Belief in reasoning

Reasoning has three types, deduction, induction, and abduction, of which we perceive deduction to be necessarily true, induction plausibly true, and abduction only hypothetically true. Syllogistic is a theory of deductive reasoning, introducing three figures of inferencing, of which figure-1 is obviously true, figure-3 and figure-2 are increasingly less transparent. We argue that the three figures of syllogistic and the three types of reasoning are related and their truth perceptions can be explained as different degrees of belief. We suggest that the source of this difference can be found in the conversion of a premise required by syllogistic processing. Experimental results illustrating our theory are included.     

基于记忆的注意捕获和注意抑制效应：ERP证据

采用工作记忆与视觉搜索双任务范式, 通过操作匹配试次出现概率来诱发不同水平的认知控制动机, 考察了基于记忆的注意引导过程的时程特点。结果：记忆匹配刺激首先诱发了N2pc成分, 随后诱发了与抑制过程相关的差异正波。并且, 认知控制动机水平越高, N2pc波幅越小、潜伏期越短; 抑制性差异正波波幅越大。结论：基于记忆的注意引导过程包括早期的注意捕获和后期的注意抑制两个阶段; 其效应量和时程受到认知控制动机水平的调节。     

Belief bias and relational reasoning

When people evaluate categorical syllogisms, they tend to reject unbelievable conclusions and accept believable ones irrespective of their validity. Typically, this effect is particularly marked for invalid conclusions that are possible, but do not necessarily follow, given the premises. However, smaller believability effects can also be detected for other types of conclusion. Three experiments are reported here, in which an attempt was made to determine whether belief bias effects can manifest themselves on the relational inference task. Subjects evaluated the validity of conclusions such as William the Conqueror was king after the Pyramids were built (temporal task) or Manchester is north of Bournemouth (spatial task) with respect to their premises. All of the majorfindings for equivalent categorical syllogism tasks were replicated. However, the overall size of the main effect of believability appears to be related to task presentation, a phenomenon not previously identified for categorical syllogisms and which current theories of belief bias have difficulty explaining.     

Belief revision and uncertain reasoning

When a new piece of information contradicts a currently held belief, one has to modify the set of beliefs in order to restore its consistency. In the case where it is necessary to give up a belief, some of them are less likely to be abandoned than others. The concept of epistemic entrenchment is used by some AI approaches to explain this fact based on formal properties of the belief set (e.g., transitivity). Two experiments were designed to test the hypothesis that contrary to such views, (i) belief is naturally represented by degrees rather than in an all-or-nothing manner, (ii) entrenchment is primarily a matter of content and not only a matter of form, and (iii) consequently prior degree of belief is a powerful factor of change. The two experiments used Elio and Pelletier's (1997) paradigm in which participants were presented with full simple deductive arguments whose conclusion was denied, following which they were asked to decide which premise to revise.     

Syllogistic reasoning and belief-bias inhibition in school children: evidence from a negative priming paradigm

Research on deductive reasoning in adolescents and adults has shown that errors in deductive logic are not necessarily due to a lack of logical ability but can stem from an executive failure to inhibit biases. Few studies have examined this dissociation in children. Here, we used a negative priming paradigm with 64 children (8-10 years old) to test the role of cognitive inhibition in syllogisms with belief-bias effects. On trials where negative priming was predicted, results were as follows: For the first syllogism (A), the strategy 'unbelievable-equals-invalid' had to be inhibited. The logic of the syllogism led to affirming a conclusion inconsistent with one's knowledge of the world, such as 'All elephants are light.' For the second syllogism (B), one's real-world knowledge and the syllogism's logic were congruent but the latter required affirming exactly what had been inhibited for A (i.e. that elephants are heavy). A negative priming effect on the A-B sequence was reflected in a significant drop in reasoning performance on B. This supports the idea that during cognitive development, inhibitory control is required for success on syllogisms where beliefs and logic interfere.     

Belief bias and figural bias in syllogistic reasoning

Belief bias is the tendency to be influenced by the believability of the conclusion when attempting to solve a syllogistic reasoning problem. Figural bias is the tendency to be influenced by the order in which the information is presented in the premises when attempting to solve a syllogistic reasoning problem. When studied simultaneously they enable an investigation of whether participants' reasoning on the syllogistic reasoning task is guided by the conclusion (backward reasoning) or the premises (forward reasoning). Experiments 1 and 2 found evidence of belief bias but not figural bias on the syllogistic evaluation task paradigm. Experiments 3 and 4 found evidence of figural bias but not belief bias on the syllogistic production task paradigm. The findings highlight that different task characteristics influence performance dependent upon the nature of task presentation. These findings are discussed in the context of current theories of belief bias in syllogistic reasoning.     

