Conditional reasoning with false premises facilitates the transition between familiar and abstract reasoning

Abstract reasoning is critical for science and mathematics, but is very difficult. In 3 studies, the hypothesis that alternatives generation required for conditional reasoning with false premises facilitates abstract reasoning is examined. Study 1 (n = 372) found that reasoning with false premises improved abstract reasoning in 12- to 15-year-olds. Study 2 (n = 366) found a positive effect of simply generating alternatives, but only in 19-year-olds. Study 3 (n = 92) found that 9- to 11-year-olds were able to respond logically with false premises, whereas no such ability was observed in 6- to 7-year-olds. Reasoning with false premises was found to improve reasoning with semiabstract premises in the older children. These results support the idea that alternatives generation with false premises facilitates abstract reasoning.     

Reasoning in Young Children: Fantasy and Information Retrieval

The present article examines 2 predictions concerning conditional reasoning in children derived from Markovits's model of conditional reasoning. The first claims that children under 12 years of age should be able to respond correctly to uncertain logical forms if the premises and context enable them to access pertinent counterexamples from memory. The second concerns the effect of reasoning in a fantasy context. Previous studies have established that young children can correctly respond to certain reasoning problems with empirically false premises when these are presented in a fantasy context. However, this model of reasoning predicts that presenting empirically true premises in a fantasy context should decrease performance on the 2 uncertain logical forms. In Study 1, a total of 48 8-year-olds, 78 10-year-olds, and 74 12-year-olds were given 4 reasoning problems involving familiar premises. These problems were embedded in either a fantasy or a realistic context and presented via video tape. Results were consistent with the predictions made. Study 2 attempted to determine whether these results could be due to context or problem formulation. A total of 40 7-year-olds and 46 8-year-olds were given reasoning problems with either no context or with a visual image preceding the problems. Results showed that children did equally well in these conditions, and that providing an image did not improve performance.     

Inferences and recall at ages four and seven

Inferences and recall at ages 4 and 7 were studied as a function of the cause of a target event, the presence and timing of questions prior to recall, and the type of inference demanded by the questions. 7-year-olds inferred and recalled well with stories containing any of the causal connections employed in the study. 4-year-olds performed better when physical causes, rather than either psychological causes or enabling relations, connected events. Timing of questions did not affect the 7-year-olds' inferences, but asking questions interfered with their recall. Questions about story events aided the 4-year-olds' ability to make inferences and to recall, especially when causal connections were least specified and when questions were asked following the story. 4- and 7-year-olds also differed in responding to demands for 3 specific types of inference. 4-year-olds produced significantly more unconstrained inferences than logical or constrained informational inferences. 7-year-olds were most responsive to logical inference questions, and produced significantly more logical than constrained inferences.     

Reasoning in a reading context: Deductive inferences in basal reading series

This study examined three basal reading programs published by Heath (1989), Silver Burdett Ginn (1993) and Houghton Mifflin (1993), to determine how frequently logically necessary relationships are expressed in text used by basal readers, and whether direct instruction in making logically necessary inferences accompanies such expressions in basal reader series. The complete contents of the basal readers, from grades one through eight, and all teachers' instructions pertaining to content read by students, were examined for each series. Frequency counts made by independent raters indicated that readers of these three series have a steady and frequent rate of opportunities to make logically necessary inferences, and to observe such inferences being modeled by the text; no significant differences were found between any of the series in the number of such opportunities. We found that while children's reading materials clearly offer a natural context in which logical understanding may be constructed, instructions for teachers in the basal series we examined did not include directly teaching students to use this kind of reasoning in reading comprehension. Suggestions are offered for how such instruction might be integrated with current teaching strategies in inference-making.     

Two levels of inferential behavior in young children.

