逻辑－信念冲突与推理难度对逻辑和信念判断的影响

双加工理论框架下的平行竞争模型和默认干涉模型对推理过程中启发式和分析式加工的启动次序和相互作用的性质提出了不同假设。本研究通过考察被试在信念判断和逻辑判断两种指导语下解决不同难度和不同类型推理问题的正确率和反应时,对两个模型的预测进行了检验。实验结果表明,解决简单问题时,问题类型对信念判断有显著影响,对逻辑判断无显著影响;解决复杂问题时,问题类型对逻辑判断的影响显著大于对信念判断的影响。实验结果支持平行竞争模型的假设,即两类加工在推理过程中同时启动,共同竞争最终的推理反应。     

逻辑训练对不同理性思维方式大学生三段论推理的影响

采用理性—经验思维方式量表对105名大学生进行测量,选出高、低理性思维方式各35名大学生进行实验,探讨了逻辑训练对不同理性思维方式大学生三段论推理的影响。结果表明：(1)高理性思维方式个体三段论推理的平均反应时快于低理性思维方式个体;非冲突类型题目推理的平均正确率高于冲突类型题目;逻辑训练可以提高个体三段论推理的平均反应时和正确率;(2)逻辑训练后非冲突任务类型题目的平均正确率高于冲突任务类型题目;(3)逻辑训练对低理性思维方式个体冲突任务类型题目平均正确率的提高效果更明显。这意味着逻辑训练可以显著提升个体的推理成绩,但不能完全消除信念偏差对推理的影响,而且逻辑训练对低理性思维方式个体推理成绩的提升效果更加明显。     

Belief-based and analytic processing in transitive inference depends on premise integration difficulty

Three experiments investigated belief-based versus analytic processing in transitive inference. Belief-based and analytic processing were inferred from conclusion acceptance rates for problems with conclusions that were either valid or invalid and believable or unbelievable. Premise integration difficulty was manipulated by varying premise integration time (Experiment 1), premise presentation order (Experiment 2), and the markedness of the relational terms in the premises (Experiment 3). In all the conditions, reasoning accuracy and rated confidence were lower on conflict problems, where belief-based and analytic processes yielded different responses. Participants relied more on analytic processing and less on belief-based processing in conditions in which premise integration was easier. Fluid intelligence and premise integration ability predicted analytical reasoning on conflict problems after reasoning on the no-conflict problems was controlled for. The findings were related to three dual-process models of belief bias. They provide the first evidence of belief bias in transitive inference.     

Working memory, metacognitive uncertainty, and belief bias in syllogistic reasoning

Studies of syllogistic reasoning have shown that the size of the belief bias effect varies with manipulations of logical validity and problem form. This paper presents a mental models-based account, which explains these findings in terms of variations in the working-memory demands of different problem types. We propose that belief bias may reflect the use of a heuristic that is applied when a threshold of uncertainty in one's processing-attributable to working-memory overload-is exceeded during reasoning. Three experiments are reported, which tested predictions deriving from this account. In Experiment 1, conclusions of neutral believability were presented for evaluation, and a predicted dissociation was observed in confidence ratings for responses to valid and invalid arguments, with participants being more confident in the former. In Experiment 2, an attempt to manipulate working-memory loads indirectly by varying syllogistic figure failed to produce predicted effects upon the size of the belief bias effect. It is argued that the employment of a conclusion evaluation methodology minimized the effect of the figural manipulation in this experiment. In Experiment 3, participants' articulatory and spatial recall capacities were calibrated as a direct test of working-memory involvement in belief bias. Predicted differences in the pattern of belief bias observed between highand lowspatial recall groups supported the view that limited working memory plays a key role in belief bias.     

The Influence of Activation Level on Belief Bias in Relational Reasoning

A novel explanation of belief bias in relational reasoning is presented based on the role of working memory and retrieval in deductive reasoning, and the influence of prior knowledge on this process. It is proposed that belief bias is caused by the believability of a conclusion in working memory which influences its activation level, determining its likelihood of retrieval and therefore its effect on the reasoning process. This theory explores two main influences of belief on the activation levels of these conclusions. First, believable conclusions have higher activation levels and so are more likely to be recalled during the evaluation of reasoning problems than unbelievable conclusions, and therefore, they have a greater influence on the reasoning process. Secondly, prior beliefs about the conclusion have a base level of activation and may be retrieved when logically irrelevant, influencing the evaluation of the problem. The theory of activation and memory is derived from the Atomic Components of Thought‐Rational (ACT‐R) cognitive architecture and so this account is formalized in an ACT‐R cognitive model. Two experiments were conducted to test predictions of this model. Experiment 1 tested strength of belief and Experiment 2 tested the impact of a concurrent working memory load. Both of these manipulations increased the main effect of belief overall and in particular raised belief‐based responding in indeterminately invalid problems. These effects support the idea that the activation level of conclusions formed during reasoning influences belief bias. This theory adds to current explanations of belief bias by providing a detailed specification of the role of working memory and how it is influenced by prior knowledge.     

