Independence and dependence in human causal reasoning

Causal graphical models (CGMs) are a popular formalism used to model human causal reasoning and learning. The key property of CGMs is the causal Markov condition, which stipulates patterns of independence and dependence among causally related variables. Five experiments found that while adult’s causal inferences exhibited aspects of veridical causal reasoning, they also exhibited a small but tenacious tendency to violate the Markov condition. They also failed to exhibit robust discounting in which the presence of one cause as an explanation of an effect makes the presence of another less likely. Instead, subjects often reasoned “associatively,” that is, assumed that the presence of one variable implied the presence of other, causally related variables, even those that were (according to the Markov condition) conditionally independent. This tendency was unaffected by manipulations (e.g., response deadlines) known to influence fast and intuitive reasoning processes, suggesting that an associative response to a causal reasoning question is sometimes the product of careful and deliberate thinking. That about 60% of the erroneous associative inferences were made by about a quarter of the subjects suggests the presence of substantial individual differences in this tendency. There was also evidence that inferences were influenced by subjects’ assumptions about factors that disable causal relations and their use of a conjunctive reasoning strategy. Theories that strive to provide high fidelity accounts of human causal reasoning will need to relax the independence constraints imposed by CGMs.     

The influence of complexity and reasoning direction on children's causal reasoning

Causal reasoning is the core and basis of cognition about the objective world. This experiment studied the development of causal reasoning in 86 3.5–4.5-year-olds using a ramp apparatus with two input holes and two output holes [Frye, D., Zelazo, P. D., & Palfai, T. (1995). Theory of mind and rule-based reasoning. Cognitive Development 10, 483–527]. Results revealed that: (1) children performed better on cause–effect inferences than on effect–cause inferences; (2) there was an effect of rule complexity such that uni-dimensional causal inferences were easier than bi-dimensional inferences which, in turn, were easier than tri-dimensional causal inferences; and (3) children's causal reasoning develops rapidly between the ages of age of 3.5 and 4 years.     

Diversity-Based Reasoning in Children

One of the hallmarks of inductive reasoning by adults is the diversity effect, namely that people draw stronger inferences from a diverse set of evidence than from a more homogenous set of evidence. However, past developmental work has not found consistent diversity effects with children age 9 and younger. We report robust sensitivity to diversity in children as young as 5, using everyday stimuli such as pictures of objects with people. Experiment 1 showed the basic diversity effect in 5- to 9-year-olds. Experiment 2 showed that, like adults, children restrict their use of diversity information when making inferences about remote categories. Experiment 3 used other stimulus sets to overcome an alternate explanation in terms of sample size rather than diversity effects. Finally, Experiment 4 showed that children more readily draw on diversity when reasoning about objects and their relations with people than when reasoning about objects' internal, hidden properties, thus partially explaining the negative findings of previous work. Relations to cross-cultural work and models of induction are discussed.     

推理方向与规则维度对儿童因果推理的影响

采用Frye和Zelazo等（1996）所设计的“二进二出”装置（斜面滚球装置）,设置了不同的推理方向、规则维度的因果推理任务,采用个别实验法,研究了60名3.5～4.5岁儿童因果推理能力的发展。结果发现：（1）儿童在不同方向的因果推理任务上成绩差异显著,因→果推理成绩要好于果→因推理;（2）不同维度下儿童的推理成绩有极显著的差异性,一维的因果推理更容易,三维合取规则的因果推理任务更难;（3）3.5～4岁左右是儿童因果推理能力发展的快速期。     

Reasoning from Suppositions

Two experiments investigated inferences based on suppositions. In Experiment 1, the subjects decided whether suppositions about individuals' veracity were consistent with their assertions—for example, whether the supposition “Ann is telling the truth and Beth is telling a lie”, is consistent with the premises: “Ann asserts: I am telling the truth and Beth is telling the truth. Beth asserts: Ann is telling the truth”. It showed that these inferences are more difficult than ones based on factual premises: “Ann asserts: I live in Dublin and Beth lives in Dublin”. There was no difference between problems about truthtellers and liars, who always told the truth or always lied, and normals, who sometimes told the truth and sometimes lied. In Experiment 2, the subjects made inferences about factual matters set in three contexts: a truth-inducing context in which friends confided their personality characteristics, a lie-inducing context in which business rivals advertised their products, and a neutral context in which computers printed their program characteristics. Given the supposition that the individuals were lying, it was more difficult to make inferences in a truth-inducing context than in the other two contexts. We discuss the implications of our results for everyday reasoning from suppositions, and for theories of reasoning based on models or inference rules.     

