Children’s causal inferences from indirect evidence: Backwards blocking and Bayesian reasoning in preschoolers

Previous research suggests that children can infer causal relations from patterns of events. However, what appear to be cases of causal inference may simply reduce to children recognizing relevant associations among events, and responding based on those associations. To examine this claim, in Experiments 1 and 2, children were introduced to a “blicket detector,” a machine that lit up and played music when certain objects were placed upon it. Children observed patterns of contingency between objects and the machine’s activation that required them to use indirect evidence to make causal inferences. Critically, associative models either made no predictions, or made incorrect predictions about these inferences. In general, children were able to make these inferences, but some developmental differences between 3- and 4-year-olds were found. We suggest that children’s causal inferences are not based on recognizing associations, but rather that children develop a mechanism for Bayesian structure learning. Experiment 3 explicitly tests a prediction of this account. Children were asked to make an inference about ambiguous data based on the base rate of certain events occurring. Four-year-olds, but not 3-year-olds were able to make this inference.     

Archetypal Forms of Inference

A form (or pattern) of inference, let us say, explicitlysubsumes just such particular inferences as are instances of the form, and implicitly subsumes thoseinferences with a premiss and conclusion logically equivalent to the premiss and conclusion of an instanceof the form in question. (For simplicity we restrict attention to one-premiss inferences.) A form ofinference is archetypal if it implicitly subsumes every correct inference. A precise definition (Section 1)of these concepts relativizes them to logics, since different logics classify different inferences ascorrect, as well as ruling differently on the matter of logical equivalence which entered into the definitionof implicit subsumption. When relativized to classical propositional logic, we find (Section 2) thatall but a handful of `degenerate' inference forms turn out to be archetypal, whereas matters are verydifferent in this respect for the case of intuitionistic propositional logic (Sections 3 and 4), and an interestingstructure emerges in this case (the poset of equivalence classes of inference forms, with respect tothe equivalence relation of implicitly subsuming the same inferences). Thus a more accurate, if excessivelylong-winded title would be 'Archetypal and Non-Archetypal Forms of Inference in Classical andIntuitionistic Propositional Logic'. Some left-overs are postponed for a final discussion (Section 5).The overall intention is to introduce a new subject matter rather than to have the last word on thequestions it raises; indeed several significant questions are left as open problems.     

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.     

Argument,Inference, and Persuasion

This paper distinguishes between two types of persuasive force arguments can have in terms of two different connections between arguments and inferences. First, borrowing from Pinto (in Argument, inference, and dialectic, Kluwer Academic Pub, Dordrecht, 2001), an arguer's invitation to inference directly persuades an addressee if the addressee performs an inference that the arguer invites. This raises the question of how invited inferences are determined by an invitation to inference. Second, borrowing from Sorenson (J Philos 88:245–266, 1991), an arguer's invitation to inference indirectly persuades an addressee if the addressee performs an inference guided by the argument even though it is uninvited. This raises the question of how an invitation to inference can guide inferences that the arguer does not use the argument to invite. Focusing on belief-inducing inference, the primary aims here are (i) to clarify what is necessary for an addressee's belief-inducing inference to be invited by an argument used as an instrument of persuasion; and (ii) to highlight the capacity of arguments to guide such inferences. The paper moves beyond Pinto's (2001) discussion by using Boghossian's (Philos Stud 169:1–18, 2014) Taking Condition in service of (i) and (ii) in way that illustrates how epistemically bad arguments can rationally persuade addressees of their conclusions.

     

文本阅读中回指推理发生的整合性因素

探讨回指距离、干扰词的精细描述、干扰词的典型性 对回指推理（先行词通达）的影响。包括2个实验,被试是华南师范大学一二年级本科生164名。采用移动窗口技术,要求被试阅读一定篇数（如,实验1a每个被试阅读15篇）的文章,对不同条件的探测词的反应时进行统计。实验1探讨干扰词精细描述类型（精细描述高和精细描述低）对回指推理的影响。结果表明,干扰的精细描述并非是影响回指推理的主要因素。实验2探讨干扰词和先行词的典型性类型的相对变化对回指推理的影响。结果表明高典型干扰在不同回指距离条件下都会对回指推理产生影响。本研究结果初步证明在影响回指推理的干扰典型性和干扰精细描述的二个因素中,起主要作用的是干扰的典型性     

