---
abstract: "An alternative account of human concept learning based on an invariance measure of the categorical\r\nstimulus is proposed. The categorical invariance model (CIM) characterizes the degree of structural\r\ncomplexity of a Boolean category as a function of its inherent degree of invariance and its cardinality or\r\nsize. To do this we introduce a mathematical framework based on the notion of a Boolean differential\r\noperator on Boolean categories that generates the degrees of invariance (i.e., logical manifold) of the\r\ncategory in respect to its dimensions. Using this framework, we propose that the structural complexity\r\nof a Boolean category is indirectly proportional to its degree of categorical invariance and directly\r\nproportional to its cardinality or size. Consequently, complexity and invariance notions are formally\r\nunified to account for concept learning difficulty. Beyond developing the above unifying mathematical\r\nframework, the CIM is significant in that: (1) it precisely predicts the key learning difficulty ordering of\r\nthe SHJ [Shepard, R. N., Hovland, C. L.,&Jenkins, H. M. (1961). Learning and memorization of classifications.\r\nPsychological Monographs: General and Applied, 75(13), 1-42] Boolean category types consisting of three\r\nbinary dimensions and four positive examples; (2) it is, in general, a good quantitative predictor of the\r\ndegree of learning difficulty of a large class of categories (in particular, the 41 category types studied\r\nby Feldman [Feldman, J. (2000). Minimization of Boolean complexity in human concept learning. Nature,\r\n407, 630-633]); (3) it is, in general, a good quantitative predictor of parity effects for this large class of\r\ncategories; (4) it does all of the above without free parameters; and (5) it is cognitively plausible (e.g.,\r\ncognitively tractable)."
altloc: []
chapter: ~
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contact_email: ~
creators_id:
- vigo@ohio.edu
creators_name:
- family: Vigo
given: Ronaldo
honourific: Professor
lineage: ''
date: 2009-06-10
date_type: published
datestamp: 2010-11-22 14:17:28
department: ~
dir: disk0/00/00/71/32
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eprint_status: archive
eprintid: 7132
fileinfo: /style/images/fileicons/application_pdf.png;/7132/1/Vigo_Invariance.pdf
full_text_status: public
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keywords: "Concept learning\r\nCategorization\r\nRule-based classification\r\nLogical manifold\r\nCategorical invariance\r\nLogical invariance\r\nStructural complexity\r\nBoolean complexity\r\nInvariance\r\nComplexity\r\nConcepts\r\n\r\n"
lastmod: 2011-03-11 08:57:49
latitude: ~
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metadata_visibility: show
note: ~
number: 4
pagerange: 203-221
pubdom: FALSE
publication: Journal of Mathematical Psychology
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refereed: TRUE
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relation_type: []
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reportno: ~
rev_number: 36
series: ~
source: ~
status_changed: 2010-11-22 14:17:28
subjects:
- cog-psy
- comp-sci-art-intel
- comp-sci-complex-theory
- comp-sci-mach-learn
- percep-cog-psy
- phil-logic
- psy-phys
succeeds: ~
suggestions: ~
sword_depositor: ~
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thesistype: ~
title: Categorical invariance and structural complexity in human concept learning
type: journalp
userid: 8925
volume: 53