4—6岁幼儿空间方位传递性推理能力的发展

该研究旨在探查4、5、6岁幼儿空间上下和前后方位传递性推理能力的发展水平及不同实验条件(一致、模糊、冲突)下儿童的传递性推理能力。为了尽量降低记忆对推理的影响,要求幼儿在前提呈现的条件下按前提方位关系进行传递性推理操作。被试为幼儿园4、5、6岁组儿童各24人,其中男女各半。主要结果表明：4岁幼儿开始萌发空间前后和上下方位的传递性推理能力;从4岁到6岁,“上下”方位传递性推理能力的发展优于“前后”方位;4—6岁幼儿还不能完全摆脱知觉干扰因素的影响,形成稳定的传递性推理能力。     

5~6岁儿童传递推理能力的发展特点

通过有效的实验设计,在控制儿童记忆容量影响的前提下,考察了5~6岁儿童在长度传递推理和重量传递推理能力上的发展水平。结果表明:(1)5~6岁是儿童传递推理能力迅速发展的时期。在大概6岁左右,大多数儿童已经能够进行真正意义上的传递推理。(2)此年龄儿童在长度传递推理和重量传递推理能力上不具有显著差异。(3)条件排列的一致与不一致对于被试的推理成绩并不具有显著影响。     

The role of cues to differential absolute size in children's transitive inferences

To investigate the role that "nonlogical" cues might play in transitive inference, 6- and 7-year-olds were given a three-term transitive task in which perceptual cues to differential absolute size were either present or absent. Relationships between the taught premises and the relational information that was physically present were manipulated using four basic conditions: "congruent," "inverse," "pretended," or "persuaded." Both age groups showed identical overall premise memory, but the younger group tended to reason more on the basis of the perceptual information rather than on the successfully encoded premise information. Contrasts between the various conditions showed that categorical effects can be circumvented in three-term problems with appropriate controls, that there may be qualitative as well as quantitative differences in transitive inference with age, and that transitive inference is not based solely on memory. The findings also indicate that, although 7-year-olds are competent in "logic-based" transitive inference, they experience great difficulty on tasks involving pretend information.     

Developmental change on a five-term transitive inference

Three experiments are reported which utilize the five-term transitive inference task developed by P. E. Bryant and T. Trabasso (Nature (London) 1971, 232, 456–458). In Experiment I, preschool children (mean age = 4 years 8 months) required fewer trials to learn the premises and showed a higher proportion of correct responses on the inferences when the presentation order was serial (i.e., AB, BC, CD, DE) throughout training as compared to when a nonserial presentation order (i.e., BC, DE, AB, CD) was used. In Experiments II and III, preschool (mean age = 4 years 7 months), second grade (mean age = 7 years 8 months), fourth grade (mean age = 9 years 9 months), and college students (mean age = 18 years 11 months) were administered the nonserial presentation version of the five-term transitive inference. An ontogenetic decrease in trials to learn the premises and corresponding increase in proportion correct on both premises and inferences was observed. A developmental model specifying changes at two stages of constructing an internal linear order is proposed to explain the results.     

Transitive choices by a simple, fully connected, backpropagation neural network: implications for the comparative study of transitive inference.

In search of the minimal requirements for transitive reasoning, a simple neural network was trained and tested on the non-verbal version of the conventional "five-term-series task" – a paradigm used with human adults, children and a variety of non-human species. The transitive performance of the network was analogous in several aspects to that reported for children and animals. The three effects usually associated with transitive choices i.e. "symbolic distance", "lexical marking" and "end-anchor", were also clearly shown by the neural network. In a second experiment, where the training conditions were manipulated, the network failed to match the behavioural pattern reported for human adults in the test following an ordered presentation of the premises. However, it mimicked young children's performance when tested with a novel comparison term. Although we do not intend to suggest a new model of transitive inference, we conclude, in line with other authors, that a simple error-correcting rule can generate transitive behaviour similar to the choice pattern of children and animals in the binary form of the five-term-series task without requiring high-order logical or paralogical abilities. The analysis of the training history and of the final internal structure of the network reveals the associative strategy employed. However, our results indicate that the scope of the associative strategy used by the network might be limited. The extent to which the conventional five-term-series task, in absence of appropriate manipulations of training and testing conditions, is suitable to detect cognitive differences across species is also discussed on the basis of our results. Accepted after revision: 29 May 2001 Electronic Publication     

Transitive inference in rats (Rattus norvegicus).