篇章阅读中影响回指推理的因素

探讨回指距离、干扰词的精细描述、干扰词的典型性对回指推理的影响。包括2个实验,164名大学生被试。实验1探讨干扰词精细描述类型的影响。结果表明,干扰的精细描述并非是影响回指推理的主要因素。实验2探讨干扰词和先行词的典型性类型的相对变化的影响。结果表明高典型干扰在不同回指距离条件下都会对回指推理产生影响。从而表明高典型的干扰项干扰了回指推理发生。     

Inferences from memory: strategy- and exemplar-based judgment models compared

What are the cognitive processes underlying people's inferences from memory? To provide an answer, the exemplar-based approach to predicting people's inferences is tested against the strategy-based approach. Exemplar models assume that people make inferences about objects by retrieving similar objects from memory. In contrast, the strategy-based approach assumes that people select cognitive strategies that make inferences based on abstracted knowledge and information the inference situation provides. In Experiment 1, in which dichotomous feedback on the level of pair-comparisons was provided, almost all participants were classified as using a simple lexicographic strategy. In Experiment 2, in which continuous feedback for single objects was provided, most participants were classified as using a compensatory strategy. Both experiments suggest that the strategy-based approach is more suitable for predicting people's inferences from memory than the exemplar-based approach. The strategy-based approach shows how people adapt to inference situations by selecting different cognitive strategies.     

The role of familiarity in binary choice inferences

In research on the recognition heuristic (Goldstein & Gigerenzer, Psychological Review, 109, 75–90, 2002), knowledge of recognized objects has been categorized as “recognized” or “unrecognized” without regard to the degree of familiarity of the recognized object. In the present article, we propose a new inference model—familiarity-based inference. We hypothesize that when subjective knowledge levels (familiarity) of recognized objects differ, the degree of familiarity of recognized objects will influence inferences. Specifically, people are predicted to infer that the more familiar object in a pair of two objects has a higher criterion value on the to-be-judged dimension. In two experiments, using a binary choice task, we examined inferences about populations in a pair of two cities. Results support predictions of familiarity-based inference. Participants inferred that the more familiar city in a pair was more populous. Statistical modeling showed that individual differences in familiarity-based inference lie in the sensitivity to differences in familiarity. In addition, we found that familiarity-based inference can be generally regarded as an ecologically rational inference. Furthermore, when cue knowledge about the inference criterion was available, participants made inferences based on the cue knowledge about population instead of familiarity. Implications of the role of familiarity in psychological processes are discussed.     

Demonstrative Induction and the Skeleton of Inference

It has been common wisdom for centuries that scientific inference cannot be deductive; if it is inference at all, it must be a distinctive kind of inductive inference. According to demonstrative theories of induction, however, important scientific inferences are not inductive in the sense of requiring ampliative inference rules at all. Rather, they are deductive inferences with sufficiently strong premises. General considerations about inferences suffice to show that there is no difference in justification between an inference construed demonstratively or ampliatively. The inductive risk may be shouldered by premises or rules, but it cannot be shirked. Demonstrative theories of induction might, nevertheless, better describe scientific practice. And there may be good methodological reasons for constructing our inferences one way rather than the other. By exploring the limits of these possible advantages, I argue that scientific inference is neither of essence deductive nor of essence inductive.     

Speaker reliability guides children's inductive inferences about novel properties

Prior work shows that children can make inductive inferences about objects based on their labels rather than their appearance (Gelman, 2003). A separate line of research shows that children's trust in a speaker's label is selective. Children accept labels from a reliable speaker over an unreliable speaker (e.g., Koenig & Harris, 2005). In the current paper, we tested whether 3- and 5-year-old children attend to speaker reliability when they make inductive inferences about a non-obvious property of a novel artifact based on its label. Children were more likely to use a reliable speaker's label than an unreliable speaker's label when making inductive inferences. Thus, children not only prefer to learn from reliable speakers, they are also more likely to use information from reliable speakers as the basis for future inferences. The findings are discussed in light of the debate between a similarity-driven and a label-driven approach to inductive inferences.     

