Properties of inductive reasoning

This paper reviews the main psychological phenomena of inductive reasoning, covering 25 years of experimental and model-based research, in particular addressing four questions. First, what makes a case or event generalizable to other cases? Second, what makes a set of cases generalizable? Third, what makes a property or predicate projectable? Fourth, how do psychological models of induction address these results? The key results in inductive reasoning are outlined, and several recent models, including a new Bayesian account, are evaluated with respect to these results. In addition, future directions for experimental and model-based work are proposed.     

归纳推理和演绎推理的关系理论及其模型

推理是人类高级认知过程的一种,相关的心理学研究一般将其分为归纳推理和演绎推理两个方面。归纳推理是从特殊到一般的推理过程,与之相对的演绎推理则是从一般到特殊的过程。归纳推理和演绎推理的关系问题是当前心理推理研究领域的一个重点问题。这一问题主要有两种理论解释：一种是单过程理论,该理论认为归纳推理和演绎推理本质上是同一个认知过程,以单过程理论为基础构建的推理模型称为单维模型;另一种是双过程理论,认为归纳推理和演绎推理是两个不同的认知过程,并不同程度地受到启发和分析过程的影响。未来研究可多关注推理的时间进程,以及采用不同的研究方法对各自理论提供数据支持。     

Erroneous knowledge of results affects decision and memory processes on timing tasks

On mental timing tasks, erroneous knowledge of results (KR) leads to incorrect performance accompanied by the subjective judgment of accurate performance. Using the start-stop technique (an analogue of the peak interval procedure) with both reproduction and production timing tasks, the authors analyze what processes erroneous KR alters. KR provides guidance (performance error information) that lowers decision thresholds. Erroneous KR also provides targeting information that alters response durations proportionately to the magnitude of the feedback error. On the production task, this shift results from changes in the reference memory, whereas on the reproduction task this shift results from changes in the decision threshold for responding. The idea that erroneous KR can alter different cognitive processes on related tasks is supported by the authors' demonstration that the learned strategies can transfer from the reproduction task to the production task but not visa versa. Thus effects of KR are both task and context dependent.     

Effects of two tasks and two levels of difficulty upon surface electrogastrograms

The effects of differentiation, novelty, and difficulty of ability tasks upon electrogastrographic activity of healthy subjects during digestion were investigated. Electrical recording of activity of the stomach by means of surface electrodes was performed in 40 healthy volunteers before and after easy or hard tasks. 20 subjects had to complete puzzles; the others had mental arithmetic. Both groups were matched in terms of scores on easy and difficult tasks. Baseline recordings were performed before each trial. The number of waves with peak amplitude greater than 100 mu v on electrogastrographic recording during each time span was measured, using a visual analysis. There was a significant decrease in number of waves/min, during task performance. A more pronounced decrease was produced by subjects working on puzzles than those working on mental calculation and by subjects working on easy tasks than those working on difficult tasks when the easy preceded the difficult ones. A larger decrease was obtained when the tasks of comparable difficulty were performed first. Emotional correlates such as anger and irritability were suggested to play a role in the interpretation of results.     

Theory-based Bayesian models of inductive learning and reasoning

Inductive inference allows humans to make powerful generalizations from sparse data when learning about word meanings, unobserved properties, causal relationships, and many other aspects of the world. Traditional accounts of induction emphasize either the power of statistical learning, or the importance of strong constraints from structured domain knowledge, intuitive theories or schemas. We argue that both components are necessary to explain the nature, use and acquisition of human knowledge, and we introduce a theory-based Bayesian framework for modeling inductive learning and reasoning as statistical inferences over structured knowledge representations.     

Context,visual salience,and inductive reasoning

An important debate in the reasoning literature concerns the extent to which inference processes are domain-free or domain-specific. Typically, evidence in support of the domain-specific position comprises the facilitation observed when abstract reasoning tasks are set in realistic context. Three experiments are reported here in which the sources of facilitation were investigated for contextualised versions of Raven's Progressive Matrices (Richardson, 1991) and non-verbal analogies from the AH4 test (Richardson & Webster, 1996). Experiment 1 confirmed that the facilitation observed for the contextualised matrices was in part due to extraneous aspects of commentaries originally intended to activate domainspecific processes. Experiments 2 and 3 indicated that the remainder of the facilitation for the matrices, and all of the facilitation for the analogies, could be explained by visual salience: Converting the item elements into realistic objects had enabled them and their transitions to be identified more easily. Hence, performance at simplified abstract items was as good as, or better than, at contextualised items. It is concluded that facilitation effects cannot be interpreted as showing that domain-specific processes constitute a self-contained system separate from domain-free processes. In turn, this means that domain-free processes cannot be dismissed as being unimportant for reasoning.     

