Categorical reasoning from multiple diagrams.

Syllogistic reasoning from categorical premise pairs is generally taken to be a multistep process. Quantifiers (all, no, some, some ... not) must be interpreted, representations constructed, and conclusions identified from these. Explanations of performance have been proposed in which errors may occur at any of these stages. The current paper contrasts (a) representation explanations of performance, in which errors occur because not all possible representations are constructed, and/or mistakes are made when doing so (e.g., mental models theory), and (b) conclusion identification explanations, in which errors occur even when information has been correctly and exhaustively represented, due to systematic difficulties that people may have when identifying particular conclusions, or in identifying conclusions in particular circumstances. Three experiments are reported, in which people identified valid conclusions from diagrams analogous to Euler circles, so that the first two stages of reasoning from premise pairs were effectively removed. Despite this, several phenomena associated with reasoning from premise pairs persisted, and it is suggested that whereas representation explanations may account for some of these phenomena, conclusion identification explanations, which have never previously been considered, are required for others.     

Leaping to Conclusions: Why Premise Relevance Affects Argument Strength

Everyday reasoning requires more evidence than raw data alone can provide. We explore the idea that people can go beyond this data by reasoning about how the data was sampled. This idea is investigated through an examination of premise non‐monotonicity, in which adding premises to a category‐based argument weakens rather than strengthens it. Relevance theories explain this phenomenon in terms of people's sensitivity to the relationships among premise items. We show that a Bayesian model of category‐based induction taking premise sampling assumptions and category similarity into account complements such theories and yields two important predictions: First, that sensitivity to premise relationships can be violated by inducing a weak sampling assumption; and second, that premise monotonicity should be restored as a result. We test these predictions with an experiment that manipulates people's assumptions in this regard, showing that people draw qualitatively different conclusions in each case.     

Illusions in modal reasoning

According to the mental model theory, models represent what is true, but not what is false. One unexpected consequence is that certain inferences should have compelling, but invalid, conclusions. Three experiments corroborated the occurrence of such illusions in reasoning about possibilities. When problems had the heading "Only one of the premises is true," the participants considered the truth of each premise in turn, but neglected the fact that when one premise is true, the others are false. When two-premise problems had the heading "One of the premises is true and one is false," the participants still neglected the falsity of one of the premises. As predicted, however, the illusions were reduced when reasoners were told to check their conclusions against the constraint that only one of the premises was true. We discuss alternative explanations for illusory inferences and their implications for current theories of reasoning.     

概称句推理与排序

概称句推理可分为主要通过演绎方式的和主要通过归纳方式的。对于演绎方式进行的推理又可根据研究关注点的不同分为结论是事实句的推理和结论是概称旬的推理。由于概称句的作用,这三种类型的推理都是非单调推理。通过分别的考察,本文指出,这三种类型的概称句推理要想真正得以刻画,都需要引入前提集的排序的概念。进而,排序将是融合这三种类型推理的纽带。     

Children's syllogistic reasoning

Most theories of the development of deductive ability propose that children acquire formal rules of inference. An alternative theory assumes that reasoning consists of constructing a mental model of the situation described in the premises, scanning the model for an informative conclusion, and then searching for alternative models that refute this conclusion. Hence, performance should reflect two principal factors: the difficulty of constructing a model, which depends on the “figure” of the premises, and the number of models that have to be evaluated to respond correctly. In Experiment 1, two groups of children (9- to 10- and 11- to 12-year-olds) drew conclusions from 20 pairs of syllogistic premises. The results confirmed that children are affected both by figure and by number of models. Experiment 2 corroborated these findings for all 64 possible forms of syllogistic premises. The development of reasoning ability may therefore depend on the acquisition, not of formal rules of logic, but of procedures for manipulating models.     

