@misc{cogprints7132,
volume = {53},
number = {4},
month = {June},
author = {Professor Ronaldo Vigo},
title = {Categorical invariance and structural complexity in human concept learning},
journal = {Journal of Mathematical Psychology},
pages = {203--221},
year = {2009},
keywords = {Concept learning
Categorization
Rule-based classification
Logical manifold
Categorical invariance
Logical invariance
Structural complexity
Boolean complexity
Invariance
Complexity
Concepts
},
url = {http://cogprints.org/7132/},
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).}
}