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Abstract
Similar to the 'guppy effect' identified in Osherson and Smith (1981), Hampton (1988a,b) measures substantial deviations from classical fuzzy set and probability models for membership weights for conjunction and disjunction, and calls them respectively 'overextension' and 'underextension'. We identify two types of non classical data and prove that membership weights of a specific item are (i) classical; (ii) non classical of the Deltatype, which is the non classicality of the 'guppy effect' or of Hampton's over  or underextension; (iii) non classical of the ktype, which is a new type of non classicality not identified before. We introduce a quantum mechanical formalism, where items are represented by vectors and concepts by subspaces of a vector space, and prove that classical items and non classical items of the ktype can be modeled within this quantum mechanical formalism, i.e. the vectors and subspaces plus the proper quantum calculation rules reproduce the experimental data of Hampton (1988a,b). We show that to represent also the Deltatype non classical items extra aspects of the quantum mechanical formalism need to be introduced, namely those aspects that make it possible to represent the formation of a new concept. An interpretation of this complete quantum mechanical representation leads us to propose a specific cognitive thought mechanism, containing a 'classical logical part', for which membership weights are classical, they would result if only this part would take place, and a 'quantum conceptual part', for which membership weights are non classical, they would result if only this part would take place.
Original language  English 

Pages (fromto)  314348 
Number of pages  34 
Journal  Journal of Mathematical Psychology 
Volume  53 
Issue number  5 
Publication status  Published  2009 
Keywords
 cognition
 quantum structures
 guppy effect
 concept modeling
 interference
 combinations of concepts
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Dive into the research topics of 'Quantum structure in cognition'. Together they form a unique fingerprint.Projects
 2 Finished

FWOAL230: Development of a contextual theory for concepts.
Aerts, D., Gabora, L., Aerts, D. & Storms, G.
1/01/02 → 31/12/05
Project: Fundamental
Activities
 1 Membership of external research organisation

Unknown (External organisation)
Diederik Aerts (Member)
1 Jan 2002 → 31 Dec 2005Activity: Membership › Membership of external research organisation