinction crosscuts the more traditional central-versus-peripheral distinction. The theoretical utility of this new distinction is discussed in the context of recent evidence suggesting that a variety of central cues can elicit reflexive orienting.     

Induction and category coherence

In studies of category formation, subjects rarely construct family resemblance categories. Instead, they divide objects into categories using a single dimension. This is a puzzling result given the widely accepted view that natural categories are organized in terms of a family resemblance principle. The observation that natural categories support inductive inferences is used here to test the hypothesis that family resemblance categories would be constructed if stimuli were first used to generate inductive inferences. In two experiments, subjects answered either induction questions, which made interproperty relationships more salient, or frequency questions, which required information only about individual properties, before they performed a sorting task. Subjects were likely to produce family resemblance sorts if they had first answered induction questions but not if they had answered frequency questions.     

Building and solving odd-one-out classification problems: A systematic approach

Classification problems (“find the odd-one-out”) are frequently used as tests of inductive reasoning to evaluate human or animal intelligence. This paper introduces a systematic method for building the set of all possible classification problems, followed by a simple algorithm for solving the problems of the R-ASCM, a psychometric test derived from this method. The average Hamming distance finds repetitions of features between and within the problems' sets; it manages to solve 97% of such problems. This performance is equaled only by superior human adults. Finally, these results demonstrate that a simple two-step algorithm can improve categorical case-based reasoning and k-NN algorithms while clarifying the cognitive basis of classification.     

Conceptions of objects across categories: Childhood patterns resemble those of adults

Studies of category‐specific disorders have suggested that categories of living and non‐living things vary in the properties that are most salient to recognition. Studies of the object features generated by normal adults have also revealed different patterns of responses to different categories. These adult patterns are likely to originate in childhood, but there are few reports of children's verbal conceptions of objects, and none at present of objects from different categories. This paper investigates the development of object conceptions, in a large group of children, aged 3 years 7 months to 11 years 6 months, in response to ‘What is a — ?’ questions directed to 72 objects, selected from two categories of living things (animals and fruit/vegetables) and two categories of artifacts (implements and vehicles). Proportions of perceptual‐to‐functional features provided by the children to living and non‐living things varied with the range of features defined as functions, just as studies of adults have found. Apart from the distribution of superordinate responses, which were significantly more salient to living than to non‐living categories, no other property separated the two categories. Only the category of implements could be distinguished from the other categories on the basis of the features generated. It is argued that the perceptual‐functional theory of category‐specific disorders receives little support from this study, but that in general the distribution of features generated by young children is similar to that produced by normal adults.     

Mathematical Practice,Fictionalism and Social Ontology

From the perspective of mathematical practice, I examine positions claiming that mathematical objects are introduced by human agents. I consider in particular mathematical fictionalism and a recent position on social ontology formulated by Cole (2013, 2015). These positions are able to solve some of the challenges that non-realist positions face. I argue, however, that mathematical entities have features other than fictional characters and social institutions. I emphasise that the way mathematical objects are introduced is different and point to the multifaceted role that relations and interconnections play in this context. Finally, I argue that mathematical entities can be considered to be pragmatically real.