5- and 6-year-old children made inferences about the spatial locations of animals and people in a series of 3 experiments. The tasks employed manipulable models to represent the spatial relations involved and were made as simple as possible. 2 levels of inferential behavior were found. The first constituted the ability to draw an inference consistent with information given, but with minimal understanding of the way in which inferences can assist in decisions between alternative outcomes. At the second level, children succeeded in discriminating inferences which were logically necessary from those which were merely consistent with the premises. Most 5-year-olds were at the first level, most 6-year-olds at the second level. 2 criteria for the identification of young children's behavior as inferential were established, and the results of the present study were discussed in terms of recent related work with both younger and older children.     

Searching and planning: young children's reasoning about past and future event sequences

Six experiments examined children's ability to make inferences using temporal order information. Children completed versions of a task involving a toy zoo; one version required reasoning about past events (search task) and the other required reasoning about future events (planning task). Children younger than 5 years failed both the search and the planning tasks, whereas 5-year-olds passed both (Experiments 1 and 2). However, when the number of events in the sequence was reduced (Experiment 3), 4-year-olds were successful on the search task but not the planning task. Planning difficulties persisted even when relevant cues were provided (Experiments 4 and 5). Experiment 6 showed that improved performance on the search task found in Experiment 3 was not due to the removal of response ambiguity.     

Use of reasoning to a contradiction in grades three to college

The primary purpose of this study was to test the hypothesis that an important intellectual acquisition during adolescence is the ability to generate arguments that involve reasoning to contradiction. Students in grades 3, 5, 7, 9, 11, and college were individually administered a four-card selection task that required them to, among other things, reason to a contradiction to falsify a hypothesis. Virtually none of the students spontaneously utilized this reasoning pattern on the initial task. Minimal verbal instruction in use of the reasoning pattern was then given followed by a logically analogous selection task. Performance on this task improved significantly with age from 12% success among third graders to 52% success among college students, providing some support for the hypothesis. Performance on an evaluation task showed similar rates of success; however, most students were able to correctly evaluate falsifying evidence when presented. This result suggested that, contrary to Piagetian theory, students from grade 3 upward comprehend the logic of falsification. It is argued that reasoning to a contradiction is a reasoning pattern of central importance in testing alternative scientific hypotheses and its use in students grades 3 through college could be enhanced through proper instruction and, if done, should increase students' ability to generate and evaluate competing hypotheses.     

Acceptance of lack of closure: is it an index of advanced reasoning?

Lunzer reported data suggestive of a stage of cognitive development manifest between 9 and 11 years of age characterized by the ability to avoid drawing premature inferences when faced with ambiguity (i.e., accept lack of closure [ALC]). The present study sought to test this hypothesis. Inference tasks emphasizing ALC, memory, and hypothetico-deductive reasoning were administered to 67 males and 74 females (5-12 years in age). Although use of ALC increased with age, considerable use was evidenced on a simple task among 7-8-year-olds. On tasks hypothesized to place increasing demands on working memory, longer tasks were found to be more difficult. Marked improvement due to memory aids suggested that task difficulty results from limitations in working memory as predicted by Pascual-Leone's theory. Tasks requiring hypothetico-deductive reasoning were found to be most difficult. Performance was related to subject's spontaneous use of ALC. Lack of appropriate strategies was hypothesized to prevent solution rather than lack of logical competence. In conclusion, the relationship of ALC to age appears to be mediated by memory development rather than logical development.     

Looking back: reasoning and metacognition with narrative texts

This study explored the abilities of 5th, 8th, and 10th graders, and College students to reason logically about what they read. Both students’ metacognitive behavior (looking back at previously read text) and their performance on logical deduction questions were recorded and analyzed in a reading task. Conditional logic premises and deductive questions were embedded in three narratives containing premise information that was factual (True Story), contrary to fact (False Story), or unverifiable via common world knowledge (Neutral Story). The texts and questions were presented one sentence at a time on a computer screen; participants controlled the presentation of sentences. For answering the questions, three response tasks were devised. One task (labeled Generate) required readers to generate their own logical conclusions in response to deduction questions. Two tasks (labeled Valid and Invalid) required readers to evaluate logically valid or logically invalid conclusions drawn by story characters in the texts. Students in early and late adolescence looked back more when asked to evaluate logical conclusions than when asked to generate conclusions on their own; College students’ lookback frequencies were not significantly affected by response task, but were greater overall than those of younger students. With conditional forms requiring an uncertainty response (Affirmed Consequent and Denied Antecedent), readers looked back more when evaluating logically invalid conclusions than when evaluating logically valid ones. Readers of all ages were more likely to agree with story characters’ (valid) uncertain conclusions with the AC and DA forms than they were to disagree with story characters’ (invalid) certain conclusions to these forms. Both lookback frequency and performance on logic questions were lowest when readers were required to reason from contrary to fact premises.     

