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.     

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.     

Syllogistic reasoning time: Disconfirmation disconfirmed

University of Saskatchewan, Saskatoon, Saskatchewan, Canada Models of deductive reasoning typically assume that reasoners dedicate more logical analysis to unbelievable conclusions than to believable ones (e.g., Evans, Newstead, Allen, & Pollard, 1994; Newstead, Pollard, Evans, & Allen, 1992). When the conclusion is believable, reasoners are assumed to accept it without much further thought, but when it is unbelievable, they are assumed to analyze the conclusion, presumably in an attempt to disconfirm it. This disconfirmation hypothesis leads to two predictions, which were tested in the present experiment: Reasoners should take longer to reason about problems leading to unbelievable conclusions, and reasoners should consider more models or representations of premise information for unbelievable conclusions than for believable ones. Neither prediction was supported by our data. Indeed, we observed that reasoners took significantly longer to reason about believable conclusions than about unbelievable ones and generated the same number of representations regardless of the believability of the premises. We propose a model, based on a modified version of verbal reasoning theory (Polk & Newell, 1995), that does not depend on the disconfirmation assumption.     

Strategy selection in causal reasoning: when beliefs and covariation collide.

The present study investigated how people combine covariation information (Cheng & Novick, 1990, 1992) with pre-existing beliefs (White, 1989) when evaluating causal hypotheses. Three experiments, using both within- and between-subjects designs, found that the use of covariation information and beliefs interacted, such that the effects of covariation were larger when people assessed hypotheses about believable than about unbelievable causal candidates. In Experiment 2, this interaction was observed when participants made judgments in stages (e.g., first evaluating covariation information about a causal candidate and then evaluating the believability of a candidate), as well as when the information was presented simultaneously. Experiment 3 demonstrated that this pattern was also reflected in participants' metacognitive judgments: Participants indicated that they weighed covariation information more heavily for believable than unbelievable candidates. Finally, Experiments 1 and 2 demonstrated the presence of individual differences in the use of covariation- and belief-based cues. That is, individuals who tended to base their causality judgments primarily on belief were less likely to make use of covariation information and vice versa. The findings were most consistent with White's (1989) causal power theory, which suggests that covariation information is more likely to be considered relevant to believable than unbelievable causes.     

Believability and syllogistic reasoning

In this paper we investigate the locus of believability effects in syllogistic reasoning. We identify three points in the reasoning process at which such effects could occur: the initial interpretation of premises, the examination of alternative representations of them (in all of which any valid conclusion must be true), and the "filtering" of putative conclusions. The effect of beliefs at the first of these loci is well established. In this paper we report three experiments that examine whether beliefs have an effect at the other two loci. In experiments 1 and 2 subjects drew their own conclusions from syllogisms that suggested believable or unbelievable ones. In the third experiment they evaluated conclusions that were presented to them. The data show that beliefs both affect the examination of alternative models and act as a filter on putative conclusions. We conclude by showing how some types of problem and some problem contents make the existence of alternative models more obvious than others.     

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。     

When fast logic meets slow belief: Evidence for a parallel-processing model of belief bias

Two experiments pitted the default-interventionist account of belief bias against a parallel-processing model. According to the former, belief bias occurs because a fast, belief-based evaluation of the conclusion pre-empts a working-memory demanding logical analysis. In contrast, according to the latter both belief-based and logic-based responding occur in parallel. Participants were given deductive reasoning problems of variable complexity and instructed to decide whether the conclusion was valid on half the trials or to decide whether the conclusion was believable on the other half. When belief and logic conflict, the default-interventionist view predicts that it should take less time to respond on the basis of belief than logic, and that the believability of a conclusion should interfere with judgments of validity, but not the reverse. The parallel-processing view predicts that beliefs should interfere with logic judgments only if the processing required to evaluate the logical structure exceeds that required to evaluate the knowledge necessary to make a belief-based judgment, and vice versa otherwise. Consistent with this latter view, for the simplest reasoning problems (modus ponens), judgments of belief resulted in lower accuracy than judgments of validity, and believability interfered more with judgments of validity than the converse. For problems of moderate complexity (modus tollens and single-model syllogisms), the interference was symmetrical, in that validity interfered with belief judgments to the same degree that believability interfered with validity judgments. For the most complex (three-term multiple-model syllogisms), conclusion believability interfered more with judgments of validity than vice versa, in spite of the significant interference from conclusion validity on judgments of belief.     

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.     

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.     

Individual differences in deductive reasoning

Three studies are reported, which examined individual differences in deductive reasoning as a function of intellectual ability and thinking style. Intellectual ability was a good predictor of logical performance on syllogisms, especially where there was a conflict between logic and believability. However, in the first two experiments there was no link between ability and performance on indicative selection tasks, in sharp contrast to previous research. This correlation did, however, return in the final study. Our data are consistent with the claim that the correlation with logical accuracy on abstract selection tasks is found primarily with participants of relatively high ability. At lower levels, pragmatically cued responses are given but those of slightly higher ability divorce the rule from the scenario and respond consistently (though incorrectly) across problems. Self-report questionnaires were generally poor predictors of performance, but a measure of the ability to generate alternative representations proved an excellent predictor. These results are consistent with a mental models approach to reasoning and also have implications for the debate about human rationality.     