Reasoning from uncertain premises: Effects of expertise and conversational context

Four experiments investigated uncertainty about a premise in a deductive argument as a function of the expertise of the speaker and of the conversational context. The procedure mimicked everyday reasoning in that participants were not told that the premises were to be treated as certain. The results showed that the perceived likelihood of a conclusion was greater when the major or the minor premise was uttered by an expert rather than a novice (Experiment 1). The results also showed that uncertainty about the conclusion was higher when the major premise was uttered by a novice and an alternative premise by an expert, compared to when the major premise was uttered by an expert and the alternative by a novice (Experiment 2). Similarly, the believability of a conclusion was considerably lower when the minor premise was uttered by a novice and denied by an expert, as opposed to when an expert uttered the minor premise and a novice denied it (Experiment 3). Experiment 4 showed that the nature of the uncertainty induced by a denial of the minor premise depended on whether or not the context was a conversation. These results pose difficult problems for current theories of reasoning, as current theories are based on the results of experiments in which the premises are treated as certain. Our discussion of the results emphasises the importance of pragmatics in reasoning, namely, the role of general knowledge about the world in assessing the probability of a premise uttered by an expert or a novice and the role of interpretations of the premise based on pragmatic inferences in revising these initial probabilities.     

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.     

Cognitive and AI models of reasoning

Although relatively few in number, cognitive neuroscience studies of reasoning have two general implications for cognitive theories of deduction. First, an important distinction among these theories is whether they focus on the effect of personally relevant content on the processes and representations underlying deductive reasoning. Evidence is reviewed indicating that there is a neuroanatomical basis for both content-independent and content-dependent theories of deduction. Clinical and neuroimaging studies appear to show that content-independent reasoning is mediated by the left hemisphere, whereas content-dependent reasoning is mediated by regions in the right hemisphere and the bilateral ventromedial frontal cortex. In normal subjects, reasoning is likely to be based on contributions from both hemispheres. Second, clinical evidence indicates that the visuospatial processes used in deductive reasoning are mediated by the posterior areas of the left hemisphere, and that verbal and visuospatial reasoning representations overlap at the neuroanatomical level. This finding weighs against the claims of mental-model theory that deduction involves a significant nonverbal component. Further investigation, particularly with contemporary neuroimaging methods, is needed to test these preliminary conclusions.     

条件推理中否定前件下信念偏差发生阶段的ERP研究

以日常生活中的条件推理语句为实验材料,采用大、小前提和结论依次呈现的“推断-判断”范式,利用事件相关电位(event-related brain potential, ERP)技术探讨了条件推理中否定前件下信念偏差效应的脑内时程动态变化。结果发现：在行为反应上,较信念促进,信念阻碍下的正确率更低反应时更长;在脑电上,两条件(信念阻碍和信念促进)诱发的ERP波形仅在大前提加工阶段出现明显的分离。这表明该推理下的信念偏差效应可能早在对大前提的语义表征阶段就已发生。     

Working Memory Constraints on Linear Reasoning with Spatial and Temporal Contents

The present article reports two experiments testing the use of working memory components during reasoning with temporal and spatial relations in four-term series problems. In the first experiment four groups of subjects performed reasoning tasks with temporal and with spatial contents either without (control) or with a secondary task (articulatory suppression, visuospatial suppression or central executive suppression). The second experiment tested the secondary task effects in a within-subjects design either on problems with a spatial content or on problems with a temporal content, and within each content domain either under conditions of self-paced or of fixed presentation of the premises. Both experiments found effects of all three secondary tasks on reasoning accuracy. This supports the hypothesis that the subjects construct spatial representations of the premise information with the support of visuo-spatial resources of working memory. The second experiment also showed that during premise intake, only visuo-spatial and central executive secondary tasks had an effect. The implications of the data for the working memory requirements of reasoning and for theories of linear reasoning are discussed.     