All Other Things Being Equal: Acquisition and Transfer of the Control of Variables Strategy

The ability to design unconfounded experiments and make valid inferences from their outcomes is an essential skill in scientific reasoning. The present study addressed an important issue in scientific reasoning and cognitive development: how children acquire a domain-general processing strategy (Control of Variables Strategy or CVS) and generalize it across various contexts. Seven- to 10-year-olds (N = 87) designed and evaluated experiments and made inferences from the experimental outcomes. When provided with explicit training within domains, combined with probe questions, children were able to learn and transfer the basic strategy for designing unconfounded experiments. Providing probes without direct instruction, however, did not improve children's ability to design unconfounded experiments and make valid inferences. Direct instruction on CVS not only improved the use of CVS, but also facilitated conceptual change in the domain because the application of CVS led to unconfounded, informative tests of domain-specific concepts. With age, children increasingly improved their ability to transfer learned strategies to remote situations. A trial-by-trial assessment of children's strategy use also allowed the examination of the source, rate, path, and breadth of strategy change.     

模糊规则间交互指标的初步研究

当模糊产生式规则应用在近似推理过程中时，前件相同而后件不同的模糊规则之间往往存在交互影响．考虑模糊规则间的交互影响，可以提高推理精度．此论文通过类比在合作游戏建论中描述交互影响的交互指标和定义在模糊规则上的模糊测度，给出一种计算模糊规则之间交互影响指标的方法．     

Understanding perspectives and emotions in contract violation: development of deontic and moral reasoning

Children between the ages of 3 and 10 years were presented with a set of pictures representing a contract with bilateral cheating options between a parent and child (Study 1) and between 2 peers (Study 2). The children had to (a) evaluate which situations violated the contract when the relevant information was presented, (b) anticipate the feelings of the violator and the victim, and (c) infer possible contract violation from 2 different perspectives when relevant information was covered. Results show that logical inferences about contract violation differ according to the type of task. Negative feelings attributed to the violator were dependent on age and type of relationship, revealing a content-sensitive codevelopment of cognitive abilities and moral reasoning in young children.     

明故知类有所止而正－中国古代逻辑中关于“说”的谬误

西方传统逻辑讲谬误，主要指形式谬误；中国古代逻辑讲谬误，主要指实质谬误。中国古代逻辑中关于“说”的谬误，主要指非必然性推理的错误。由于在推理的过程中不知类，不明故或不知止，就会产生各种实质性谬误。古代逻辑学不仅分析了产生谬误的原因，而且分析了不同的谬误形式，这些探索和分析有助于我们进一步提高思辩能力，防止逻辑错误。     

Trait Understanding or Evaluative Reasoning? An Analysis of Children''s Behavioral Predictions

This study tested the hypothesis that in predicting the future behavior of an actor, older children rely on trait inferences, whereas younger children rely on global, evaluative inferences. Vignettes depicting actors engaging in trait-relevant behaviors were presented to 5- and 6-year-olds (N = 67) and 9- and 10-year-olds (N = 71). For each actor, children made predictions of future behavior, evaluated the goodness and badness of the actor, and rated each actor on a relevant trait. A mediational analysis found that the behavioral predictions of older children were mediated solely by trait ratings, whereas those of younger children were mediated by evaluative ratings. Furthermore, unlike older children, younger children made trait-like predictions only when they made an evaluation of the actor. These results suggest that young children utilize evaluative reasoning when making behavioral predictions, and therefore rely on an inferential process that is distinct from that of older children.     