Although Piagetian theory proposes that the ability to make transitive inferences is confined to humans above age 7, recent evidence has suggested that this logical ability may be more broad based. In nonverbal tests, transitive inference has been demonstrated in preschool children and 2 species of nonhuman primates. In these experiments, I demonstrate evidence of transitive inference in rats (Rattus norvegicus). I used an ordered series of 5 olfactory stimuli (A < B < C < D < E) from which correct inferences were made about the novel B versus D pair. Control procedures indicated that performance did not depend on the recency with which the correct answer was rewarded during training and may be disrupted by the addition of logically inconsistent premises (F > E and A > F). The possibility that logical transitivity may reflect a form of spatial paralogic rather than formal deductions from a syllogistic-verbal system is discussed.     

Counterexamples in sentential reasoning

How do logically naive individuals determine that an inference is invalid? In logic, there are two ways to proceed: (1) make an exhaustive search but fail to find a proof of the conclusion and (2) use the interpretation of the relevant sentences to construct a counterexample—that is, a possibility consistent with the premises but inconsistent with the conclusion. We report three experiments in which the strategies that individuals use to refute invalid inferences based on sentential connectives were examined. In Experiment 1, the participants’ task was to justify their evaluations, and it showed that they used counterexamples more often than any other strategy. Experiment 2 showed that they were more likely to use counterexamples to refute invalid conclusions consistent with the premises than to refute invalid conclusions inconsistent with the premises. In Experiment 3, no reliable difference was detected in the results between participants who wrote justifications and participants who did not.     

小学儿童一维空间方位传递性推理能力的发展

研究了小学儿童一维空间方位传递性推理能力的发展水平及认知策略 ,同时 ,对心理模型理论进行了检验。被试为城市中等小学 7岁、9岁、11岁儿童各 2 4名 ,男女各半。 4种实验任务分别为三前提单模型、三前提双模型、四前提单模型和四前提双模型。采用个别实验 ,儿童在前提呈现的情况下进行推理。主要研究结果 :(1)从小学 7岁到 11岁 ,儿童的一维空间方位传递性推理能力明显提高 ,7岁儿童初步形成了一维空间方位推理能力 ,9岁和 11岁基本具有了这种能力 ;(2 )随着年龄增长 ,使用模型建构策略解决问题的儿童人次越来越多 ,绝大部分 11岁儿童都能使用这一策略进行推理。但即使儿童使用了模型建构策略 ,他们的推理成绩也没有反映出模型数量所造成的任务难度差异 ,即不符合心理模型理论关于模型数量的主要预期。     

3—7岁儿童不同类型的传递性推理的发展研究

本研究从发展的角度研究了3-7岁儿童在解决三类传递性推理问题时能力发展和策略发展状况,真传递性推理指推理的传递性是确定的,个体根据前提关系可以做出确定的传递性推理结论,不确定性传递性推理指该类推理的传递性是不确定的,关系是否传递需要根据实际的情况和社会经验来确定,否定性传递性推理指根据前提关系得出不能进行传递性的必然结论。结果表明：（1）三类传递性推理的解题能力随年龄的增长而不断增强,在7岁左右初步形成。（2）三类传递性推理,能力发展有不同的起始点、快速发展期以及初步形成期。真传递性推理发展最早最快,不确定传递性推理最晚最慢。（3）3-7岁儿童解决三类传递性推理问题时使用了猜测、视觉判断、定向反应、经验推测和逻辑推理等策略,然而随着年龄的增大,主导策略由准策略向真策略转换。     

3～5岁幼儿在视野阻隔任务中的长度传递性推理

设计视野阻隔任务,控制了短时记忆和直接比较的两难问题,考察3～5岁幼儿长度传递性推理能力的发展趋势和传递性推理这一认知过程的发展序列。以2(间隔长度)×2(摆放方式)×4(年龄)的三因素混合设计,研究了240名幼儿,结果表明:(1)3～4岁是长度传递性推理能力的快速发展期,4岁以后的幼儿大部分具备了这一能力,发展速度趋于平缓;(2)任务类型影响推理成绩;(3)基于传递关系的推理依据与推理总成绩显著正相关。研究认为:年仅4岁幼儿具备传递性推理能力蕴含教育价值;传递性推理的认知过程经历了四个可辨别的发展序列,依次主要发生在36～42个月、43～48个月、49～54个月和55～60个月的幼儿当中。     

