Logic and belief across the lifespan: the rise and fall of belief inhibition during syllogistic reasoning

Popular reasoning theories postulate that the ability to inhibit inappropriate beliefs lies at the heart of the human reasoning engine. Given that people's inhibitory capacities are known to rise and fall across the lifespan, we predicted that people's deductive reasoning performance would show similar curvilinear age trends. A group of children (12‐year‐olds), young adults (20‐year‐olds), and older adults (65+‐year‐olds) were presented with a classic syllogistic reasoning task and a decision‐making questionnaire. Results indicated that on syllogisms where beliefs and logic conflicted, reasoning performance showed the expected curvilinear age trend: Reasoning performance initially increased from childhood to early adulthood but declined again in later life. On syllogisms where beliefs and logic were consistent and sound reasoning did not require belief inhibition, however, age did not affect performance. Furthermore, across the lifespan we observed that the better people were at resisting intuitive temptations in the decision‐making task, the less they were biased by their beliefs on the conflict syllogisms. As with the effect of age, one's ability to override intuitions in the decision‐making task did not mediate reasoning performance on the no‐conflict syllogisms. Results lend credence to the postulated central role of inhibitory processing in those situations where beliefs and logic conflict.     

Confidence judgments in syllogistic reasoning: the role of consistency and response cardinality

In two experiments, we examined the resolution of confidence judgments in syllogistic reasoning and their heuristic bases. Based on the assumptions of Koriat's Self-Consistency Model of confidence, we expected the confidence judgments to be related to conclusion consensuality, reflecting the role of consistency as a heuristic cue to confidence. In Experiment 1, the participants evaluated 24 syllogisms with conclusions that varied with respect to validity and consensuality. In Experiment 2, the participants produced conclusions to 64 pairs of premises. The correlation between confidence and reasoning accuracy was low. In both experiments confidence was related to the consensuality of the responses. For consensually correct items, correlation between confidence and accuracy was positive; however, for consensually incorrect items it was negative. In Experiment 2, confidence was lower for syllogisms with higher response cardinality, or syllogisms that elicited a greater variety of conclusions.     

Strategies in Syllogistic Reasoning

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies revealed by the participants' use of paper and pencil as aids to reasoning. Experiment 3 used a new technique to externalize thinking. The participants had to refute, if possible, putative conclusions by constructing external models that were examples of the premises but counterexamples of the conclusions. Experiment 4 used the same techniques to examine the participants' strategies as they drew their own conclusions from syllogistic premises. The results of the experiments showed that individuals not trained in logic can construct counterexamples, that they use similar operations to those implemented in the computer model, but that they rely on a much greater variety of interpretations of premises and of search strategies than the computer model does. We re-evaluates current theories of syllogistic reasoning in the light of these results.     

Syllogistic reasoning tasks and working memory: Evidence from sequential presentation of premises

An experiment is reported concerning the role of working memory components in syllogistic reasoning. In this study, the syllogistic premises were presented sequentially and subjects attempted the syllogisms with and without three secondary tasks (articulatory suppression; spatial suppression and verbal random generation). Taking account of possible trade-offs among the dual tasks, it appeared that syllogisms with sequentially presented premises markedly loaded the central executive and the phonological loop components of working memory and also showed an involvement of the visuo-spatial scratchpad. It appears that the “slave” systems of working memory were more heavily loaded when sequential presentation of premises was used than was found previously with simultaneous premise presentation (Gilhooly, Logie, Wetherick & Wynn, 1993).     

Syllogistic reasoning tasks and working memory: Evidence from sequential presentation of premises

An experiment is reported concerning the role of working memory components in syllogistic reasoning. In this study, the syllogistic premises were presented sequentially and subjects attempted the syllogisms with and without three secondary tasks (articulatory suppression; spatial suppression and verbal random generation). Taking account of possible trade-offs among the dual tasks, it appeared that syllogisms with sequentially presented premises markedly loaded the central executive and the phonological loop components of working memory and also showed an involvement of the visuo-spatial scratchpad. It appears that the “slave” systems of working memory were more heavily loaded when sequential presentation of premises was used than was found previously with simultaneous premise presentation (Gilhooly, Logie, Wetherick & Wynn, 1993).     

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.     

Working memory and syllogistic reasoning

The purpose of this study was to examine the relation between working memory span and syllogistic reasoning performance. In addition, performance for the reasoning task was compared to predictions made by mental model theory and the probability heuristics model. According to mental model theory, syllogisms that require the use of more mental models are more difficult. According to the probability heuristics model difficulty is related to the number of probabilistic heuristics that must be applied, or (for invalid syllogisms) inconsistencies between the derived and correct conclusion. The predictions of these theories were examined across two experiments. In general, people with larger working memory capacities reasoned better. Also, the responses made by people with larger capacities were more likely to correspond to the predictions made by both mental model theory and the probability heuristics model. Relations between working memory span and performance were also consistent with both theories.     