Young children's comprehension of montage

2 studies examined children's comprehension of brief stop-animation televised segments incorporating elements of cinematic montage such as pans, zooms, and cuts. Children reconstructed the action and dialogue in these segments using the same dolls and settings depicted. In Study 1, there was no effect of cinematic techniques on reconstruction performance of 3- and 5-year-olds as compared to control segments filmed without these techniques. The results challenged the assumption that the use of such techniques per se contributes to young children's poor comprehension of television shows. In Study 2, 12 new segments were produced in which comprehending the montage required inferences of character perspective, implied action sequences, spatial relationships, and simultaneity of different actions. Averaging across all segments, 62% of the 4-year-olds and 88% of the 7-year-olds demonstrated clear comprehension of the montage. Inferences concerning implied action sequences were easiest for both ages. Inferences of simultaneity were most difficult for 4-year-olds, whereas inferences of character perspective were most difficult for 7-year-olds. Preschool children are thus capable of understanding cinematic events conveyed through camera techniques and film editing, despite previous assertions to the contrary. This ability nevertheless substantially increases with age.     

Preschool children's reasoning about ability

Young children's reasoning about ability was investigated among 155 preschoolers (M = 4 years, 10 months) across 3 studies. Results suggest that preschoolers are sensitive to mental state information when making judgments about another child's ability: They judged a child who finds a task easy to be smarter than one who finds the same task hard. Systematic patterns of errors on recall tasks suggest that preschoolers perceive positive correlations between (a) exerting effort and experiencing academic success, and (b) being nice and having high academic ability. Results from a comparison group of forty 9- to 10-year-olds (M = 9 years, 10 months) suggest that the preschool findings generally reflect emerging patterns of reasoning about ability that persist into later childhood, but that the perceived correlations between high effort and academic outcomes and between social and academic traits diminish with age.     

Speech and Language Difficulties in Children With and Without a Family History of Dyslexia

According to recent psychological theories of situation model construction, readers routinely and quickly construct inferences that elaborate causal antecedents of explicit events in the text, but not inferences about causal consequences. The process of forecasting lengthy causal chains into the future is taxing on working memory, so these inferences are either not constructed or their construction consumes a comparatively large amount of reading time. This study collected self-paced sentence reading times from younger and older adults who read expository texts on scientific and technological mechanisms. Readers were also measured on working memory span, general world knowledge, reasoning ability, and reading frequency. Multiple regression analyses on the reading times revealed that (a) causal consequence inferences were more time consuming than causal antecedent inferences and (b) noncausal elaborative inferences were not constructed. The pattern of beta weights for inference variables was remarkably similar for younger and older adults and was unaffected by other measures of individual differences. The process of constructing causal inferences is therefore stable and predictable across different groups of readers.     

Young children's responses to "when" questions: issues of directionality

On the basis of the bulk of the available literature, it appears that in talking or reasoning about temporal sequences, preschoolers lack bidirectional flexibility and are limited to forward order, antecedent toward consequent movement. 3-, 4-, and 5-year-olds and adults responded to when-questions designed to permit assessment of directional preferences. All questions referred to the second sentence of 3-sentence stories, so that before-type (antecedent to consequent) and after-type (consequent to antecedent) responses were possible for all questions. Children showed a strong preference for giving after-responses. Contrary to claims made in previous literature, preschoolers are quite capable of reasoning from consequences to antecedents when provided with a context, such as responding to when-questions, for which such movement is appropriate. Children's apparent lack of bidirectional reasoning on problems involving temporal sequence may reflect preferred directionality based on conventions associated with particular tasks rather than a lack of flexibility in temporal reasoning per se.     

略论法律推理与逻辑推理

逻辑推理和法律推理的关系十分密切,法律推理是逻辑推理的一般方法在法律领域中广泛、综合的运用,逻辑推理是法律推理重要的理性工具之一。法律推理中的逻辑推理形式必须是有效的,有效的逻辑推理可以消解裁判中的任意性,避免谬误,帮助获得正当的裁判结论。