Cognitive control in belief‐laden reasoning during conclusion processing: An ERP study

Belief bias is the tendency to accept conclusions that are compatible with existing beliefs more frequently than those that contradict beliefs. It is one of the most replicated behavioral findings in the reasoning literature. Recently, neuroimaging studies using functional magnetic resonance imaging (fMRI) and event‐related potentials (ERPs) have provided a new perspective and have demonstrated neural correlates of belief bias that have been viewed as supportive of dual‐process theories of belief bias. However, fMRI studies have tended to focus on conclusion processing, while ERPs studies have been concerned with the processing of premises. In the present research, the electrophysiological correlates of cognitive control were studied among 12 subjects using high‐density ERPs. The analysis was focused on the conclusion presentation phase and was limited to normatively sanctioned responses to valid–believable and valid–unbelievable problems. Results showed that when participants gave normatively sanctioned responses to problems where belief and logic conflicted, a more positive ERP deflection was elicited than for normatively sanctioned responses to nonconflict problems. This was observed from ?400 to ?200 ms prior to the correct response being given. The positive component is argued to be analogous to the late positive component (LPC) involved in cognitive control processes. This is consistent with the inhibition of empirically anomalous information when conclusions are unbelievable. These data are important in elucidating the neural correlates of belief bias by providing evidence for electrophysiological correlates of conflict resolution during conclusion processing. Moreover, they are supportive of dual‐process theories of belief bias that propose conflict detection and resolution processes as central to the explanation of belief bias.     

Individual differences in working memory capacity and resistance to belief bias in syllogistic reasoning

In two experiments, we investigated the possibility that individual differences in working memory capacity (WMC) would provide resistance to belief bias in syllogistic reasoning. In Experiment 1 (N?=?157), participants showed a belief bias effect in that they had longer response times and decreased accuracy on syllogisms with conflict between the validity and believability of the conclusion than on syllogisms with no such conflict. However, this effect did not differ as a function of individual differences in WMC. Experiment 2 (N?=?122) replicated this effect with the addition of decontextualized (i.e., nonsense) syllogisms as a different means of measuring the magnitude of the belief bias effect. Although individual differences in WMC and fluid intelligence were related to better reasoning overall, the magnitude of the belief bias effect was not smaller for participants with greater WMC. The present study offers two novel findings: (a) The belief bias effect is independent of individual differences in WMC and fluid intelligence, and (b) resolving conflict in verbal reasoning is not a type of conflict resolution that correlates with individual differences in WMC, further establishing boundary conditions for the role of WMC in human cognitive processes.     

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.     

Rapid responding increases belief bias: Evidence for the dual-process theory of reasoning

In this study, we examine the belief bias effect in syllogistic reasoning under both standard presentation and in a condition where participants are required to respond within 10 seconds. As predicted, the requirement for rapid responding increased the amount of belief bias observed on the task and reduced the number of logically correct decisions, both effects being substantial and statistically significant. These findings were predicted by the dual-process account of reasoning, which posits that fast heuristic processes, responsible for belief bias, compete with slower analytic processes that can lead to correct logical decisions. Requiring rapid responding thus differentially inhibits the operation of analytic reasoning processes, leading to the results observed.     

Predicting belief in paranormal phenomena: a comparison of conditional and probabilistic reasoning

Previous studies, using student participants, have investigated conditional reasoning (Wierzbicki, 1985) and probabilistic reasoning (Blackmore and Troscianko, 1985) separately as predictors of belief in paranormal phenomena. Findings show that the fewer reasoning errors made, the less likely people are to believe. The current study investigated both types of reasoning within the same analysis in order to find the extent to which each would predict paranormal belief by itself. Sixty‐five non‐undergraduate participants completed two self‐report questionnaires to ascertain their degree of belief in the paranormal, and a reasoning test. The expected negative correlation between reasoning ability and paranormal belief was found. However, while conditional reasoning scores predicted paranormal belief (r=−0.27), probabilistic reasoning scores did not (r=0.01). It was noted that the sample used was possibly biased, due to a lack of sufficiently sceptical participants, and that future studies may need to target people with different degrees of belief. Copyright © 1999 John Wiley & Sons, Ltd.     

