Information processing and reasoning with premises that are empirically false: Interference,working memory,and processing speed

In this study, we looked at the contributions of individual differences in susceptibility to interference and working memory to logical reasoning with premises that were empirically false (i.e., not necessarily true). A total of 97 university students were given a sentence completion task for which a subset of stimuli was designed to generate inappropriate semantic activation that interfered with the correct response, a measure of working memory capacity, and a series of logical reasoning tasks with premises that were not always true. The results indicate that susceptibility to interference, as measured by the error rate on the relevant subset of the sentence completion task, and working memory independently account for variation in reasoning performance. The participants who made more errors in the relevant portion of the sentence completion task also showed more empirical intrusions in the deductive reasoning task, even when the effects of working memory were partialed out. Working memory capacity was more clearly related to processes involved in generating uncertainty responses to inferences for which there was no certain conclusion. A comparison of the results of this study with studies of children's reasoning suggests that adults are capable of more selective executive processes than are children. An analysis of latency measures on the sentence completion task indicated that high working memory participants who made no errors on the sentence completion task used a strategy that involved slower processing speed, as compared with participants with similar levels of working memory who did make errors. In contrast, low working memory participants who made no errors on the sentence completion task had relatively shorter reaction times than did comparable participants who did make errors.     

The development of reasoning with causal conditionals.

A total of 512 children in Grades 1 through 6 received a conditional inference task using causal conditionals (If cause P, then effect Q) and a generation of alternatives task. The inference task used premises for which there were few or many possible alternative causes. Results show a steady age-related increase in uncertainty responses to the two uncertain logical forms, affirmation of consequent (AC) and denial of antecedent (DA), and an increase in production of disabling conditions for modus ponens. More uncertainty responses were produced to AC and DA with premises with many possible alternatives. Individual differences in inference production were related to numbers of alternatives produced in the generation task. Results support the idea that both developmental and individual differences in reasoning can be at least partially explained by differential access to knowledge stored in long-term memory.     

Multiple layers of information processing in deductive reasoning: combining dual strategy and dual-source approaches to reasoning

The idea that inferential performance cannot be analyzed within a single model has been suggested within two theoretical contexts. The dual strategy model suggests that people reason using different approaches to processing statistical information. The dual-source model suggests that people reason probabilistically using both statistical information and some intuition about logical form. Each model suggests that people have different approaches to processing information while making inferences. The following studies examined whether these different forms of information processing were equally present during reasoning. Participants were given a series of problems designed to distinguish counterexample from statistical reasoners. They were then given a series of MP or AC inferences for which identical statistical information was provided. Results show that MP inferences were considered to be deductively valid more often than equivalent AC inferences. The effect of logical form was independent of reasoning strategy, and of relatively equivalent size for both counterexample and statistical reasoners. The second study examined explicitly probabilistic inferences, and showed smaller effects of logical form and of reasoning strategy, although with a complex set of interactions. These results show that understanding the way that people use information when making inferences requires a multidimensional approach.     

The logic sense: exploring the role of executive functioning in belief and logic-based judgments

Abstract

The Default Interventionist account suggests that by default, we often generate belief-based responses when reasoning and find it difficult to draw the logical inference. Recent research, however, shows that in some instances belief judgments take longer, are more prone to error and are more affected by cognitive load. One interpretation is that some logical inferences are available automatically and require intervention in order to respond according to beliefs. In two experiments, we investigate the effortful nature of belief judgments and the automaticity of logical inferences by increasing the inhibitory demands of the task. Participants were instructed to judge conclusion validity, believability and either font colour or font style, to increase the number of competing responses. Results showed that conflict more strongly affects judgments of believability than validity and when inhibitory demands are increased, the validity of an argument impacts more on belief judgments. These findings align with the new Parallel Processing model of belief bias.     

