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I've read many papers on concepts, but their tests are sparsely described or abstractly mentioned. I want to test for classic, prototype and exemplar theories. How do you approach the problem?

Some publications I've read:

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 A Generalization of Hebbian Learning in Perceptual and Conceptual 
 Categorization
 Family resemblance : Internal structure of categaries
 Categorization of Natural Objects
 Reclaiming Concepts
 Categories, Concepts, Fuzzy Sets, and Logical Deduction
 Principals of Categorization
 Basic objects in natural categories
 Concept and conceptual structure
 http://www.foundalis.com/res/poc/PrinciplesOfCognition.htm
 https://www.iep.utm.edu/concepts/#H3
 .... and many more.

most of them are from Eleanor Rosch, ..

Reading also the big book on concepts


this seem to be informative :

Category norms: An updated and expanded version of the Battig and Montague (1969) norms http://www.lcs.pomona.edu/HewlettCognitiveScience/resources/assets/CategoryNorms2004.pdf

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There's no one good answer to this unfortunately, the question is too broad. Seems like you have made a decent start, here are two more quite different methods-focused references to add to your reading that might help:

Divjak, Dagmar, and Antti Arppe. "Extracting prototypes from exemplars What can corpus data tell us about concept representation?." (2013): 221-274.

Lee, Michael D., and Wolf Vanpaemel. "Exemplars, prototypes, similarities, and rules in category representation: An example of hierarchical Bayesian analysis." Cognitive Science 32.8 (2008): 1403-1424.

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