A Connectionist Approach to Knowledge Representation and Limited Inference

Although the connectionist approach has lead to elegant solutions to a number of problems in cognitive science and artificial intelligence, its suitability for dealing with problems in knowledge representation and inference has often been questioned. This paper partly answers this criticism by demonstrating that effective solutions to certain problems in knowledge representation and limited inference can be found by adopting a connectionist approach. The paper presents a connectionist realization of semantic networks, that is, it describes how knowledge about concepts, their properties, and the hierarchical relationship between them may be encoded as an interpreter-free massively parallel network of simple processing elements that can solve an interesting class of inheritance and recognition problems extremely fast—in time proportional to the depth of the conceptual hierarchy. The connectionist realization is based on an evidential formulation that leads to principled solutions to the problems of exceptions and conflicting multiple inheritance situations during inheritance, and the best-match or partial-match computation during recognition. The paper also identifies constraints that must be satisfied by the conceptual structure in order to arrive at an efficient parallel realization.     

Familiarity-Matching: An Ecologically Rational Heuristic for the Relationships-Comparison Task

Previous studies have shown that people often use heuristics in making inferences and that subjective memory experiences, such as recognition or familiarity of objects, can be valid cues for inferences. So far, many researchers have used the binary choice task in which two objects are presented as alternatives (e.g., “Which city has the larger population, city A or city B?”). However, objects can be presented not only as alternatives but also in a question (e.g., “Which country is city X in, country A or country B?”). In such a situation, people can make inferences based on the relationship between the object in the question and each object given as an alternative. In the present study, we call this type of task a “relationships-comparison task.” We modeled the three inference strategies that people could apply to solve it (familiarity-matching [FM; a new heuristic we propose in this study], familiarity heuristic [FH], and knowledge-based inference [KI]) to examine people's inference processes. Through Studies 1, 2, and 3, we found that (a) people tended to rely on heuristics, and that FM (inferences based on similarity in familiarity between objects) well explained participants' inference patterns; (b) FM could work as an ecologically rational strategy for the relationships–comparison task since it could effectively reflect environmental structures, and that the use of FM could be highly replicable and robust; and (c) people could sometimes use a decision strategy like FM, even in their daily lives (consumer behaviors). The nature of the relationships–comparison task and human cognitive processes is discussed.     

Inference using categories

How do people use category membership and similarity for making inductive inferences? The authors addressed this question by examining the impact of category labels and category features on inference and classification tasks that were designed to be comparable. In the inference task, participants predicted the value of a missing feature of an item given its category label and other feature values. In the classification task, participants predicted the category label of an item given its feature values. The results from 4 experiments suggest that category membership influences inference even when similarity information contradicts the category label. This tendency was stronger when the category label conveyed class inclusion information than when the label reflected a feature of the category. These findings suggest that category membership affects inference beyond similarity and that category labels and category features are 2 different things.     

主题关系在4~5岁儿童不同属性归纳推理发展中的作用

为探讨主题关系在儿童归纳推理中的作用,采用经典的三角归纳范式,设计了主题关系和知觉相似冲突、主题关系和分类学关系冲突两种情形,来考察4~5岁儿童在内在属性和情境性属性任务中的归纳推理。结果显示：当主题关系和知觉相似冲突时,从4.5岁开始儿童主要基于主题关系对情境性属性进行归纳推理,而对于内在属性的推论,4~5岁儿童在基于主题关系和基于知觉相似上没有显著差异。当主题关系和分类学关系冲突时,从4.5岁开始儿童主要基于主题关系对情境性属性进行归纳推理,从5岁开始儿童主要基于分类学关系对内在属性进行归纳推理。两个实验结果均发现5岁和5.5岁儿童能够依据不同的属性使用不同的关系推理,表现出归纳灵活性     

类别特征推理的认知机制与神经基础

分类及类别特征推理是类别知识的两大重要功能。研究表明, 两种任务之间存在本质差异。因此, 探讨类别特征推理的认知及神经机制对于拓展类别相关理论非常重要。已有研究发现, 类别标签、典型性程度以及类别特征间的因果关系都会影响类别特征推理任务, 而且, 类别特征推理任务与分类任务的神经基础不同。未来研究方向应当关注类别标签以及类别特征间的因果关系分别与典型性程度之间的交互作用, 在未来神经机制方面的进一步研究应当设计更符合自然情境下的特征推理任务范式。     