演绎推理是基于规则还是模型?——来自空间推理的证据

对空间推理的研究有助于探明其加工机制以及验证心理逻辑理论和心理模型理论。行为研究通过考察多种影响空间推理的因素(如心理模型数量、前提的对象顺序等)证实了心理模型理论的预测。脑成像的研究表明,空间推理活动主要激活枕-顶-额脑区网络,顶区可能是推理的特异性脑区。研究的结果同样支持心理模型理论。未来的研究应该整合演绎推理的不同理论,加强对不同演绎推理任务的研究,并将脑成像技术与EEG或ERP结合起来,进一步探明人类空间推理的机制。     

Effects of content on inclusive disjunction reasoning

An experiment is reported which establishes that inclusive disjunction arguments embedded in concrete content are not always easier to reason with than those involving abstract content. The subjects had to assess conclusions drawn from pairs of premises such as “Either Joan is intelligent or she is rich (or both); Joan is intelligent” or “Either Joan is intelligent or she is rich (or both); Joan is not intelligent”. The terms in the disjunctive premise were varied systematically across three content dimensions (i.e. compatible, abstract and contradictory). An analysis of variance revealed significant differences according to both principle of inference and type of content, and a significant interaction between these factors. The results demonstrated that semantically incompatible premise content had a marked influence on comprehension of inclusive disjunction reasoning schemes. The response patterns suggest that these reasoning schemes invited erroneous judgments based on other logical connectives.     

Content and strategy in syllogistic reasoning.

Syllogistic reasoning has been investigated as a general deductive process (Johnson-Laird & Byrne, 1991; Revlis, 1975; Rips, 1994). However, several studies have demonstrated the role of cognitive strategies in this type of reasoning. These strategies focus on the method used by the participants (Ford, 1995; Gilhooly, Logie, Wetherick, & Wynn, 1993) and strategies related to different interpretations of the quantified premises (Roberts, Newstead, & Griggs, 2001). In this paper, we propose that content (as well as individual cognitive differences) is an important factor in inducing a certain strategy or method for syllogistic resolution. Specifically, we suggest that syllogisms with a causal conditional premise that can be extended by an agency premise induce the use of a conditional method. To demonstrate this, we carried out two experiments. Experiment 1 provided evidence that this type of syllogism leads participants to draw the predicted conditional conclusions, in contrast with control content syllogisms. In Experiment 2, we demonstrated that the drawing of conditional conclusions is based on a causal conditional to an agent representation of the syllogism premises. These results support the role of content as inducing a particular strategy for syllogistic resolution. The implications of these results are discussed.     

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.     

归纳推理的抽样理论

作者提出归纳推理的抽样理论,认为归纳推理实质是根据与归纳特征有关的抽样样本情况来推断结论类别具有归纳特征的可能性,其中的抽样可分为类别抽样和特征抽样两种。以大学生为被试的两个实验结果一致支持抽样理论而不是别的归纳推理理论。对于归纳推理的主要现象,抽样理论比其它的相似性解释具有更大的解释范围,特别是能够解释其它理论严格不能解释的归纳推理非对称性现象     

归纳推理中相似性和类别标签的作用

该文采用“篇章阅读”实验范式探索了归纳推理中前提类别和结论类别间相似性、结论类别标签属性对归纳推理的作用。90名大学生被试参加了3个实验。实验1结果表明,归纳推理受前提类别和结论类别之间相似性的影响,相似性越高归纳推理力度越强;实验2结果表明,归纳推理还受结论类别上位类别知识的影响,当类别属性和相似性冲突情况下,被试更倾向按照类别属性进行推理;实验3结果表明,归纳推理通达上位类别知识是一个主动建构的过程,即使是在类别标签不确定的情况下,被试仍然依赖类别标签进行推理。并初步提出了“归纳推理力度=两事物相似性×归类概率”模型设想。     

The probability heuristics model of syllogistic reasoning

A probability heuristic model (PHM) for syllogistic reasoning is proposed. An informational ordering over quantified statements suggests simple probability based heuristics for syllogistic reasoning. The most important is the "min-heuristic": choose the type of the least informative premise as the type of the conclusion. The rationality of this heuristic is confirmed by an analysis of the probabilistic validity of syllogistic reasoning which treats logical inference as a limiting case of probabilistic inference. A meta-analysis of past experiments reveals close fits with PHM. PHM also compares favorably with alternative accounts, including mental logics, mental models, and deduction as verbal reasoning. Crucially, PHM extends naturally to generalized quantifiers, such as Most and Few, which have not been characterized logically and are, consequently, beyond the scope of current mental logic and mental model theories. Two experiments confirm the novel predictions of PHM when generalized quantifiers are used in syllogistic arguments. PHM suggests that syllogistic reasoning performance may be determined by simple but rational informational strategies justified by probability theory rather than by logic.     