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.     

Using forced choice to test belief bias in syllogistic reasoning

In deductive reasoning, believable conclusions are more likely to be accepted regardless of their validity. Although many theories argue that this belief bias reflects a change in the quality of reasoning, distinguishing qualitative changes from simple response biases can be difficult (Dube, Rotello, & Heit, 2010). We introduced a novel procedure that controls for response bias. In Experiments 1 and 2, the task required judging which of two simultaneously presented syllogisms was valid. Surprisingly, there was no evidence for belief bias with this forced choice procedure. In Experiment 3, the procedure was modified so that only one set of premises was viewable at a time. An effect of beliefs emerged: unbelievable conclusions were judged more accurately, supporting the claim that beliefs affect the quality of reasoning. Experiments 4 and 5 replicated and extended this finding, showing that the effect was mediated by individual differences in cognitive ability and analytic cognitive style. Although the positive findings of Experiments 3–5 are most relevant to the debate about the mechanisms underlying belief bias, the null findings of Experiments 1 and 2 offer insight into how the presentation of an argument influences the manner in which people reason.     

Comparative Versus Noncomparative Advertising: The Moderating Impact of Prepurchase Attribute Verifiability

We employed an attributional framework to test the differences between comparative and noncomparative ads when different attribute types were featured. Our experimental findings suggest that noncomparative ads might be more believable than comparative ads for experience attribute claims; however, for search attribute claims, the 2 might elicit similar levels of believability. We also find some support for the attributional underpinnings of lower believability associated with comparative‐experience claims.     

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.     

Complexity of categorical syllogisms: An integration of two metrics

The complexity of categorical syllogisms was assessed using the relational complexity metric, which is based on the number of entities that are related in a single cognitive representation. This was compared with number of mental models in an experiment in which adult participants solved all 64 syllogisms. Both metrics accounted for similarly large proportions of the variance, showing that complexity depends on the number of categories that are related in a representation of the combined premises, whether represented in multiple mental models, or by a single model. This obviates the difficulty with mental models theory due to equivocal evidence for construction of more than one mental model. The “no valid conclusion” response was used for complex syllogisms that had valid conclusions. The results are interpreted as showing that the relational complexity metric can be applied to syllogistic reasoning, and can be integrated with mental models theory, which together account for a wide range of cognitive performances.     

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.     

On belief bias in syllogistic reasoning

A multinomial model is used to disentangle the respective contributions of reasoning processes and response bias in conclusion-acceptance data that exhibit belief bias. A model-based meta-analysis of 22 studies reveals that such data are structurally too sparse to allow discrimination of different accounts of belief bias. Four experiments are conducted to obtain richer data, allowing deeper tests through the use of the multinomial model. None of the current accounts of belief bias is consistent with the complex pattern of results. A new theory of belief bias is proposed that assumes that most reasoners construct only one mental model representing the premises as well as the conclusion or, in the case of an unbelievable conclusion, its logical negation. New predictions derived from the theory are confirmed in 4 additional studies.     

Inhibitory mechanism of the matching heuristic in syllogistic reasoning

A number of heuristic-based hypotheses have been proposed to explain how people solve syllogisms with automatic processes. In particular, the matching heuristic employs the congruency of the quantifiers in a syllogism — by matching the quantifier of the conclusion with those of the two premises. When the heuristic leads to an invalid conclusion, successful solving of these conflict problems requires the inhibition of automatic heuristic processing. Accordingly, if the automatic processing were based on processing the set of quantifiers, no semantic contents would be inhibited. The mental model theory, however, suggests that people reason using mental models, which always involves semantic processing. Therefore, whatever inhibition occurs in the processing implies the inhibition of the semantic contents.     

Logic, beliefs, and instruction: a test of the default interventionist account of belief bias

According to dual-process accounts of thinking, belief-based responses on reasoning tasks are generated as default but can be intervened upon in favor of logical responding, given sufficient time, effort, or cognitive resource. In this article, we present the results of 5 experiments in which participants were instructed to evaluate the conclusions of logical arguments on the basis of either their logical validity or their believability. Contrary to the predictions arising from these accounts, the logical status of the presented conclusion had a greater impact on judgments concerning its believability than did the believability of the conclusion on judgments about whether it followed logically. This finding was observed when instructional set was presented as a between-participants factor (Experiment 1), when instruction was indicated prior to problem presentation by a cue (Experiment 2), and when the cue appeared simultaneously with conclusion presentation (Experiments 3 and 4). The finding also extended to a range of simple and more complex argument forms (Experiment 5). In these latter experiments, belief-based judgments took significantly longer than those made under logical instructions. We discuss the implications of these findings for default interventionist accounts of belief bias.