How do people learn from negative evidence? Non-monotonic generalizations and sampling assumptions in inductive reasoning (original) (raw)
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Negative evidence and inductive generalisation
Thinking & Reasoning, 2007
How do people use past experience to generalise to novel cases? This paper reports four experiments exploring the significance on one class of past experiences: encounters with negative or contrasting cases. In trying to decide whether all ravens are black, what is the effect of learning about a non-raven that is not black? Two experiments with preschool-aged, young school-aged, and adult participants revealed that providing a negative example in addition to a positive example supports generalisation. Two additional experiments went on to ask which kinds of negative examples offer the most support for generalisations. These studies contrasted similarity-based and category-based accounts of inductive generalisation. Results supported category-based predictions, but only for preschool-aged children. Overall, the younger children showed a greater reliance on negative evidence than did older children and adults. Most things we encounter in the world are negative evidence for our generalisations. Understanding the role of negative evidence is central for psychological theories of inductive generalisation.
Raising argument strength using negative evidence: a constraint on models of induction
Memory & Cognition, 2011
Both intuitively, and according to similaritybased theories of induction, relevant evidence raises argument strength when it is positive and lowers it when it is negative. In three experiments, we tested the hypothesis that argument strength can actually increase when negative evidence is introduced. Two kinds of argument were compared through forced choice or sequential evaluation: single positive arguments (e.g., "Shostakovich's music causes alpha waves in the brain; therefore, Bach's music causes alpha waves in the brain") and double mixed arguments (e.g., "Shostakovich's music causes alpha waves in the brain, X's music DOES NOT; therefore, Bach's music causes alpha waves in the brain"). Negative evidence in the second premise lowered credence when it applied to an item X from the same subcategory (e.g., Haydn) and raised it when it applied to a different subcategory (e.g., AC/DC). The results constitute a new constraint on models of induction.
An Analysis of Psychological Experiments on Non-Monotonic Reasoning
ABSTRACT Since hardly any of people's everyday decisions are made,with certainty, it is often necessary to retract earlier conclusions on the basis of new input. This aspect of common-sense reasoning in humans,is often cited as a raison d'dtre for non-monotonic theories. Going beyond this intuitive notion, this paper is based on well-documented psychological experiments. In these experiments it turns out that inferences are often remarkably unresponsive to new,input even,if the original basis for the inferences is discredited. The focus in the present paper, therefore, is on modeling this pervasive, yet counter-intuitive retraction behavior.
Various learning theories stress the importance of negative learning (e.g., Bruner, 1959;. However, the effects of negative premises have rarely been discussed in any detail within theories of inductive reasoning (with the exception of . Although have proposed some computational models that can cope with negative premises and verified their psychological validity, they did not consider cases where category-based induction theory is ineffective, such as when the entities in both negative and positive premises belong to the same category. The present study was conducted to test the hypothesis that, even when negative and positive premises involve same-category entities, people can estimate the likeliness of an argument conclusion by comparing feature similarities. Based on this hypothesis, two computational models are proposed to simulate this cognitive mechanism. While both these models were able to simulate the results obtained from the psychological experiment, a perceptron model could not. Finally, we argue that the mathematical equivalence (from Support Vector Machines perspective) of these two models suggests that they represent a promising approach to modeling the effects of negative premises, and, thus, to fully handling the complexities of feature-based induction on neural networks.
The relevance framework for category-based induction: Evidence from garden-path arguments
2010
Relevance theory suggests that people expend cognitive effort when processing information in proportion to the cognitive effects to be gained from doing so. This theory has been used to explain how people apply their knowledge appropriately when evaluating category-based inductive arguments . In such arguments, people are told that a property is true of premise categories and are asked to evaluate the likelihood that it is also true of conclusion categories. According to the relevance framework, reasoners generate hypotheses about the relevant relation between the categories in the argument. We reasoned that premises inconsistent with early hypotheses about the relevant relation would have greater effects than consistent premises. We designed three premise garden-path arguments where the same 3rd premise was either consistent or inconsistent with likely hypotheses about the relevant relation. In Experiments 1 and 2, we showed that effort expended processing consistent premises (measured via reading times) was significantly less than effort expended on inconsistent premises. In Experiment 2 and 3, we demonstrated a direct relation between cognitive effect and cognitive effort. For garden-path arguments, belief change given inconsistent 3rd premises was significantly correlated with Premise 3 (Experiment 3) and conclusion (Experiments 2 and 3) reading times. For consistent arguments, the correlation between belief change and reading times did not approach significance. These results support the relevance framework for induction but are difficult to accommodate under other approaches.
A considerable amount of work has focused on the processes that underlie children's inductive reasoning. For instance, numerous studies explored the role of linguistic labels, perceptual similarity, and children's beliefs in generalization of properties to novel cases. The present studies investigated an aspect of induction that has received considerably less attention in prior developmental research, namely-the effect of the statistical properties of evidence on inductive reasoning. Studies presented below were motivated by the hypothesis that induction involves an evaluation of the statistical properties available in the evidence. From this perspective, sample size, or the amount of available evidence, should influence inductive reasoning. Sample size effects were investigated in three experiments with 90 5-year-olds and 90 adults. Results indicated that children made higher rate of projections for larger than smaller samples, particularly when samples were represented by a set of diverse exemplars.
Descriptive and Inferential Problems of Induction: Toward a Common Framework
There are many accounts of how humans make inductive inferences. Two broad classes of accounts are characterized as “theory based” or “similarity based.” This distinction has organized a substantial amount of empirical work in the field, but the exact dimensions of contrast between the accounts are not always clear. Recently, both accounts have used concepts from formal statistics and theories of statistical learning to characterize human inductive inference. We extend these links to provide a unified perspective on induction based on the relation between descriptive and inferential statistics. Most work in Psychology has focused on descriptive problems: Which patterns do people notice or represent in experience? We suggest that it is solutions to the inferential problem of generalizing or applying those patterns that reveals the more fundamental distinction between accounts of human induction. Specifically, similarity-based accounts imply that people make transductive inferences, while theory-based accounts imply that people make evidential inferences. In characterizing claims about descriptive and inferential components of induction, we highlight points of agreement and disagreement between alternative accounts. Adopting the common framework of statistical inference also motivates a set of empirical hypotheses about inductive inference and its development across age and experience. The common perspective of statistical inference reframes debates between theory-based and similarity-based accounts: These are not conflicting theoretical perspectives, but rather different predictions about empirical results.