TRANSITIVE INFERENCE IN RATS:

Abstract— Rats were trained to discriminate between boxes covered with distinctive odors There were six stimulus odors, labeled A through F, and the problems learned formed the five premises A+B−, B+C−, C+D−, D+E−, and E+F− Combming the premises, the relative values of the stimuli were A>B>C>D>E>F In two experiments, linear arrangement groups learned these premises with Boxes A through F placed in a linear spatial sequence Nonlinear groups had boxes either randomly changed from one position to another (Experiment 1) or placed m a circular arrangement (Experiment 2) Tests of transitive inference between the B and D stimuli were carried out in an environment different from that m which premise training took place Only the groups trained with a linear arrangement of boxes showed evidence of transitive inference These findings offer support for a spatial coding hypothesis of transitive inference in animals     

Relational learning with and without awareness: Transitive inference using nonverbal stimuli in humans

Learning complex relationships among items and representing them flexibly have been shown to be highly similar in function and structure to conscious forms of learning. However, it is unclear whether conscious learning is essential for the exhibition of flexibility in learning. Successful performance on the transitive inference task requires representational flexibility. Participants learned four overlapping premise pairs (A > B, B > C, C > D, D > E) that could be encoded separately or as a sequential hierarchy (A > B > C > D > E). Some participants (informed) were told prior to training that the task required an inference made from premise pairs. Other participants (uninformed) were told simply that they were to learn a series of pairs by trial and error. Testing consisted of unreinforced trials that included the non-adjacent pair, B versus D, to assess capacity for transitive inference. Not surprisingly, those in the informed condition outperformed those in the uninformed condition. After completion of training and testing, uninformed participants were given a postexperimental questionnaire to assess awareness of the task structure. In contrast with expectations, successful performance on the transitive inference task for uninformed participants does not depend on or correlate with postexperimental awareness. The present results suggest that relational learning tasks do not necessarily require conscious processes.     

Logical versus Associative Performance on Transitive Reasoning Tasks by Children: Implications for the Status of Animals Performance

Although monkeys, pigeons, rats and chimpanzees all appear to be able to draw transitive inferences, young children fail to do so in some situations. If we take successful performance to be indicative of rationality-as animal researchers sometimes do (Monkeys are rational!McGonigle & Chalmers, 1992)-we have the paradox that animals are, on this criterion, more rational than are school-age children. It is possible, however, to complete 5-term transitive tasks by recruiting associative rather than logical processes; and, indeed, the tasks given to animals not only afford associative solutions but seem to require them (M&C tasks, after McGonigle & Chalmers, 1992). We asked whether 5- to 6-year-old children find a task that naturally affords the application of a logical rule (a B&T task, after Bryant & Trabasso, 1971) easier to perform than an M&C task that does not. The children found the B&T task easiera difference that could not be explained in terms of difference in memory for the premises. This leaves open the possibility that, although children are not restricted to associative strategies when completing 5-term series tasks, animals may be thus restricted.     

Is awareness necessary for true inference?

In transitive inference, participants learn a set of context-dependent discriminations that can be organized into a hierarchy that supports inference. Several studies show that inference occurs with or without task awareness. However, some studies assert that without awareness, performance is attributable to pseudoinference. By this account, inference-like performance is achieved by differential stimulus weighting according to the stimuli's proximity to the end items of the hierarchy. We implement an inference task that cannot be based on differential stimulus weighting. The design itself rules out pseudoinference strategies. Success on the task without evidence of deliberative strategies would therefore suggest that true inference can be achieved implicitly. We found that accurate performance on the inference task was not dependent on explicit awareness. The finding is consistent with a growing body of evidence that indicates that forms of learning and memory supporting inference and flexibility do not necessarily depend on task awareness.     