Chilean children's essentialist reasoning about poverty

Two studies are reported that examine the hypothesis that children construct representations of poverty based on a theory of causal essentialism. One hundred and twenty Chilean kindergartners, half from low socio‐economic status (SES) schools and the other half from high‐SES schools, participated in the study. The results showed children's tendency towards an essentialist reasoning about poverty. All children in the study privileged internal features over external ones when deciding who is poor, and also used wealth category as a preferred clue to make inferences about people's attributes. However, only high‐SES children's answers were consistent with the belief that poverty is inherited and resistant to growth. Implications of these findings for theory and practice, as well as remaining questions, are addressed.     

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.     

Variability in children's level of reasoning about friendship

Maturity and variability in level of friendship reasoning were evaluated in 4th-7th grade children. Peer reputation in the classroom was also assessed. Results indicated greater intraindividual variability in friendship reasoning than previous reports have suggested. In addition, friendship reasoning maturity made significant contributions in accounting for variance in Positive and Isolated peer reputation even after sex, socio-economic status (SES), and IQ were taken into account, while reasoning variability was the only variable accounting for significant variance in Disruptive peer reputation. Implications for social cognition research and intervention are discussed.     

The importance of gesture in children's spatial reasoning

On average, men outperform women on mental rotation tasks. Even boys as young as 4 1/2 perform better than girls on simplified spatial transformation tasks. The goal of our study was to explore ways of improving 5-year-olds' performance on a spatial transformation task and to examine the strategies children use to solve this task. We found that boys performed better than girls before training and that both boys and girls improved with training, whether they were given explicit instruction or just practice. Regardless of training condition, the more children gestured about moving the pieces when asked to explain how they solved the spatial transformation task, the better they performed on the task, with boys gesturing about movement significantly more (and performing better) than girls. Gesture thus provides useful information about children's spatial strategies, raising the possibility that gesture training may be particularly effective in improving children's mental rotation skills.     

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.     

Causal relations and feature similarity in children's inductive reasoning

Four experiments examined the development of property induction on the basis of causal relations. In the first 2 studies, 5-year-olds, 8-year-olds, and adults were presented with triads in which a target instance was equally similar to 2 inductive bases but shared a causal antecedent feature with 1 of them. All 3 age groups used causal relations as a basis for property induction, although the proportion of causal inferences increased with age. Subsequent experiments pitted causal relations against featural similarity in induction. It was found that adults and 8-year-olds, but not 5-year-olds, preferred shared causal relations over strong featural similarity as a basis for induction. The implications for models of inductive reasoning and development are discussed.     

The law of large numbers in children's diversity-based reasoning

Adults increase the certainty of their inductive inferences by observing more diverse instances. However, most young children fail to do so. The present study tested the hypothesis that children's sensitivity to instance diversity is determined by three variables: ability to discriminate among instances (Discrimination); an intuition that large numbers of instances increase the strength of conclusion (Monotonicity); ability to detect subcategories and evaluate numerical differences between the subcategories, or Extraction. A total of 219 Chinese children aged 6 to 11 were tested for sensitivity to diversity by means of Discrimination, Monotonicity, and Extraction. The results indicated that children at all ages were able to discriminate instances and attend to set size. However, only 9- and 11-year-olds demonstrated Extraction and sensitivity to diversity. Furthermore, among all children diversity scores increased linearly with the level of Extraction. These results suggest that the law of large numbers plays a role in children's diversity-based reasoning.     

The role of relational reasoning in children's addition concepts

The study addresses the relational reasoning of different‐aged children and how addition reasoning is related to problem‐solving skills within addition and to reasoning skills outside addition. Ninety‐two 5‐ to 8‐year‐olds were asked to solve a series of conceptually related and unrelated addition problems, and the speed and accuracy of all self‐reported strategies were used to monitor their addition performance. Children were also given a series of general relational reasoning tasks to assess their ability to solve problems based on thematic, causal and visual relations. The results revealed that, while children were able to reason about commutativity relations, recognition of relations based on additive composition was rare. Furthermore, children's ability to reason about addition concepts increased with age and problem‐solving proficiency. Reasoning about addition concepts was related to performance on the thematic, causal and visual reasoning tasks for older children but not for younger children. Overall, the findings suggest that while children's early knowledge of addition relations is domain specific, as children develop in their broader reasoning abilities these developments enhance their addition reasoning.     

