Quantum structure in cognition

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236 Citations (Scopus)

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 Delta-type, which is the non classicality of the 'guppy effect' or of Hampton's over - or underextension; (iii) non classical of the k-type, 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 k-type 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 Delta-type 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 languageEnglish
Pages (from-to)314-348
Number of pages34
JournalJournal of Mathematical Psychology
Volume53
Issue number5
Publication statusPublished - 2009

Keywords

  • cognition
  • quantum structures
  • guppy effect
  • concept modeling
  • interference
  • combinations of concepts

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