“如果P,那么Q,……?”─—儿童充分条件假言演绎推理能力发展初探

以日常生活事件为内容的三套测验题探查了9－15岁儿童充分条件假言推理能力的发展。研究发现被试有关能力的发展可以区分出三种不同水平；儿童对充分条件假言推理规则的掌握没有固定的难易顺序，这取决于课题任务的性质和主体思维发展水平。研究还探查了发展的个体内部差异和个体之间的差异以及影响差异的各种内外因素。     

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。     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

Reconnecting interpretation to reasoning through individual differences

Computational theories of mind assume that participants interpret information and then reason from those interpretations. Research on interpretation in deductive reasoning has claimed to show that subjects' interpretation of single syllogistic premises in an “immediate inference” task is radically different from their interpretation of pairs of the same premises in syllogistic reasoning tasks (Newstead, 1989, 1995; Roberts, Newstead, & Griggs, 2001). Narrow appeal to particular Gricean implicatures in this work fails to bridge the gap. Grice's theory taken as a broad framework for credulous discourse processing in which participants construct speakers' “intended models” of discourses can reconcile these results, purchasing continuity of interpretation through variety of logical treatments. We present exploratory experimental data on immediate inference and subsequent syllogistic reasoning. Systematic patterns of interpretation driven by two factors (whether the subject's model of the discourse is credulous, and their degree of reliance on information packaging) are shown to transcend particular quantifier inferences and to drive systematic differences in subjects' subsequent syllogistic reasoning. We conclude that most participants do not understand deductive tasks as experimenters intend, and just as there is no single logical model of reasoning, so there is no reason to expect a single “fundamental human reasoning mechanism”.     

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.     

12岁儿童充分条件假言推理能力发展的个体差异研究

以三类不同题目（与生活经验密切联系、与生活经验相悖、与生活经验“脱离”）,探查了12岁普通儿童与数学成绩优异儿童充分条件假言推理能力发展的个体差异。通过对测查成绩的聚类分析,可将被试划分为四种不同的类型,从而显示出同一年龄儿童不同的推理能力发展水平：普通组儿童有关推理能力已有初步发展,但推理过程仍经常受其具体内容的束缚;数学成绩优异组儿童假设思维和演绎推理能力协调发展,“形式”从“内容”的束缚中解放出来,推理思维活动能较好地符合有关逻辑规则。这两组儿童假言推理能力的差异可能跟智能水平有关。     

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.     

Children's Reasoning in Solving Relational Problems of Deduction

This article reports on a study of children's deductive reasoning in solving novel relational problems. Detailed protocols were obtained from 264 children (aged 9- 12 years) who verbalised their thinking as they solved the problems. The study included the development of a three-phase theory based on Johnson-Laird and Byrne's mental models perspective, but with some distinct modifications. These include a focus on the relational complexity entailed in model construction and in premise integration, and the advancement of four reasoning principles that are applied throughout problem solution (in contrast to Johnson-Laird's falsification processes as the hallmark of deductive reasoning). The reported case studies and the results of statistical analyses supported predictions arising from the proposed theory, including the key role of the reasoning principles. The results also showed that problem difficulty is a function of relational complexity, not of the number of models to be constructed, as argued by Johnson-Laird and Byrne.     

Effects of directionality in deductive reasoning: II. Premise integration and conclusion evaluation

Previous research (Oberauer & Wilhelm, 2000) has shown an inherent directionality between the two terms linked in premises of typical deductive reasoning tasks. With three experiments we investigated the effect of inherent directionality on the time to integrate two premises and for the derivation of a conclusion. We varied figure (i.e., order of terms in the premises) and direction of inference (i.e., order of terms in the conclusion) in deduction tasks from various domains (propositional reasoning, syllogisms, spatial, temporal, and linear order reasoning). Effects of figure on premise reading times varied with the directionality of the relations. Effects of direction of inference reflected the same directionality for a subset of relations. We propose that two factors are jointly responsible for a large part of observed directionality effects in premise integration: the inherent directionality of relational statements and a general advantage for a given-new order of terms in the second premise. Difficulty of deriving a conclusion is affected by the directionality or relations if and only if the relation is semantically asymmetric, so that the directionality must be preserved in the integrated mental model.     

Components of syllogistic reasoning

The present research sought to understand the components of syllogistic reasoning used in a syllogistic evaluation task. In this task, subjects must indicate whether a conclusion such as “Some Yale professors are humbugs” is definitely true, or never true of a set of premises such as “Some humbugs study syllogistic reasoning; some Yale professors study syllogistic reasoning”. A modified form of componential analysis (Sternberg 1977, 1978) was used to decompose the syllogistic evaluation task with abstract content into encoding and encoding plus combination subtasks. The response-choice data from these subtasks were used to provide (a) direct tests of a proposed theory of syllogistic reasoning, and in particular, of its assumptions about sources of error in syllogistic reasoning; and (b) direct inferences regarding the representation of relations between the subject and predicate of the premises as encoded and combined. The results supported a proposed transitive-chain model of syllogistic reasoning.     

Visuelle und räumliche Interferenzen beim Schlußfolgern

The present paper provides evidence for a differential involvement of spatial and visual mental resources in propositional and spatial reasoning. Two experiments consider the load on visuospatial working memory during reasoning. Subjects solve propositional and spatial reasoning tasks either alone or in combination with visual tracking. In the first experiment, subjects resource allocation strategy is manipulated. Independently of the allocation of mental resources to the reasoning tasks or the tracking task, tracking is found to interfere much more with spatial than with propositional reasoning. In the second experiment, propositional reasoning after a comprehension training is disrupted by a simultaneous secondary spatial task, but not by the visual tracking task.     