Negative valence can evoke a liberal response bias in syllogistic reasoning

Recently, studies have demonstrated that negative valence reduces the magnitude of the belief-bias effect in syllogistic reasoning. This effect has been localized in the reasoning stage, in the form of increased deliberation on trials where validity and conclusion believability are incongruent. Here, using signal detection theory, we show that the attenuation of belief bias observed when valence was negative can also be evoked by a liberal response bias at the decision stage. Indeed, when valence was negative participants adopted a more liberal criterion for judging syllogisms as “valid,” and were overconfident in their judgments. They also displayed less sensitivity in distinguishing between valid and invalid syllogisms. Our findings dovetail with recent evidence from memory research suggesting that negative valence can evoke a liberal response bias without improving performance. Our novel contribution is the demonstration that the attenuating effect of negative valence on belief bias can take multiples routes—by influencing the decision stage as was the case here, the reasoning stage as has been demonstrated elsewhere, and potentially both stages.     

关系推理中信念偏差效应的研究

采用结论评估范式,考察时向和空间关系推理中信念偏差效应的表现形式,以及心理模型理论对关系推理中信念偏差效应的解释力。研究结果表明,关系推理中信念偏差效应的表现形式与三段论有所不同,不论是时间推理还是空间推理中都存在信念主效应,但没有发现信念与逻辑的交互作用;心理模型理论不能对关系推理中信念偏差效应作出合理解释。     

Algebraic reasoning and bat-and-ball problem variants: Solving isomorphic algebra first facilitates problem solving later

The classic bat-and-ball problem is used widely to measure biased and correct reasoning in decision-making. University students overwhelmingly tend to provide the biased answer to this problem. To what extent might reasoners be led to modify their judgement, and, more specifically, is it possible to facilitate problem solution by prompting participants to consider the problem from an algebraic perspective? One hundred ninety-seven participants were recruited to investigate the effect of algebraic cueing as a debiasing strategy on variants of the bat-and-ball problem. Participants who were cued to consider the problem algebraically were significantly more likely to answer correctly relative to control participants. Most of this cueing effect was confined to a condition that required participants to solve isomorphic algebra equations corresponding to the structure of bat-and-ball question types. On a subsequent critical question with differing item and dollar amounts presented without a cue, participants were able to generalize the learned information to significantly reduce overall bias. Math anxiety was also found to be significantly related to bat-and-ball problem accuracy. These results suggest that, under specific conditions, algebraic reasoning is an effective debiasing strategy on bat-and-ball problem variants, and provide the first documented evidence for the influence of math anxiety on Cognitive Reflection Test performance.     

Self‐specific Optimism Bias in Belief Updating Is Associated with High Trait Optimism

People learn more from new information when it leads to favorable future outlooks and thus can maintain optimism despite conflicting evidence. In two studies (N = 20 and 26), we investigated whether this optimism bias in belief updating is self‐specific by modifying a recently introduced learning paradigm. In each trial, participants had to estimate the probability of experiencing a negative future event, were then presented with the population base rate of that event, and were subsequently asked for a second, updated estimation. In half of the 88 trials with varying events, estimations were made for oneself, in the other half for a similar other. We tested whether the updates (differences between the first and second estimates) following undesirable base rate were lower than those following desirable base rates, and whether this difference was greater for self relative to other. In both studies, the overall results support the presence of a self‐specific optimism bias in belief updating. However, taking into account trait optimism (TO) as a moderator variable revealed that this was the case only in participants with high TO, whereas those with low TO showed optimistic belief updating for both self and other. In Study 2, we additionally controlled for possible misclassifications of base rate desirability. Taken together, the optimism bias in belief updating was demonstrated by a selective neglect of unfavorable information. A self‐specific influence of this bias in individuals with high TO may ultimately cause the impression of a more positive future outlook relative to others. Copyright © 2014 John Wiley & Sons, Ltd.     

Does a concurrent memory load interfere with reasoning?

Adult participants were required to solve algebraic problems involving identification of unknown operations while they held a concurrent load in short-term memory. The load was varied in relation to participants’ previously measured spans for the same materials. The algebra problems were at two levels of difficulty, Level 2 or Level 3, as defined by Halford and Wilson (1980). An interaction was found between difficulty of the algebra problem and concurrent memory load, but the point at which interference occurred was at or above span. These results support the contentions of Baddeley and Hitch (1974) and refute those of Evans and Brooks (1981). Several findings from the literature on concurrent memory and reasoning tasks are considered, and it is argued that competition between reasoning and memory occurs only when the memory task entails some form of active processing (such as encoding or rehearsal) that occurs simultaneously with reasoning. Simple storage of a concurrent memory load, or rehearsal that can be alternated with reasoning, does not interfere. It is also suggested that future studies of this problem should take care to adjust memory loads in relation to spans and to analyze the basis of the task difficulty manipulation they employ.     