Culture,category salience,and inductive reasoning

The role of category salience in category-based induction was demonstrated in two ways: (i) temporarily increasing category salience facilitated category-based induction, and (ii) this effect was moderated by cultural differences that we predicted would be related to chronic category salience. Subjects for whom categories were presumed to be more accessible (Americans) were not as much influenced by manipulations to increase category salience as subjects who were presumed to have lower chronic accessibility of categories (Koreans). However, as anticipated, this pattern was reversed for inferences about behavioral properties of social categories. Due to the `interdependent' nature of their culture, Koreans presumably have relatively higher chronic accessibility for social categories than do relatively `independent' Americans, and hence were not influenced as much by increasing category salience.     

Causal relations and feature similarity in children's inductive reasoning

Four experiments examined the development of property induction on the basis of causal relations. In the first 2 studies, 5-year-olds, 8-year-olds, and adults were presented with triads in which a target instance was equally similar to 2 inductive bases but shared a causal antecedent feature with 1 of them. All 3 age groups used causal relations as a basis for property induction, although the proportion of causal inferences increased with age. Subsequent experiments pitted causal relations against featural similarity in induction. It was found that adults and 8-year-olds, but not 5-year-olds, preferred shared causal relations over strong featural similarity as a basis for induction. The implications for models of inductive reasoning and development are discussed.     

Logical knowledge and ordinary reasoning

This paper argues that the prominent accounts of logical knowledge have the consequence that they conflict with ordinary reasoning. On these accounts knowing a logical principle, for instance, is having a disposition to infer according to it. These accounts in particular conflict with so-called ‘reasoned change in view’, where someone does not infer according to a logical principle but revise their views instead. The paper also outlines a propositional account of logical knowledge which does not conflict with ordinary reasoning.     

Practical reasoning and practical knowledge

The judgement that provides the content of intention and coincides with the conclusion of practical reasoning is a normative judgement about what to do, and not, as Anscombe and McDowell argue, a factual judgement about what one is doing. Treating the conclusion of practical reasoning as expressing a recommendation rather than a verdict undermines McDowell’s argument; the special nature of practical reasoning does not preclude its conclusions being normative. Anscombe’s and McDowell’s claim that practical self-knowledge is productive of action may be accommodated by identifying the content of practical knowledge not with the conclusion but with a premise of practical reasoning – a kind of practical reasoning that occurs within rather than before action.     

Training research in aging on the fluid ability of inductive reasoning

The modifiability of older adults' performance on Induction tasks was examined through cognitive training. The posttraining performance of 52 older adults ($\text{X}\text{age = 70.3}\text{years}$) was assessed with regard to a transfer-of-training paradigm and maintenance of training effects at three posttests (one week, one month, six months). A pattern of differential training transfer across the posttest battery of fluid and crystallized intelligence measures was predicted, with the largest training effects expected for near transfer (Induction) measures. The predicted pattern of training transfer was obtained at one-week and one-month posttests, with significant training effects to the nearest Induction measure. Large retest (practice) effects across posttests also occurred for training and control groups. This research contributes to the position that modifiability of intellectual performance through cognitive intervention extends across the adult life span.     

Predicting the difficulty of complex logical reasoning problems

The aim of the present research was to develop a difficulty model for logical reasoning problems involving complex ordered arrays used in the Graduate Record Examination. The approach used involved breaking down the problems into their basic cognitive elements such as the complexity of the rules used, the number of mental models required to represent the problem, and question type. Weightings for these different elements were derived from two experimental studies and from the reasoning literature. Based on these weights, difficulty models were developed which were then tested against new data. The models had excellent predictive validity and showed the relative influence of rule based factors and factors relating to the number of underlying models. Different difficulty models were needed for different question types, suggesting that people used a variety of approaches and, at a wider level, that both mental models and mental rules may be used in reasoning.     

Deductive and inductive conditional inferences: Two modes of reasoning

A number of single- and dual-process theories provide competing explanations as to how reasoners evaluate conditional arguments. Some of these theories are typically linked to different instructions—namely deductive and inductive instructions. To assess whether responses under both instructions can be explained by a single process, or if they reflect two modes of conditional reasoning, we re-analysed four experiments that used both deductive and inductive instructions for conditional inference tasks. Our re-analysis provided evidence consistent with a single process. In two new experiments we established a double dissociation of deductive and inductive instructions when validity and plausibility of conditional problems were pitted against each other. This indicates that at least two processes contribute to conditional reasoning. We conclude that single-process theories of conditional reasoning cannot explain the observed results. Theories that postulate at least two processes are needed to account for our findings.     