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.     

Neuroscientific insights into the development of analogical reasoning

Analogical reasoning, or the ability to find correspondences between entities based on shared relationships, supports knowledge acquisition. As such, the development of this ability during childhood is thought to promote learning. Here, we sought to better understand the mechanisms by which analogical reasoning about semantic relations improves over childhood and adolescence (e.g. chalk is to chalkboard as pen is to…?). We hypothesized that age‐related differences would manifest as differences in the brain regions associated with one or more of the following cognitive functions: (1) controlled semantic retrieval, or the ability to retrieve task‐relevant semantic associations; (2) response control, or the ability to override the tendency to respond to a salient distractor; and/or (3) relational integration, or the ability to consider jointly two mental relations. In order to test these hypotheses, we analyzed patterns of fMRI activation during performance of a pictorial propositional analogy task across 95 typically developing children between the ages of 6 and 18 years old. Despite large age‐related differences in task performance, particularly over ages 6–10 but through to around age 14, participants across the whole age range recruited a common network of frontal, parietal and temporal regions. However, activation in a brain region that has been implicated in controlled semantic retrieval – left anterior prefrontal cortex (BA 47/45) – was positively correlated with age, and also with performance after controlling for age. This finding indicates that improved performance over middle childhood and early adolescence on this analogical reasoning task is driven largely by improvements in the ability to selectively retrieve task‐relevant semantic relationships.     

Abstraction and Individual Style in Syllogistic and Heterogeneous Reasoning

Syllogistic reasoning can be modelled with mental models. Heterogeneous reasoning brings together propositional and visual information, and in the Hyperproof logic-teaching system, the visual can act as a model for the propositional. Both mental models notation and Hyperproof’s visual representations allow abstractions of a limited kind. Individual differences in reasoning performance have been found in both domains. We suggest that at least some of the differences can be attributed to students’ differing ability to manipulate abstractions.     

Individual differences in strategies for syllogistic reasoning

Current theories of reasoning such as mental models or mental logic assume a universal cognitive mechanism that underlies human reasoning performance. However, there is evidence that this is not the case, for example, the work of Ford (1995), who found that some people adopted predominantly spatial and some verbal strategies in a syllogistic reasoning task. Using written and think-aloud protocols, the present study confirmed the existence of these individual differences. However, in sharp contrast to Ford, the present study found few differences in reasoning performance between the two groups, in terms of accuracy or type of conclusion generated. Hence, reasoners present an outward appearance of ubiquity, despite underlying differences in reasoning processes. These findings have implications for theoretical accounts of reasoning, and for attempts to model reasoning data. Any comprehensive account needs to account for strategic differences and how these may develop in logically untrained individuals.     

Reasoning with quantifiers

In the semantics of natural language, quantification may have received more attention than any other subject, and one of the main topics in psychological studies on deductive reasoning is syllogistic inference, which is just a restricted form of reasoning with quantifiers. But thus far the semantical and psychological enterprises have remained disconnected. This paper aims to show how our understanding of syllogistic reasoning may benefit from semantical research on quantification. I present a very simple logic that pivots on the monotonicity properties of quantified statements--properties that are known to be crucial not only to quantification but to a much wider range of semantical phenomena. This logic is shown to account for the experimental evidence available in the literature as well as for the data from a new experiment with cardinal quantifiers ("at least n" and "at most n"), which cannot be explained by any other theory of syllogistic reasoning.     

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.     

Dual systems Competence ←-→ Procedural processing: A relational developmental systems approach to reasoning

Many current psychological models of reasoning minimize the role of deductive processes in human thought. In the present paper, we argue that deduction is an important part of ordinary cognition and we propose that a dual systems Competence ←-→ Procedural processing model conceptualized within relational developmental systems theory offers the most coherent and productive framework for integrating and explaining the sometimes conflicting findings on the development of deductive reasoning across the lifespan. This model invokes a distinction that is quite similar to, though not identical with, the system 2–system 1 dichotomy employed in other dual systems models. In addition, the Competence ←-→ Procedural processing model maintains the more specific distinction between algorithmic and reflective subsystems of system 2. In this account, the algorithmic system is represented as a kind of mental logic while the reflective system is the seat of practical and epistemic self-regulation, including emergent epistemic and metalogical norms. While the proposed systems of mind often appear as split-off component features in other dual systems models, relational developmental systems theory conceives of them as the highly complex and relationally integrated outcome of a self-organizing and self-regulating adaptive developmental process.     

The wording of conclusions in relational reasoning

Literature on relational reasoning mainly focuses on the performance question. It is typically argued that problem difficulty relies on the number of "mental models" compatible with the problem. However, no study has ever investigated the wording of conclusions that participants formulate. In the present work, we analyze the relational terms that people use in drawing conclusions from spatial relation problems (A is to the left of B, B is to the left C, D is in front of A, E is in front C, What is the relation between D and E?). We observed a general preference for expressing conclusions with 'left' rather than conclusions with 'right'. We also found that three factors had an influence on the wording of the conclusions: the linguistic form of premises, the question type and the presentation format. On the other hand, the number of models and premise order did not affect the wording of conclusions. Our study shows that the type of conclusion produced provides a new key to identifying the mental processes involved in spatial reasoning. Implications for the two main approaches to reasoning processes (i.e. the analogical and the propositional approaches) are discussed.     

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.