Diagnostic causal reasoning with verbal information

In diagnostic causal reasoning, the goal is to infer the probability of causes from one or multiple observed effects. Typically, studies investigating such tasks provide subjects with precise quantitative information regarding the strength of the relations between causes and effects or sample data from which the relevant quantities can be learned. By contrast, we sought to examine people’s inferences when causal information is communicated through qualitative, rather vague verbal expressions (e.g., “X occasionally causes A”). We conducted three experiments using a sequential diagnostic inference task, where multiple pieces of evidence were obtained one after the other. Quantitative predictions of different probabilistic models were derived using the numerical equivalents of the verbal terms, taken from an unrelated study with different subjects. We present a novel Bayesian model that allows for incorporating the temporal weighting of information in sequential diagnostic reasoning, which can be used to model both primacy and recency effects. On the basis of 19,848 judgments from 292 subjects, we found a remarkably close correspondence between the diagnostic inferences made by subjects who received only verbal information and those of a matched control group to whom information was presented numerically. Whether information was conveyed through verbal terms or numerical estimates, diagnostic judgments closely resembled the posterior probabilities entailed by the causes’ prior probabilities and the effects’ likelihoods. We observed interindividual differences regarding the temporal weighting of evidence in sequential diagnostic reasoning. Our work provides pathways for investigating judgment and decision making with verbal information within a computational modeling framework.     

Correlational reasoning in an everyday context

In the context of everyday reasoning, individuals inferring a causal relation between an antecedent (A) and event (E) rarely have available as evidence for their inferences frequencies of all the four possible occurences, AE, A$\text{E}$, $\text{A}$E, and $\text{AE}$. The present study investigated the willingness of subjects in fourth, seventh, and tenth grades, and college to infer such a relation under the more typical condition of incomplete frequency data. There was some improvement with age, but even college subjects were remarkably willing to infer a relationship based on minimal data, notably the presence of cases in the AE cell. No subjects indicated the need for information regarding the remaining cells. Subsequent presentations of datafor the A$\text{E}$ cell did not substantially alter subjects' willingness to infer a relation, nor did subsequent presentation of data for the remaining two cells, despite the fact that complete frequency data indicated independence of A and E. A comparison group of subjects presented with all four cells at once showed somewhat more frequent application of quantitative reasoning strategies, but their willingness to infer a relationship between A and E was not notably less than that of subjects to whom the data were presented sequentially.     

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     

Children's Use of Social Categories in Thinking About People and Social Relationships

A series of studies investigated White U.S. 3- and 4-year-old children's use of gender and race information to reason about their own and others’ relationships and attributes. Three-year-old children used gender- but not race-based similarity between themselves and others to decide with whom they wanted to be friends, as well as to determine which children shared their own preferences for various social activities. Four-year-old (but not younger) children attended to gender and racial category membership to guide inferences about others’ relationships but did not use these categories to reason about others’ shared activity preferences. Taken together, the findings provide evidence for three suggestions about these children's social category-based reasoning. First, gender is a more potent category than race. Second, social categories are initially recruited for first-person reasoning but later become broad enough to support third-person inferences. Finally, at least for third-person reasoning, thinking about social categories is more attuned to social relationships than to shared attributes.     

Spontaneous inferential processing while reading interleaved expository texts enables learners to discover the underlying regularities

Recent studies on text sequencing found learning advantages of interleaving over blocking in terms of high‐level inferences. We conducted a 2 × 2 × 2 mixed factorial experiment with college students (n = 117) by manipulating text sequence (interleaved vs. blocked) and self‐questioning activity while reading (spontaneous vs. prompted) between subjects and testing delay (immediately vs. 1‐week delay) within subjects. Results revealed that students are spontaneously engaged in self‐questioning and inferential processing while reading an interleaved text. Students who were spontaneously engaged while reading an interleaved text outperformed their counterparts in all other conditions in the immediate and delayed test on comparative reasoning, inductive reasoning, and memorization of factual details. The learning advantages were mediated by inductive inferences made while reading an interleaved text. Results support the discriminative contrast view that readers are encouraged to discover the underlying regularities when differences and similarities among categories are accentuated by their juxtaposition.     

The Blicket Within: Preschoolers' Inferences About Insides and Causes

Four experiments examined children's inferences about the relation between objects' internal parts and their causal properties. In Experiment 1, 4-year-olds recognized that objects with different internal parts had different causal properties, and those causal properties transferred if the internal part moved to another object. In Experiment 2, 4-year-olds made inferences from an object's internal parts to its causal properties without being given verbal labels for objects or being shown that insides and causal properties covaried. Experiment 3 found that 4-year-olds chose an object with the same internal part over one with the same external property when asked which object had the same causal property as the target (which had both the internal part and external property). Finally, Experiment 4 demonstrated that 4-year-olds made similar inferences from causal properties to internal parts, but 3-year-olds relied more on objects' external perceptual appearance. These results suggest that by the age of 4, children have developed an understanding of a relation between an artifact's internal parts and its causal properties.     