Understanding children's and adults' limitations in mental state reasoning

Young children exhibit several deficits in reasoning about their own and other people's mental states. We propose that these deficits, along with more subtle limitations in adults' social-cognitive reasoning, are all manifestations of the same cognitive bias. This is the 'curse of knowledge' - a tendency to be biased by one's own knowledge when attempting to appreciate a more na?ve or uninformed perspective. We suggest the developmental differences in mental state reasoning exist because the strength of this bias diminishes with age, not because of a conceptual change in how young children understand mental states. By pointing out the common denominator in children's and adults' limitations in mental state reasoning we hope to provide a unified framework for understanding the nature and development of social cognition.     

Epistemic trust: modeling children's reasoning about others' knowledge and intent

A core assumption of many theories of development is that children can learn indirectly from other people. However, indirect experience (or testimony) is not constrained to provide veridical information. As a result, if children are to capitalize on this source of knowledge, they must be able to infer who is trustworthy and who is not. How might a learner make such inferences while at the same time learning about the world? What biases, if any, might children bring to this problem? We address these questions with a computational model of epistemic trust in which learners reason about the helpfulness and knowledgeability of an informant. We show that the model captures the competencies shown by young children in four areas: (1) using informants’ accuracy to infer how much to trust them; (2) using informants’ recent accuracy to overcome effects of familiarity; (3) inferring trust based on consensus among informants; and (4) using information about mal‐intent to decide not to trust. The model also explains developmental changes in performance between 3 and 4 years of age as a result of changing default assumptions about the helpfulness of other people.     

Belief bias is stronger when reasoning is more difficult

Three studies examine the influence of varying the difficulty of reasoning on the extent of belief bias, while minimising the possibility that the manipulation would influence the way participants approach the task. Specifically, reasoning difficulty was manipulated by making variations in problem content, while maintaining all other aspects of the problems constant. In Study 1, 191 participants were presented with consistent and conflict problems varying in two levels of difficulty. The results showed a significant influence of problem difficulty on the extent of the belief bias, such that the effect of belief was more pronounced for difficult problems. This effect was stronger in Study 2 (73 participants) where the difference in the difficulty of the problems was purposely accentuated. The results of both studies stress the importance of controlling for problem difficulty when studying belief bias. Study 3 examined one consequence of this, i.e., the classic belief vs. logic interaction could be eliminated by manipulating problem difficulty. Theoretical implications for dual-process accounts of belief bias are also discussed.     

Belief bias during reasoning among religious believers and skeptics

We provide evidence that religious skeptics, as compared to believers, are both more reflective and effective in logical reasoning tasks. While recent studies have reported a negative association between an analytic cognitive style and religiosity, they focused exclusively on accuracy, making it difficult to specify potential underlying cognitive mechanisms. The present study extends the previous research by assessing both performance and response times on quintessential logical reasoning problems (syllogisms). Those reporting more religious skepticism made fewer reasoning errors than did believers. This finding remained significant after controlling for general cognitive ability, time spent on the problems, and various demographic variables. Crucial for the purpose of exploring underlying mechanisms, response times indicated that skeptics also spent more time reasoning than did believers. This novel finding suggests a possible role of response slowing during analytic problem solving as a component of cognitive style that promotes overriding intuitive first impressions. Implications for using additional processing measures, such as response time, to investigate individual differences in cognitive style are discussed.     

Feedback influences children's reasoning about math equivalence: A meta-analytic review

ABSTRACT

Decades of research have focused on children's reasoning about math equivalence problems for both practical and theoretical insights. Not only are math equivalence problems foundational in arithmetic and algebra, they also represent a class of problems on which children's thinking is resistant to change. Feedback is one instructional tool that can serve as a key trigger of cognitive change. In this paper, we review all experimental studies (N = 8) on the effects of feedback on children's (ages 6–11) understanding of math equivalence. Meta-analytic results indicate that feedback has positive effects for low-knowledge learners and negative effects for high-knowledge learners, and these effects are stronger for procedural outcomes than conceptual outcomes. Findings highlight the variable influences of feedback on math equivalence understanding and suggest that models of thinking and reasoning need to consider learner characteristics, learning outcomes, and learning materials, as well as the dynamic interactions among them.