Evidence of deontic reasoning in 3- and 4-year-old children

Deontic reasoning is reasoning about what one may, ought, or ought not do in a given set of circumstances. Virtually all of our social institutions and child-rearing practices presume the capacity to reason about deontic concepts, such as what is permitted, obligated, or prohibited. Despite this, very little is known about the development of deontic reasoning. Two experiments were conducted that contrasted children’s reasoning performance on deontic and indicative reasoning tasks (i.e., the reduced array selection version of the Wason card selection task). Like adults, children as young as 3 years of age were found to adopt a violation-detecting strategy more often when reasoning about the deontic case than when reasoning about the indicative case. These results indicate that violation detection emerges as an effective deontic reasoning very early in human development.     

分心抑制和关系整合对学前儿童类比推理的影响

为探究分心抑制和关系整合对学前儿童类比推理的影响,实验一先初步探究分心抑制和关系整合对25名3~4岁和26名5~6岁儿童完成含有知觉分心的类比情景任务的影响。其次,揭示知觉分心与关系整合在类比推理中的具体作用模式。实验二先初步探究分心抑制和关系整合对30名3~4岁和28名5~6岁儿童完成含有语义分心的类比情景任务的影响。其次,揭示语义分心与关系整合在类比推理中的具体作用模式。结果表明,抑制控制能显著预测儿童完成各种类型类比推理成绩,工作记忆能显著预测儿童完成含有语义分心的类比推理成绩而不能显著预测含有知觉分心的类比推理成绩。儿童完成类比情景中的分心抑制是在关系整合中完成的,当类比情景中的关系整合没有超过儿童的工作记忆容量时,知觉或语义分心才能造成对儿童类比推理的影响。     

Priming divergent thinking promotes logical reasoning in 6- to 8-year olds: But more for high than low SES students

Divergent thinking is a component of creativity. In the following study, we argue that this form of thinking also underlies logical reasoning. A total of 205 early elementary school children in Grades 1 and 2, from high and moderately low SES environments, were given a short-term prime for divergent thinking and simple reasoning problems. Overall, receiving this prime significantly improved logical reasoning at both grade levels. High and low SES students had similar levels of working memory, inhibitory control, performance on the divergent thinking task, and levels of logical reasoning without the prime. However, also consistent with our predictions, only high SES students showed overall improved logical reasoning following the divergent thinking prime, with the SES difference concentrated in the younger students. These results suggest that environmental differences in openness to alternatives and divergent thinking might underlie developing SES differences in levels of logical thinking.     

Different developmental patterns of simple deductive and probabilistic inferential reasoning

In three studies, we examined simple counterexample-based and probabilistic reasoning in children 6, 7, and 9 years of age. In the first study, participants were asked to make conditional (if-then) inferences under both categorical (certain or uncertain) and probabilistic instructions. Results showed that 6-year-olds respond to both forms of inference in similar ways, but whereas probabilistic conditional inferences showed little development over this period, categorical inferences clearly improved between 6 and 7 years of age. An analysis of the children's justifications indicated that performance under categorical instructions was strongly related to counterexample generation at all ages, whereas this was true only for the younger children for inferences under probabilistic instructions. These findings were replicated in a second study, using problems that referred to concrete stimuli with varying probabilities of inference. A third study tested the hypothesis that children confused probability judgments with judgments of confidence and demonstrated a clear dissociation between these two constructs. Overall, these results show that children are capable of accurate conditional inferences under probabilistic instructions at a very early age and that the differentiation between categorical and probabilistic conditional reasoning is clear by at least 9 years ofage. These results are globally consistent with dual-process theories but suggest some difficulties for the way that the analytic-heuristic distinction underlying these theories has been conceptualized.     

Context sensitivity in children's reasoning about ability across the elementary school years

Children's sensitivity to context when making inferences about ability was investigated. In three studies, elementary school children (ages 5 to 10, total N = 332) were asked to reason about the relation between academic ability and the speed with which characters completed puzzle tasks. Participants were primed to interpret the characters' task completion rates with reference to either (1) the character's perceptions of the difficulty of the task, or (2) the character's level of effort on the task. Children who were primed to consider the perceived difficulty of the task were more likely to view ability as a static quality, a pattern of reasoning that included a tendency to associate task completion rates with ability, and to agree that not all individuals are capable of achieving high levels of success. These results provide evidence that even early elementary school children are sensitive to subtle contextual cues when making inferences about ability, and are consistent with the possibility that children make use of implicit cues available to them in their social environment to derive meaning from achievement situations.     