Properties of the diversity effect in category-based inductive reasoning

Four experiments investigated how people judge the plausibility of category-based arguments, focusing on the diversity effect, in which arguments with diverse premise categories are considered particularly strong. In Experiment 1 we show that priming people as to the nature of the blank property determines whether sensitivity to diversity is observed. In Experiment 2 we find that people's hypotheses about the nature of the blank property predict judgements of argument strength. In Experiment 3 we examine the effect of our priming methodology on people's tendency to bring knowledge about causality or similarity to bear when evaluating arguments, and in Experiment 4 we show that whether people's hypotheses about the nature of the blank property were causal predicted ratings of argument strength. Together these results suggest that diversity effects occur because diverse premises lead people to bring general features of the premise categories to mind. Although our findings are broadly consistent with Bayesian and Relevance-based approaches to category-based inductive reasoning, neither approach captures all of our findings.     

Effects of difficulty and diagnosticity on choice among tasks in relation to achievement motivation and perceived ability.

The experiment is a partial replication of a study conducted by Trope. It investigates the effects of two person characteristics (achievement motive and perceived own ability) and two task characteristics (difficulty and diagnostic value about own ability) on choice among achievement tasks. In accordance with the results of Trope, it was found that high-diagnostic tasks were preferred to low-diagnostic tasks, independent of their difficulty. Trope's finding that high resultant achievers choose high-diagnostic tasks over low-diagnostic tasks to a greater extent than low resultant achievers was not replicated. However, the perceived degree of own ability affected choice behavior: When easy and difficult tasks were both high in diagnosticity, subjects high in perceived ability preferred difficult over easy tasks, whereas subjects low in perceived ability preferred easy over difficult tasks. From this latter finding it is concluded that a self-informational conception of choice behavior has to include the subjective probability of success at tasks as a determinant of choice, in addition to objective difficulty and diagnostic value.     

Knowledge, expectations, and inductive reasoning within conceptual hierarchies

Previous research (e.g. Cognition 64 (1997) 73) suggests that the privileged level for inductive inference in a folk biological conceptual hierarchy does not correspond to the “basic” level (i.e. the level at which concepts are both informative and distinct). To further explore inductive inference within conceptual hierarchies, we examine relations between knowledge of concepts at different hierarchical levels, expectations about conceptual coherence, and inductive inference. In Experiments 1 and 2, 5- and 8-year-olds and adults listed features of living kind (Experiments 1 and 2) and artifact (Experiment 2) concepts at different hierarchical levels (e.g. plant, tree, oak, desert oak), and also rated the strength of generalizations to the same concepts. For living kinds, the level that showed a relative advantage on these two tasks differed; the greatest increase in features listed tended to occur at the life-form level (e.g. tree), whereas the greatest increase in inductive strength tended to occur at the folk-generic level (e.g. oak). Knowledge and induction also showed different developmental trajectories. For artifact concepts, the levels at which the greatest gains in knowledge and induction occurred were more varied, and corresponded more closely across tasks. In Experiment 3, adults reported beliefs about within-category similarity for concepts at different levels of animal, plant and artifact hierarchies, and rated inductive strength as before. For living kind concepts, expectations about category coherence predicted patterns of inductions; knowledge did not. For artifact concepts, both knowledge and expectations predicted patterns of induction. Results suggest that beliefs about conceptual coherence play an important role in guiding inductive inference, that this role may be largely independent of specific knowledge of concepts, and that such beliefs are especially important in reasoning about living kinds.     

Training the elderly on the ability factors of spatial orientation and inductive reasoning

We examined the effects of cognitive training with elderly participants from the Seattle Longitudinal Study. Subjects were classified as having remained stable or having declined over the previous 14-year interval on each of two primary abilities, spatial orientation and inductive reasoning. Subjects who had declined on one of these abilities received training on that ability; subjects who had declined on both abilities or who had remained stable on both were randomly assigned to the spatial orientation or inductive reasoning training programs. Training outcomes were examined within an ability-measurement framework with empirically determined factorial structure. Significant training effects, at the level of the latent ability constructs, occurred for both spatial orientation and inductive reasoning. These effects were general, in that no significant interactions with decline status or gender were found. Thus, training interventions were effective both in remediating cognitive decline on the target abilities and in improving the performance of stable subjects.     

ERP characteristics of sentential inductive reasoning in time and frequency domains

Earlier studies have examined the issues of brain spatial localization in human sentential inductive reasoning using PET/fMRI. However, the temporal characteristics of such reasoning remain unclear. In our present study, we have used ERP (Event-related Potential) to further study human inductive reasoning involving sentential tasks. For congruent induction tasks, in which premises and conclusions are related, participants need to synthesize semantic information from the premises, conclusions, as well as background knowledge, while for incongruent induction tasks (baseline), in which premises and conclusions are unrelated, participants can respond “no” immediately. Behavioral data have been obtained that is consistent with expectations. ERPs imply that participants may integrate semantic information within the time window of 350–650 ms. Statistical analysis in the frequency domain has revealed a significant increase in the power of the gamma band (30–50 Hz) for congruent induction tasks in contrast to incongruent induction tasks.