Reasoning with exclusive disjunction arguments

An experiment was performed to determine the effects of negation in the major premise and/or conclusion of exclusive disjunction arguments on adults' abilities to apply two basic principles of exclusive disjunction. The component of the disjunctive premise that was referred to in the minor premise was varied systematically so that the influence of this factor could also be explored. The results indicated that arguments involving the confirmation of one of the components of the disjunctive premise followed by the denial of the other component of this premise were easier to evaluate than those in which this confirmation/denial sequence was reversed. In addition, arguments in which the disjunctive premise had two affirmative components were easier than those in which the disjunctive premise contained at least one negative component, but arguments with affirmative conclusions were more difficult than those with negative conclusions. Most importantly, an examination of subjects' errors and their response patterns revealed primitive response tendencies that paralleled those reported in previous studies of adults' propositional reasoning abilities.     

Do children have to remember to reason? A fuzzy-trace theory of transitivity development

An idea that has become commonplace in the literature on cognitive development is that the solution of thinking and reasoning problems requires that children retain accurate representations of certain background facts in short-term memory. This reasoning/remembering hypothesis is reexamined with reference to the one childhood cognitive task for which the validity of the hypothesis seems to be firmly established, transitive inference. Although the hypothesis says that children's transitive inferences are critically dependent on memory for the initial premise information, it is shown in six experiments that transitivity and premise memory are independent abilities in children. A fuzzy-trace theory is developed to explain this surprising independence effect. The theory assumes that children retain only degraded, schematic representations (fuzzy traces) of the overall pattern of an ordered series and that performance on subsequent test trials is mediated by processing operations that flesh out vague pattern information. Some further experiments that were designed to test various predictions of the fuzzy-trace theory are reported. Last, it is shown that reasoning and remembering are independent abilities in some other childhood cognitive tasks for which the initial background facts are not logically inescapable components of the eventual solution. These reasoning/remembering independence effects argue for an increased emphasis on encoding selectivity in theories of cognitive development.     

Transitivity for height versus speed: To what extent do the under-7s really have a transitive capacity?

Transitive inference underpins many human reasoning competencies. The dominant task (the “extensive training paradigm”) employs many items and large amounts of training, instilling an ordered series in the reasoner's mind. But findings from an alternative “three-term paradigm” suggest transitivity is not present until 7 + years. Interestingly, a second alternative paradigm (the “spatial task”), using simultaneously displayed height relationships to form premise pairs, can uphold the 4-year estimate. However, this paradigm risks cueing children and hence is problematic. We investigated whether a height-task variant might correspond to a more ecologically valid three-term task. A total of 222 4–6-year-olds either completed a modified height task, including an increased familiarisation phase, or a computer-animated task about cartoon characters running a race in pairs. Findings confirmed that both tasks were functionally identical. Crucially, 4-year-olds were at chance on both, whereas 6-year-olds performed competently. These findings contrast with estimates from all three paradigms considered. A theoretical evaluation of our tasks and procedures against previous ones, leads us to two conclusions. First, our estimate slightly amends the 7-year estimate offered by the three-term paradigm, with the difference explained in terms of its greater relevance to child experiences. Second, our estimate can coexist alongside the 4-year estimate from the extensive training paradigm. This is because, applying a recently developed “dual-process” conception of reasoning, anticipates that extensive training benefits a species-general associative system, while the spatial paradigm and three-term paradigm can potentially index a genuinely deductive system, which has always been the target of transitive research.