信息的充分性和情绪性对推理的影响：时间压力的调节作用

主要探讨推理中信息相关因素对分析系统与启发式系统的影响。通过两个实验考察信息的充分性和情绪性对突发事件情境下推理的影响。实验1任务无时间压力,结果发现：信息充分性对推理的影响显著,表现为信息越充分,被试推理的逻辑指数越高,更多使用了分析系统;且信息充分时,接受积极信息的被试的信念指数显著增高。实验2任务有时间压力,结果发现：信息的情绪性对推理的影响显著,表现为接受积极信息的被试推理的逻辑指数显著大于接受消极信息组,更多使用了分析系统。两个实验结果表明,信息的充分性主要通过分析系统对推理产生影响,而信息的情绪性可通过双系统影响推理过程,即积极信息在推理时间充裕时促进启发式系统,但在有时间压力下促进分析系统。     

The predictive validity of belief in future occurrence

Prospection is associated, in varying degrees, with a sense that imagined events will (or will not) happen in the future—referred to as belief in future occurrence. The present research investigated to what extent this belief is justified and predicts the actual occurrence of events in the future. In two studies, participants rated their belief in the future occurrence of events imagined to happen in the coming month (Study 1) or week (Study 2), and the actual occurrence of events was then assessed. Results showed that the odds of event occurrence were about 2 times higher with an increase of 1 unit on the belief scale. Belief was particularly pronounced for temporally close events and was largely determined by the congruence of events with autobiographical knowledge. These results suggest that belief in future occurrence has some truth value and may inform decisions and actions.     

Ideological belief bias with political syllogisms

Abstract

The belief bias in reasoning occurs when individuals are more willing to accept conclusions that are consistent with their beliefs than conclusions that are inconsistent. The present study examined a belief bias in syllogisms containing political content. In two experiments, participants judged whether conclusions were valid, completed political ideology measures, and completed a cognitive reflection test. The conclusions varied in validity and in their political ideology (conservative or liberal). Participants were sensitive to syllogisms’ validity and conservatism. Overall, they showed a liberal bias, accepting more liberal than conservative conclusions. Furthermore, conservative participants accepted more conservative conclusions than liberal conclusions, whereas liberal participants showed the opposite pattern. Cognitive reflection did not magnify this effect as predicted by a motivated system 2 reasoning account of motivated ideological reasoning. These results suggest that people with different ideologies may accept different conclusions from the same evidence.     

Debiasing by instruction: The case of belief bias

Abstract

The study is concerned with the question of whether robust biases in reasoning can be reduced or eliminated by verbal instruction in principles of reasoning. Three experiments are reported in which the effect of instructions upon the belief bias effect in syllogistic reasoning is investigated. Belief bias is most clearly marked by a tendency for subjects to accept invalid conclusions which are a priori believable. Experiment 1 attempted to replicate and extend an experiment reported by Newstead, Pollard, Evans and Allen (1992). In contrast with their experiment, it was found that belief bias was maintained despite the use of augmented instructions which emphasised the principle of logical necessity. Experiment 2 provided an exact replication of the augmented instructions condition of Newstead et al., including the presence of problems with belief-neutral conclusions. Once again, significant effects of conclusion believability were found. A third experiment examined the use of elaborated instructions which lacked specific reference to the notion of logical necessity. The use of these instructions significantly reduced the effects of belief on the reasoning observed.

Taking the current findings together with the experiment of Newstead et al., the overall conclusion is that elaborated instructions can reduce the belief bias effect in syllogistic reasoning, but not eliminate it. This conclusion is discussed with reference to (1) the practical implications for improving thinking and reasoning via verbal instruction and (2) the nature of the belief bias phenomenon.     

Highly reflective reasoners show no signs of belief inhibition

The processes underlying individual differences in reasoning performance are not entirely understood. What do people who do well on reasoning tasks where beliefs and logic conflict do differently from other people? Because abundant evidence shows that even poorer reasoners detect these conflicts, it has been suggested that individual differences in reasoning performance arise from inhibition failures later in the reasoning process. The present paper argues that a minority of highly skilled reasoners may deviate from this general reasoning process from an early stage. Two studies investigated signs of belief inhibition using a lexical access paradigm (Study 1) and a negative priming paradigm (Study 2). Study 1 showed that while other people exhibited signs of belief inhibition following a belief–logic conflict, people with the highest disposition for cognitive reflection did not. In Study 2, this finding was replicated and similar results were also obtained when comparing groups with higher and lower general cognitive ability. Two possible explanations are discussed.