A Rational Analysis of Rule‐Based Concept Learning

Goodman, Noah D.; Tenenbaum, Joshua B.; Feldman, Jacob; Griffiths, Thomas L.

doi:10.1080/03640210701802071

Cited by 316 publications

(394 citation statements)

References 62 publications

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“…The most likely candidates are SUSTAIN, which, given its representation of concepts in terms of separable clusters, shares a broad conceptual similarity with the model theory, and algebraic complexity, which Feldman (2006) describes as the analytic counterpart of SUSTAIN. A recent rule-based approach to concept learning is due to Goodman, Tenenbaum, Feldman, and Griffiths (2008). It uses rational rules and also has some similarity to the model theory.…”

Section: Discussionmentioning

confidence: 99%

Mental models of Boolean concepts

Goodwin

Johnson‐Laird

2011

Cognitive Psychology

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a b s t r a c tNegation, conjunction, and disjunction are major building blocks in the formation of concepts. This article presents a new model-based theory of these Boolean components. It predicts that individuals simplify the models of instances of concepts. Evidence corroborates the theory and challenges alternative accounts, such as those based on minimal descriptions, algebraic complexity, or structural invariance. A computer program implementing the theory yields more accurate predictions than these rival accounts. Two experiments showed that the numbers of models of a Boolean concept predict the difficulty of formulating a description of it. As mental models may also underlie deductive reasoning, the present theory integrates two hitherto separate areas of investigation.

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Section: Discussionmentioning

confidence: 99%

Mental models of Boolean concepts

Goodwin

Johnson‐Laird

2011

Cognitive Psychology

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“…Our framework has room for many kinds of structures and stochastic processes, and these components can be combined to capture many kinds of background knowledge and to provide many different inductive biases. We described four specific applications of our framework, but our framework also has room for models that rely on theories more complex than any of the examples presented here, including theories formulated using grammars (N. D. Goodman, 57 Tenenbaum, Feldman, & Griffiths, 2008) or logical representations (Kemp, Goodman, & Tenenbaum, 2008). …”

Section: Specific Modelsmentioning

confidence: 99%

Structured statistical models of inductive reasoning.

Kemp¹,

Tenenbaum²

2009

Psychological Review

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226

282

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Everyday inductive inferences are often guided by rich background knowledge. Formal models of induction should aim to incorporate this knowledge, and should explain how different kinds of knowledge lead to the distinctive patterns of reasoning found in different inductive contexts. We present a Bayesian framework that attempts to meet both goals and describe four applications of the framework: a taxonomic model, a spatial model, a threshold model, and a causal model. Each model makes probabilistic inferences about the extensions of novel properties, but the priors for the four models are defined over different kinds of structures that capture different relationships between the categories in a domain. Our framework therefore shows how statistical inference can operate over structured background knowledge, and we argue that this interaction between structure and statistics is critical for explaining the power and flexibility of human reasoning. 2 Structured statistical models of inductive reasoningHumans are adept at making inferences that take them beyond the limits of their direct experience. Even young children can learn the meaning of a novel word from a single labeled example (Heibeck & Markman, 1987), predict the trajectory of a moving object when it passes behind an occluder (Spelke, 1990), and choose a gait that allows them to walk over terrain they have never before encountered. Inferences like these may differ in many respects, but common to them all is the need to "go beyond the information given" (Bruner, 1973).Two different ways of going beyond the available information can be distinguished.Deductive inferences draw out conclusions that may have been previously unstated but were implicit in the data provided. Inductive inferences go beyond the available data in a more fundamental way, and arrive at conclusions that are likely but not certain given the available evidence. Both kinds of inferences are of psychological interest, but inductive inferences appear to play a more central role in everyday cognition. We have already seen examples related to language, vision, and motor control, and many other inductive problems have been described in the literature (Holland, Holyoak, Nisbett, & Thagard, 1986;Anderson, 1990). This paper describes a formal approach to inductive inference that should apply to many different problems, but we will focus on the problem of property induction (Sloman & Lagnado, 2005). In particular, we consider cases where one or more more categories in a domain are observed to have a novel property, and the inductive task is to predict how the property is distributed over the remaining categories in the domain. For instance, given that bears have sesamoid bones, which species is more likely to share this property: moose or salmon (Rips, 1975; Osherson, Smith, Wilkie, Lopez, & Shafir, 1990)? Moose may seem like the better choice since they are more similar biologically to bears, but different properties can lead to different patterns of inference. For example, given that a c...

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“…Nosofsky, Palemeri, & McKinley, 1994;Goodman, Tenenbaum, Feldman, & Griffiths, 2008), inferring prototypes (e.g. Posner & Keele, 1968), storing exemplars (e.g.…”

Section: Previous Approaches To Category Learningmentioning

confidence: 99%

A probabilistic model of cross-categorization

et al. 2011

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Most natural domains can be represented in multiple ways: we can categorize foods in terms of their nutritional content or social role, animals in terms of their taxonomic groupings or their ecological niches, and musical instruments in terms of their taxonomic categories or social uses. Previous approaches to modeling human categorization have largely ignored the problem of cross-categorization, focusing on learning just a single system of categories that explains all of the features. Cross-categorization presents a difficult problem: how can we infer categories without first knowing which features the categories are meant to explain? We present a novel model that suggests that human cross-categorization is a result of joint inference about multiple systems of categories and the features that they explain. We also formalize two commonly proposed alternative explanations for cross-categorization behavior: a features-first and an objects-first approach. The features-first approach suggests that cross-categorization is a consequence of attentional processes, where features are selected by an attentional mechanism first and categories are derived second. The objects-first approach suggests that crosscategorization is a consequence of repeated, sequential attempts to explain features, where categories are derived first, then features that are poorly explained are recategorized. We present two sets of simulations and experiments testing the models' predictions about human categorization. We find that an approach based on joint inference provides the best fit to human categorization behavior, and we suggest that a full account of human category learning will need to incorporate something akin to these capabilities.People explain different aspects of everyday objects in different ways. For example, steak is high in iron because it is a meat; however, it is often served with wine because it is a dinner food. The different ways of thinking about steak underscore different ways of thinking about the domain of foods: as a system of taxonomic categories including meats and vegetables, or as a system of

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A Rational Analysis of Rule‐Based Concept Learning

Cited by 316 publications

References 62 publications

Mental models of Boolean concepts

Mental models of Boolean concepts

Structured statistical models of inductive reasoning.

A probabilistic model of cross-categorization

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