Transitive and pseudo-transitive inferences

Given that A is longer than B, and that B is longer than C, even 5-year-old children can infer that A is longer than C. Theories of reasoning based on formal rules of inference invoke simple axioms ("meaning postulates") to capture such transitive inferences. An alternative theory proposes instead that reasoners construct mental models of the situation described by the premises in order to draw such inferences. An unexpected consequence of the model theory is that if adult reasoners construct simple models of typical situations, then they should infer transitive relations where, in certain cases, none exists. We report four studies corroborating the occurrence of these "pseudo-transitive" fallacies. Experiment 1 established that individuals' diagrams of certain non-transitive relations yield transitive conclusions. Experiment 2 showed that these premises also give rise to fallacious transitive inferences. Experiment 3 established that when the context suggested alternatives to the simple models, the participants made fewer errors. Experiment 4 showed that tense is an important aspect of meaning which affects whether individuals draw transitive conclusions. We discuss the implications of these results for various theories of reasoning.     

Getting one step closer to deduction: Introducing an alternative paradigm for transitive inference

Transitive inference is claimed to be “deductive”. Yet every group/species ever reported apparently uses it. We asked 58 adults to solve five-term transitive tasks, requiring neither training nor premise learning. A computer-based procedure ensured all premises were continually visible. Response accuracy and RT (non-discriminative nRT) were measured as is typically done. We also measured RT confined to correct responses (cRT). Overall, very few typical transitive phenomena emerged. The symbolic distance effect never extended to premise recall and was not at all evident for nRT; suggesting the use of non-deductive end-anchor strategies. For overall performance, and particularly the critical B?D inference, our findings indicate that deductive transitive inference is far more intellectually challenging than previously thought. Contrasts of our present findings against previous findings suggest at least two distinct transitive inference modes, with most research and most computational models to date targeting an associative mode rather than their desired deductive mode. This conclusion fits well with the growing number of theories embracing a “dual process” conception of reasoning. Finally, our differing findings for nRT versus cRT suggest that researchers should give closer consideration to matching the RT measure they use to the particular conception of transitive inference they pre-held.     

‘Atmosphere’, matching,and logic in syllogistic reasoning

The frequency of error in syllogism solving suggests that not all subjects are using logic. The atmosphere and matching hypotheses suggest what they might be doing instead but predict some of the same (correct and incorrect) responses. Reexamination of the data supporting the atmosphere hypothesis (Sells, 1936) shows that the procedure employed was unsatisfactory and that the results obtained support the matching hypothesis as well as they support the atmosphere hypothesis. It is argued on theoretical grounds that the matching hypothesis should be preferred. An experiment is reported in which subjects (N=71) were required to draw conclusions from syllogistic premises and to construct premises from which given conclusions followed. It is shown that subjects may be divided into three groups: (n=16) consisting of subjects who used logic and made few errors; (n=25) of subjects whose correct and incorrect responses were in accordance with the matching hypothesis; and (n=30) of subjects who were not matching but trying to do logic and not doing it well.     

小学儿童在不同刺激材料中的左右空间方位传递性推理能力及策略分析

采用定性和定量相结合的研究方法,从图形刺激材料和文字刺激材料入手,探查了7岁、9岁、11岁儿童的一维空间方位传递性推理能力的发展水平及其认知策略。主要研究结果表明:(1)小学儿童的一维空间方位传递性推理能力从7岁到9岁,从9岁到11岁都有显著性提高。7岁儿童处于能力的初步形成期,9岁儿童是能力的提高和发展期,11岁儿童已基本具有了一维空间方位单模型条件下的传递性推理能力;(2)小学儿童在图形刺激材料条件下的推理成绩显著优于文字刺激材料条件下的推理成绩;(3)前提数量的增加没有对小学儿童的推理造成显著性影响;(4)随着儿童年龄的增长,模型建构策略的使用者越来越多,但在图形刺激材料和文字刺激材料下,儿童解决问题的策略有所不同。在图形刺激材料下,大部分7岁和9岁的儿童采用知觉策略,11岁儿童中只有少部分人使用这一策略。在文字刺激材料下,模型建构策略是儿童推理的主要策略。少部分7岁儿童使用模型建构策略,大部分9岁儿童和绝大部分11岁儿童使用模型建构策略来解决问题。     

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.