Logic feels so good-I like it! Evidence for intuitive detection of logicality in syllogistic reasoning

When people evaluate syllogisms, their judgments of validity are often biased by the believability of the conclusions of the problems. Thus, it has been suggested that syllogistic reasoning performance is based on an interplay between a conscious and effortful evaluation of logicality and an intuitive appreciation of the believability of the conclusions (e.g., Evans, Newstead, Allen, & Pollard, 1994). However, logic effects in syllogistic reasoning emerge even when participants are unlikely to carry out a full logical analysis of the problems (e.g., Shynkaruk & Thompson, 2006). There is also evidence that people can implicitly detect the conflict between their beliefs and the validity of the problems, even if they are unable to consciously produce a logical response (e.g., De Neys, Moyens, & Vansteenwegen, 2010). In 4 experiments we demonstrate that people intuitively detect the logicality of syllogisms, and this effect emerges independently of participants' conscious mindset and their cognitive capacity. This logic effect is also unrelated to the superficial structure of the problems. Additionally, we provide evidence that the logicality of the syllogisms is detected through slight changes in participants' affective states. In fact, subliminal affective priming had an effect on participants' subjective evaluations of the problems. Finally, when participants misattributed their emotional reactions to background music, this significantly reduced the logic effect.     

A transitive-chain theory of syllogistic reasoning

A new theory of syllogistic reasoning, called the transitive-chain theory, is presented. The transitive-chain theory proposes that information about set relations is represented in memory by pairs of informational components. The theory further proposes that information about set relations is integrated by applying a small set of rules to transitive chains of these set relations. The rules that are applied to these chains are specified in detail. The theory is cast in terms of information-processing models for variants of the syllogistic reasoning task, and then mathematical models that quantify each of these information-processing models are presented. In a series of five experiments, the transitive-chain theory provides a good account of the response-choice data for syllogisms with various types of content, quantifiers, and logical relations (categorical and conditional). The results of these experiments offer tentative answers to four issues in the theory of syllogistic reasoning: (a) representation of premise information; (b) combination of premise information; (c) sources of difficulty in syllogistic reasoning; and (d) generality of the processes used in syllogistic reasoning.     

The role of imagination in facilitating deductive reasoning in 2-, 3- and 4-year-olds.

When 4- and 6-year-olds are cued to use their imagination, they can overcome the belief bias effect and demonstrate deductive reasoning ability on syllogisms containing contrary-to-fact material. This study tested whether 2- and 3-year-olds could also reason with incongruent syllogisms when encouraged to use their imagination. Eighty-four 2-, 3- and 4-year-olds were randomly assigned to one of four conditions: no cue, word cue, fantasy planet or imagery. Children were then presented with six syllogistic reasoning problems containing incongruent information. In the imagination conditions, 2- and 3-year-olds performed as competently as 4-year-olds. The findings are discussed in relation to other research which suggests that under certain circumstances 2- and 3-year-olds have the capacity for counterfactual thinking.     

A modality congruency effect in verbal false memory

The involvement of working memory sub-systems in syllogistic reasoning problems was assessed by dual task methods. Effects of skill level and training on working memory involvement in syllogistic reasoning were examined. In Study 1, participants were pre-selected into groups of High and Low skill at syllogistic reasoning on the basis of a pencil-and-paper screening test. Six separate High and Low skill groups completed syllogistic reasoning tasks in control conditions and each group was also tested under one of the following six dual task conditions: articulatory suppression, unattended speech, verbal random generation, spatial random generation, tapping in a simple pattern, unattended pictures. The results indicated that the more skilled participants were generally following a high demand strategy, which loaded the central executive, phonological loop and imagery sub-systems, but that lower skill participants were generally following a less demanding strategy which did not load working memory components so heavily. In two Pilot Studies a training procedure was assessed and validated. In Study 2, participants were selected, on the basis of a screening test, as being unskilled at solving syllogisms but as performing above guessing level. These participants underwent the training regime validated in the Pilot Studies. Following training, separate groups of participants carried out syllogistic tests with and without one of the following four secondary tasks: articulatory suppression, unattended pictures, spatial random generation, and verbal random generation. The pattern of results indicated that training had induced high demand strategies (often logic-equivalent), which loaded the central executive and to a lesser extent the phonological loop.     

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.     

Falsifying mental models: Testing the predictions of theories of syllogistic reasoning

Four experiments are reported that tested the claim, drawn from mental models theory, that reasoners attempt to construct alternative representations of problems that might falsify preliminary conclusions they have drawn. In Experiment 1, participants were asked to indicate which alternative conclusion(s) they had considered in a syllogistic reasoning task. In Experiments 2-4, participants were asked to draw diagrams consistent with the premises, on the assumption that these diagrams would provide insights into the mental representation being used. In none of the experiments was there any evidence that people constructed more models for multiple-model than for single-model syllogisms, nor was there any correlation between number of models constructed and overall accuracy. The results are interpreted as showing that falsification of the kind proposed by mental models theory may not routinely occur in reasoning.     

