--- abstract: "Invariance principles underlie many key theories in modern science. They provide the explanatory and predictive framework necessary for the rigorous study of natural phenomena ranging from the structure of crystals, to magnetism, to relativistic mechanics. Vigo (2008, 2009)introduced a new general notion and principle of invariance from which two parameter-free (ratio and exponential) models were derived to account for human conceptual behavior. Here we introduce a new parameterized \r\nexponential “law” based on the same invariance principle. The law accurately predicts the subjective degree of difficulty that humans experience when learning different types of concepts. In addition, it precisely fits the data from a large-scale experiment which examined a total of 84 category structures across 10 category families (R-Squared =.97, p < .0001; r= .98, p < .0001). Moreover, it overcomes seven key challenges that had, hitherto, been grave obstacles for theories of concept learning." altloc: [] chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ contact_email: ~ creators_id: - vigo@ohio.edu creators_name: - family: Vigo given: Ronaldo honourific: Professor lineage: '' date: 2011-07 date_type: published datestamp: 2012-11-09 17:47:35 department: ~ dir: disk0/00/00/79/60 edit_lock_since: ~ edit_lock_until: 0 edit_lock_user: ~ editors_id: [] editors_name: [] eprint_status: archive eprintid: 7960 fileinfo: application/pdf;http://cogprints.org/7960/7/Vigo%20(2011a).pdf full_text_status: public importid: ~ institution: ~ isbn: ~ ispublished: pub issn: ~ item_issues_comment: [] item_issues_count: ~ item_issues_description: [] item_issues_id: [] item_issues_reported_by: [] item_issues_resolved_by: [] item_issues_status: [] item_issues_timestamp: [] item_issues_type: [] keywords: "Concepts; concept learning; categorization; law of \r\ninvariance; mathematical model; pattern perception; ideotype." lastmod: 2012-11-09 17:47:35 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: 2580-2585 pubdom: TRUE publication: 'Proceedings of the 33rd Annual Meeting of the Cognitive Science Society ' publisher: 'Cognitive Science Society ' refereed: TRUE referencetext: "Bourne, L. E. (1966). Human conceptual behavior. Boston: \r\nAllyn and Bacon.\r\nEstes, W. K. (1994). Classification and Cognition. Oxford \r\nPsychology Series, 22, Oxford University Press, Oxford.\r\nFeldman, J. (2000). Minimization of Boolean complexity in \r\nhuman concept learning. Nature, 407, 630-633.\r\nGarner, W. R. (1970). Good patterns have few alternatives. \r\nAmerican Scientist, 58, 34-42.\r\nGarner, W. R. (1974). The processing of information and \r\nstructure. New York: Wiley.\r\nGibson, J. J. (1966). The senses considered as perceptual \r\nsystems. Boston: Houghton Mifflin.\r\nHaygood, R. C., & Bourne, L. E., Jr. (1965). Attribute-andrule learning aspects of conceptual behavior. Psychological \r\nReview, 72, 175-195.\r\nKruschke, J. K. (1992). ALCOVE: An exemplar-based \r\nconnectionist model of category learning. Psychological \r\nReview, 99, 22-44.\r\nLove, B. C., and Medin, D. L. (1998). SUSTAIN: A model of \r\nhuman category learning. Proceedings of the Fifteenth \r\nNational Conference on Artificial Intelligence, 15, 671-676.\r\nMurphy, G. L. (2002). The big book of concepts. MIT Press.\r\nNosofsky, R. M. (1984). Choice, similarity, and the context \r\ntheory of classification. Journal of Experimental Psychology: \r\nLearning, Memory, and Cognition, 10(1), 104-114.\r\nNosofsky, R. M. (1991). Typicality in logically defined \r\ncategories: Exemplar-similarity versus rule instantiation. \r\nMemory and Cognition, 19(2), 131-150. \r\nShepard, R. N., Hovland, C. L., & Jenkins, H. M. (1961). \r\nLearning and memorization of classifications. Psychological \r\nMonographs: General and Applied, 75(13), 1-42.\r\nVigo, R. (2006). A note on the complexity of Boolean \r\nconcepts. Journal of Mathematical Psychology, 50(5), 1-10.\r\nVigo, R. (2009). Categorical invariance and structural \r\ncomplexity in human concept learning. Journal of \r\nMathematical Psychology, Vol. 53, 203-221.\r\nVigo, R. (2011). Towards a General Law of Human \r\nConceptual Behavior (under review, contact the author for a \r\ncopy)" relation_type: [] relation_uri: [] reportno: ~ rev_number: 24 series: ~ source: ~ status_changed: 2012-01-24 17:58:52 subjects: - appl-cog-psy - 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: ~ sword_slug: ~ thesistype: ~ title: Towards a Law of Invariance in Human Concept Learning type: journalp userid: 15877 volume: ~