Bayesian Inference for Growth Mixture Models with Latent Class Dependent Missing Data

Growth mixture models (GMMs) with nonignorable missing data have drawn increasing attention in research communities but have not been fully studied. The goal of this article is to propose and to evaluate a Bayesian method to estimate the GMMs with latent class dependent missing data. An extended GMM is first presented in which class probabilities depend on some observed explanatory variables and data missingness depends on both the explanatory variables and a latent class variable. A full Bayesian method is then proposed to estimate the model. Through the data augmentation method, conditional posterior distributions for all model parameters and missing data are obtained. A Gibbs sampling procedure is then used to generate Markov chains of model parameters for statistical inference. The application of the model and the method is first demonstrated through the analysis of mathematical ability growth data from the National Longitudinal Survey of Youth 1997 (Bureau of Labor Statistics, U.S. Department of Labor, 1997). A simulation study considering 3 main factors (the sample size, the class probability, and the missing data mechanism) is then conducted and the results show that the proposed Bayesian estimation approach performs very well under the studied conditions. Finally, some implications of this study, including the misspecified missingness mechanism, the sample size, the sensitivity of the model, the number of latent classes, the model comparison, and the future directions of the approach, are discussed.     

The Comparative Set Fallacy

This paper argues for the validity of inferences that take the form of: A is more X than B; therefore A and B are both X. After considering representative counterexamples, it is claimed that these inferences are valid if and only if the comparative terms in the inference are taken from no more than one comparative set, where a comparative set is understood to be comprised of a positive, comparative, and superlative, represented as {X, more X than, most X}. In all instances where arguments appearing to be of this form are invalid, it is the case that the argument has fallaciously taken terms from more than one comparative set. The fallacy of appealing to more than one comparative set in an inference involving comparative terms is shown to be analogous to the fallacy of equivocation in argumentation. The paper concludes by suggesting a conflation of logical issues with grammatical issues is the core difficulty leading some to consider inferences in the form of A is more X than B; therefore A and B are X to be invalid.     

Bridging the gap: Causality-at-a-distance in children's categorization and inferences about internal properties

Previous research has shown that preschoolers extend labels and internal properties of objects based on those objects’ causal properties, even when the causal properties conflict with the objects’ perceptual appearance [Nazzi, T., & Gopnik, A. (2000). A shift in children's use of perceptual and causal cues to categorization. Developmental Science, 3, 389–396; Sobel, D. M., Yoachim, C. M., Gopnik, A., Meltzoff, A. N., & Blumenthal, E. J. (2007). The blicket within: Preschoolers’ inferences about insides and causes. Journal of Cognition and Development, 8, 159–182]. These studies, however, only presented causal relations that acted on contact. In two studies, contact causality was replaced by distance causality. In contrast to the contact causality case, 4- and 5-year-olds extended labels to objects with similar perceptual properties over objects with similar causal properties when those properties acted at a distance. When children were asked to make inferences about object's internal properties, they were more likely to make causal responses, with 5-year-olds doing so to a greater extent than 4-year-olds. In a second study, 4-year-olds registered causal properties that acted at a distance and used them to make inferences when no perceptual conflict was present. These results support a hypothesis that young children develop an understanding of the specific mechanisms that link causal relations.     

Reconceptualizing the Transitive Inference Ability: A Framework for Existing and Future Research

It has often been claimed that to demonstrate transitive inference is to demonstrate a logical ability, and by implication that transitivity as a property is generally a logical entity. Both claims are considered using a theoretically driven analysis together with consideration of relevant existing experimental research and some newly reported findings. This approach suggests an account of transitivity and transitive inferential reasoning that differs not only from the classic Piagetian account, but also from the information processing account so dominant today. We begin by considering one important issue, that the “logical” definitional criterion can only be approached if individuals are required to demonstrate a capacity for transitive inference that is discriminative in nature. This, together with interpretation of findings from existing transitive tasks, leads to the postulate of a three-component psychological system, with the components relying on perceptual, linguistic, and conceptual subprocesses and sensitivity to simple cues. The framework is testable and accommodates important aspects of classic and modern accounts of “transitive development” that until now have been taken to be mutually exclusive. It also readily accommodates both human and nonhuman research, yet neither a formal logical structure nor memory in any general sense need be assigned the primary role.