Pretense,Counterfactuals, and Bayesian Causal Models: Why What Is Not Real Really Matters

Young children spend a large portion of their time pretending about non‐real situations. Why? We answer this question by using the framework of Bayesian causal models to argue that pretending and counterfactual reasoning engage the same component cognitive abilities: disengaging with current reality, making inferences about an alternative representation of reality, and keeping this representation separate from reality. In turn, according to causal models accounts, counterfactual reasoning is a crucial tool that children need to plan for the future and learn about the world. Both planning with causal models and learning about them require the ability to create false premises and generate conclusions from these premises. We argue that pretending allows children to practice these important cognitive skills. We also consider the prevalence of unrealistic scenarios in children's play and explain how they can be useful in learning, despite appearances to the contrary.     

The difference between generating counterexamples and using them during reasoning

The aim of this article is to provide insight into the types of long-term knowledge that are used for solving causal conditional inferences. Two taxonomies were constructed to map the types of counterexample. The available counterexamples are traditionally probed via a counterexample generation task. We observed that there are some significant differences in the types of counterexample retrieved in the reasoning task versus the generation task. The generation task can be used for predicting answers that sprout from a reasoning process that takes counterexample into account, but some participants use a different reasoning process in which the available semantic information is not used as contrasting evidence. Nonetheless, we found that the results of the generation task validly predicted the proportion of inferences accepted as well as the number of counterexamples used during reasoning.     

The Development of Diagnostic Inference About Uncertain Causes

Young children can engage in diagnostic reasoning. However, almost all research demonstrating such capacities has investigated children’s inferences when the individual efficacy of each candidate cause is known. Here we show that there is development between ages five and seven in children’s ability to reason about the number of candidate causes whose efficacy is unknown (Study 1). We also find development between ages six and seven in these abilities when children are presented with several uncertain candidate causes in an additive causal system (Study 2). These findings demonstrate how children’s diagnostic reasoning abilities develop beyond the preschool years and illustrate possible relations between children’s developing diagnostic inference and scientific reasoning capacities.     

Counting strategies and semantic analysis as applied to class inclusion

This study examined strategic and semantic aspects of the answers given by preschool children to class inclusion problems. The Piagetian logical model for class inclusion was contrasted with an alternative, problem processing model in three experiments. A major component of the alternative model is an enumeration strategy which is advantageous for learning reliable counting skills. The counting strategy was found to explain the inclusion errors of young children better than did the logic of the task. It was also found that young children understand the semantics of inclusion but are unable to coordinate their semantic knowledge with their counting strategy. Methodologically, one of the experiments suggested a fruitful extension of task analysis (Simon, 1969) to experimental design.     

KNOWING ABOUT READING BEFORE READING: PRESCHOOL CHILDREN'S CONCEPTS OF READING

This paper reports findings from an investigation of preschool children's concepts about reading. Three tasks related to several basic ideas about reading were presented to 60 preschool children, ranging in age from three to five years. The first task assessed children's ability to identify oral and silent reading. The number of children who correctly identified both forms of reading increased with age, with almost all five‐year‐olds giving accurate responses. The second task was aimed at establishing children's perceptions of their own reading ability. Only four of the 60 children incorrectly evaluated their own reading ability. The third task investigated children's ability to recognize what it is on a page that is read. Three‐year‐olds were, on the whole, quite unaware of the salient information in books. Even among the five‐year‐olds, who performed significantly better than three‐ and four‐year‐olds on this task, some children's responses indicated an ambiguity about the role of print in reading. Suggestions for adults who guide young children through their early experiences with print are drawn from the findings of this investigation.     