Belief inhibition in children's reasoning: memory-based evidence

Adult reasoning has been shown as mediated by the inhibition of intuitive beliefs that are in conflict with logic. The current study introduces a classic procedure from the memory field to investigate belief inhibition in 12- to 17-year-old reasoners. A lexical decision task was used to probe the memory accessibility of beliefs that were cued during thinking on syllogistic reasoning problems. Results indicated an impaired memory access for words associated with misleading beliefs that were cued during reasoning if syllogisms had been solved correctly. This finding supports the claim that even for younger reasoners, correct reasoning is mediated by inhibitory processing as soon as intuitive beliefs conflict with logical considerations.     

Effects of belief and logic on syllogistic reasoning: Eye-movement evidence for selective processing models

Studies of syllogistic reasoning have demonstrated a nonlogical tendency for people to endorse more believable conclusions than unbelievable ones. This belief bias effect is more dominant on invalid syllogisms than valid ones, giving rise to a logic by belief interaction. We report an experiment in which participants' eye movements were recorded in order to provide insights into the nature and time course of the reasoning processes associated with manipulations of conclusion validity and believability. Our main dependent measure was people's inspection times for syllogistic premises, and we tested predictions deriving from three contemporary mental-models accounts of the logic by belief interaction. Results supported recent "selective processing" theories of belief bias (e.g., Evans, 2000; Klauer, Musch, & Naumer, 2000), which assume that the believability of a conclusion biases model construction processes, rather than biasing the search for falsifying models (e.g., Oakhill & Johnson-Laird, 1985) or a response stage of reasoning arising from subjective uncertainty (e.g., Quayle & Ball, 2000). We conclude by suggesting that the eye-movement analyses in reasoning research may provide a useful adjunct to other process-tracing techniques such as verbal protocol analysis.     

The effects of presentation and content on syllogistic reasoning by children with and without specific language impairment

This study examines performance at a syllogistic reasoning task for a group of children (age 10 years) with specific language impairment (SLI) along with age- and language-matched controls. The syllogisms were presented either verbally or verbally/pictorially, and contained two types of item: imaginary versus real, both intended not to evoke strong beliefs. Children with SLI performed worse than age-matched controls, and equivalently to language-matched controls. Patterns of performance indicate this may be due to cognitive ability deficits rather than specific language deficits. For all groups, pictorial presentation interfered with reasoning processes. It is suggested that, for syllogisms, this pictorial information contextualises the interpretation of the task, and that in turn either raises working memory load or evokes belief bias. Additionally, these results suggest that caution should be exhibited before using visual aids to help children with SLI in the classroom.     

The effects of externalization on syllogistic reasoning

An experiment is reported that investigated the effects of externalization of mental models in syllogistic reasoning. Although there was no evidence that the requirement to “externalize” mental models of syllogisms improved reasoning, an unexpected recognition test demonstrated that subjects' memory for the meaning of the premises was improved by externalization. In particular, where the correct conclusion had been deduced using the externalization procedure, responses in the recognition test reflected an appreciation of the relations between the end terms of the premises.     

The effects of belief on the spontaneous production of syllogistic conclusions

Two experiments examined the effects of subjects' beliefs on syllogistic inference. The first experiment showed that beliefs biased the spontaneous conclusions that subjects drew for themselves. These effects were more marked for indeterminate premises (which yield no non-trivial valid conclusions) than for determinate premises (which yield valid conclusions). There was also an effect of the nature of the beliefs: conclusions that were false by definition had a bigger effect on deductions than those that were false as a matter of fact. The second experiment replicated the finding for determinate syllogisms, using problems in moods in which the status of the valid conclusion could not be altered by conversion of the premises. Beliefs accordingly appear to affect the process of reasoning rather than the interpretation of premises.     

范畴三段论推理中信念偏差效应的实验研究

本研究利用三段论评价任务,分析了已有信念与三段论逻辑状态间的交互影响,探讨了三段论推理判断中信念偏差的存在与作用机制,同时从信念偏差角度对心理模型理论进行了初步验证。结果发现：1．范畴三段论推理的逻辑判断过程中存在信念偏差效应;2．信念偏差效应以逻辑状态与结论可信性交互作用的方式存在;3当逻辑结果与信念相一致时,信念会促进逻辑反应,反之则妨碍逻辑反应;4．信念偏差效应对逻辑有效、结论不可信的单模型三段论问题影响最大,而对逻辑有效、结论不可信的多模型三段论问题相对影响最小。     

Theories of categorical reasoning and extended syllogisms

The aim of this study was to examine the predictions of three theories of human logical reasoning, (a) mental model theory, (b) formal rules theory (e.g., PSYCOP), and (c) the probability heuristics model, regarding the inferences people make for extended categorical syllogisms. Most research with extended syllogisms has been restricted to the quantifier “All” and to an asymmetrical presentation. This study used three-premise syllogisms with the additional quantifiers that are used for traditional categorical syllogisms as well as additional syllogistic figures. The predictions of the theories were examined using overall accuracy as well as a multinomial tree modelling technique. The results demonstrated that all three theories were able to predict response selections at high levels. However, the modelling analyses showed that the probability heuristics model did the best in both Experiments 1 and 2.