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Categorical invariance and structural complexity in human concept learning

Vigo, Professor Ronaldo (2009) Categorical invariance and structural complexity in human concept learning. [Journal (Paginated)]

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Abstract

An alternative account of human concept learning based on an invariance measure of the categorical stimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural complexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or size. To do this we introduce a mathematical framework based on the notion of a Boolean differential operator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the category in respect to its dimensions. Using this framework, we propose that the structural complexity of a Boolean category is indirectly proportional to its degree of categorical invariance and directly proportional to its cardinality or size. Consequently, complexity and invariance notions are formally unified to account for concept learning difficulty. Beyond developing the above unifying mathematical framework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of the SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications. Psychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three binary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the degree of learning difficulty of a large class of categories (in particular, the 41 category types studied by Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature, 407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of categories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g., cognitively tractable).

Item Type:Journal (Paginated)
Keywords:Concept learning Categorization Rule-based classification Logical manifold Categorical invariance Logical invariance Structural complexity Boolean complexity Invariance Complexity Concepts
Subjects:Psychology > Cognitive Psychology
Computer Science > Artificial Intelligence
Computer Science > Complexity Theory
Computer Science > Machine Learning
Psychology > Perceptual Cognitive Psychology
Philosophy > Logic
Psychology > Psychophysics
ID Code:7132
Deposited By:Vigo, Professor Ronaldo
Deposited On:22 Nov 2010 14:17
Last Modified:11 Mar 2011 08:57

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