Facts and Possibilities: A Model‐Based Theory of Sentential Reasoning

This article presents a fundamental advance in the theory of mental models as an explanation of reasoning about facts, possibilities, and probabilities. It postulates that the meanings of compound assertions, such as conditionals (if) and disjunctions (or), unlike those in logic, refer to conjunctions of epistemic possibilities that hold in default of information to the contrary. Various factors such as general knowledge can modulate these interpretations. New information can always override sentential inferences; that is, reasoning in daily life is defeasible (or nonmonotonic). The theory is a dual process one: It distinguishes between intuitive inferences (based on system 1) and deliberative inferences (based on system 2). The article describes a computer implementation of the theory, including its two systems of reasoning, and it shows how the program simulates crucial predictions that evidence corroborates. It concludes with a discussion of how the theory contrasts with those based on logic or on probabilities.     

Inferential reasoning by exclusion in great apes, lesser apes, and spider monkeys

Using the cups task, in which subjects are presented with limited visual or auditory information that can be used to deduce the location of a hidden reward, Call (2004) found prima facie evidence of inferential reasoning by exclusion in several great ape species. One bonobo (Pan paniscus) and two gorillas (Gorilla gorilla) appeared to make such inferences in both the visual and auditory domains. However, common chimpanzees (Pan troglodytes) were successful only in the visual domain, and Bornean orangutans (Pongo pygmaeus) in neither. The present research built on this paradigm, and Experiment 1 yielded prima facie evidence of inference by exclusion in both domains for two common chimpanzees, and in the visual domain for two Sumatran orangutans (Pongo abelii). Experiments 2 and 3 demonstrated that two specific associative learning explanations could not readily account for these results. Because an important focus of the program of research was to assess the cognitive capacities of lesser apes (family Hylobatidae), we modified Call's original procedures to better suit their attentional and dispositional characteristics. In Experiment 1, testing was also attempted with three gibbon genera (Symphalangus, Nomascus, Hylobates), but none of the subjects completed the standard task. Further testing of three siamangs (Symphalangus syndactylus) and a spider monkey (Ateles geoffroyi) using a faster method yielded prima facie evidence of inferential reasoning by exclusion in the visual domain among the siamangs (Experiment 4).     

The role of learning data in causal reasoning about observations and interventions

Recent studies have shown that people have the capacity to derive interventional predictions for previously unseen actions from observational knowledge, a finding that challenges associative theories of causal learning and reasoning (e.g., Meder, Hagmayer, & Waldmann, 2008). Although some researchers have claimed that such inferences are based mainly on qualitative reasoning about the structure of a causal system (e.g., Sloman, 2005), we propose that people use both the causal structure and its parameters for their inferences. We here employ an observational trial-by-trial learning paradigm to test this prediction. In Experiment 1, the causal strength of the links within a given causal model was varied, whereas in Experiment 2, base rate information was manipulated while keeping the structure of the model constant. The results show that learners’ causal judgments were strongly affected by the observed learning data despite being presented with identical hypotheses about causal structure. The findings show furthermore that participants correctly distinguished between observations and hypothetical interventions. However, they did not adequately differentiate between hypothetical and counterfactual interventions.     

Components of syllogistic reasoning

The present research sought to understand the components of syllogistic reasoning used in a syllogistic evaluation task. In this task, subjects must indicate whether a conclusion such as “Some Yale professors are humbugs” is definitely true, or never true of a set of premises such as “Some humbugs study syllogistic reasoning; some Yale professors study syllogistic reasoning”. A modified form of componential analysis (Sternberg 1977, 1978) was used to decompose the syllogistic evaluation task with abstract content into encoding and encoding plus combination subtasks. The response-choice data from these subtasks were used to provide (a) direct tests of a proposed theory of syllogistic reasoning, and in particular, of its assumptions about sources of error in syllogistic reasoning; and (b) direct inferences regarding the representation of relations between the subject and predicate of the premises as encoded and combined. The results supported a proposed transitive-chain model of syllogistic reasoning.     