Causal conditional reasoning and semantic memory retrieval: a test of the semantic memory framework

This study tested and refined a framework that proposes a mechanism for retrieving alternative causes and disabling conditions (Cummins, 1995) during reasoning. Experiment 1 examined the relation between different factors affecting retrieval. The test revealed high correlations between the number of possible alternative causes or disabling conditions and their strength of association and plausibility. Experiment 2 explored the hypothesis that due to a more extended search process, conditional inferences would last longer when many alternative causes or disabling conditions were available. Affirmation of the consequent (AC) and modus ponens (MP) latencies showed the hypothesized pattern. Denial of the antecedent (DA) and modus tollens (MT) inferences did not show latency effects. The experiment also identified an effect of the number of disabling conditions on AC and DA acceptance. Experiment 3 measured efficiency of disabler retrieval by a limited time, disabler generation task. As predicted, better disabler retrieval was related to lower acceptance of the MP and MT inferences.     

Counterfactual syllogistic reasoning in normal 4-year-olds, children with learning disabilities, and children with autism

Instruction encouraging imagery improves logical reasoning with counterfactual premises by normal preschool children. In contrast, children with autism have been reported to reason accurately with counterfactual premises in the absence of such instruction (F. J. Scott, S. Baron-Cohen, & A. M. Leslie, 1999). To investigate this pattern of findings, we compared the performance of children with autism, children with learning disabilities, and normally developing 4-year-olds, who were given reasoning problems both with and without instruction in two separate testing sessions 2 to 3 weeks apart. Overall, instruction to use imagery led to persistent logical performance. However, children with autism displayed a distinctive pattern of responding, performing around chance levels, showing a simple response bias, and rarely justifying their responses by elaborating on the premises. We propose that instruction boosts logical performance by clarifying the experimenter's intention that a false proposition be accepted as a basis for reasoning and that children with autism have difficulty grasping this intention.     

A curious belief-bias effect: reasoning with false premises and inhibition of real-life information

Many studies have shown that inferential behavior is strongly affected by access to real-life information about premises. However, it is also true that both children and adults can often make logically appropriate inferences that lead to empirically unbelievable conclusions. One way of reconciling these is to suppose that logical instructions allow inhibition of information about premises that would otherwise be retrieved during reasoning. On the basis of this idea, we hypothesized that it should be easier to endorse an empirically false conclusion on the basis of clearly false premises than on the basis of relatively believable premises. Two studies are presented that support this hypothesis.     

The contribution of logical reasoning to the learning of mathematics in primary school

It has often been claimed that children's mathematical understanding is based on their ability to reason logically, but there is no good evidence for this causal link. We tested the causal hypothesis about logic and mathematical development in two related studies. In a longitudinal study, we showed that (a) 6‐year‐old children's logical abilities and their working memory predict mathematical achievement 16 months later; and (b) logical scores continued to predict mathematical levels after controls for working memory, whereas working memory scores failed to predict the same measure after controls for differences in logical ability. In our second study, we trained a group of children in logical reasoning and found that they made more progress in mathematics than a control group who were not given this training. These studies establish a causal link between logical reasoning and mathematical learning. Much of children's mathematical knowledge is based on their understanding of its underlying logic.     

Theories of conditional reasoning: a developmental examination of competing hypotheses

Children and adolescents were presented with problems that contained deontic (i.e., if action p is taken, then precondition q must be met) or causal (i.e., if event p occurs, then event q will transpire) conditionals and that varied in the ease with which alternative antecedents could be activated. Results showed that inferences were linked to the availability of alternative antecedents and the generation of "disabling" conditions (claims that the conditionals were false under specific circumstances). Age-related developments were found only on problems involving indeterminate inferences. Correlations among inferences differed for children and adolescents. The findings provide stronger support for domain-general theories than for domain-specific theories of reasoning and suggest, under some conditions, age-related changes in the roles of implicit and explicit processing.