The capacity to generate alternative ideas is more important than inhibition for logical reasoning in preschool-age children

There is little consensus about the nature of logical reasoning and, equally important, about how it develops. To address this, we looked at the early origins of deductive reasoning in preschool children. We examined the contribution of two factors to the reasoning ability of very young children: inhibitory capacity and the capacity to generate alternative ideas. In a first study, a total of 32 preschool children were all given generation, inhibition, and logical reasoning measures. Logical reasoning was measured using knowledge-based premises such as “All dogs have legs,” and two different inferences: modus ponens and affirmation of the consequent. Results revealed that correctly reasoning with both inferences is not related to the measure of inhibition, but is rather related to the capacity to generate alternative ideas. In a second study, 32 preschool children were given either the generation or the inhibition task before the logical reasoning measure. Results showed that receiving the generation task beforehand significantly improved logical reasoning compared to the inhibition task given beforehand. Overall, these results provide evidence for the greater importance of idea generation in the early development of logical reasoning.     

Betting on transitivity in probabilistic causal chains

Causal reasoning is crucial to people’s decision making in probabilistic environments. It may rely directly on data about covariation between variables (correspondence) or on inferences based on reasonable constraints if larger causal models are constructed based on local relations (coherence). For causal chains an often assumed constraint is transitivity. For probabilistic causal relations, mismatches between such transitive inferences and direct empirical evidence may lead to distortions of empirical evidence. Previous work has shown that people may use the generative local causal relations A → B and B → C to infer a positive indirect relation between events A and C, despite data showing that these events are actually independent (von Sydow et al. in Proceedings of the thirty-first annual conference of the cognitive science society. Cognitive Science Society, Austin, 2009, Proceedings of the 32nd annual conference of the cognitive science society. Cognitive Science Society, Austin, 2010, Mem Cogn 44(3):469–487, 2016). Here we used a sequential learning scenario to investigate how transitive reasoning in intransitive situations with negatively related distal events may relate to betting behavior. In three experiments participants bet as if they were influenced by a transitivity assumption, even when the data strongly contradicted transitivity.     

Beliefs and inferences: a test of a rational-emotive hypothesis: 2. On the prospect of seeing a spider

96 subjects were asked to imagine that they were about to enter a room in which there may have been one or more spiders. They were also asked to imagine that (a) they either held a rational or an irrational belief about spiders, (b) they were about to enter the room either alone or with someone, and (c) that the room was either dark or light. Having absorbed their assigned role, the subjects were then asked to make inferences about various elements of their situation. The results supported the hypothesis that holding an irrational belief leads to more negative inferences. It was also found that the lighting conditions in the room and whether the subject was alone or with someone affected the negativity of the inferences made. In addition, there were several two-way and three-way interactions between the independent variables which indicated that entering a light room or being with someone else tended to moderate the negativity of inferences made by those holding a rational belief rather than the opposite, amplifying the negativity of inferences made by those holding an irrational belief. The results supported Ellis's (1985) recent formulation concerning the complex relationship between events and inferences (A), beliefs (B), and emotional and behavioral consequences of beliefs (C).     

Test-Anxiety,inferential reasoning and working memory load

Abstract

Subjects high and low in test-anxiety were presented with an inferential reasoning task requiring the verification of necessary and unnecessary inferences. The task was performed whilst holding either two or six digits in memory. On the verification task, the performance of high-test-anxious subjects was slower and less accurate than that of the low-test-anxious subjects. In addition, unnecessary inferences took longer to process than necessary inferences for the high-test-anxiety group only. The high-test-anxious subjects studied the memory loads for longer than the low-test-anxious group, but their recognition accuracy did not differ. Findings support Eysenck and Calvo's (Cognition and Emotion, 6, 409–434, 1992) processing efficiency theory. The high-test-anxious group's performance on the sentence verification task was impaired overall, and was particularly impaired when performing the unnecessary inference task. However, we also demonstrated that the high-test-anxious group's performance on a secondary memory task was unimpaired as a result of increased effort.     

Logically Speaking: Evidence for Item-Based Acquisition of the Connectives AND & OR

Error is a pervasive and inescapable aspect of empirical science, and it often plays a causal role in experimental outcomes. But little is known about children's understanding of the causes and consequences of experimental error. In this article, we propose a new framework for characterizing experimental error and we use that framework to guide an empirical assessment of elementary school children's understanding of error, their use of theory and evidence in guiding this understanding, and the role of context in reasoning about error. We found that 2nd- and 4th-grade children could both propose and recognize potential sources of error before they could design unconfounded experiments. They used evidence to guide their reasoning, making predictions and drawing conclusions based on the design of their experiments, and they were sensitive to the context of reasoning: They differentiated the role of error in relative and absolute measurements. Long before children have acquired the formal procedures necessary to control error, they have a surprisingly rich-albeit unsystematic-understanding of its various sources.