---
abstract: "We propose a theory for modeling concepts that uses the state-context-property theory (SCOP), a generalization of the quantum formalism, whose basic notions are states, contexts and properties. This theory enables us to incorporate context into the mathematical structure used to describe a concept, and thereby model how context influences the typicality of a single exemplar and the applicability of a single property of a concept. We introduce the notion `state of a concept' to account for this contextual influence, and show that the structure of the set of contexts and of the set of properties of a concept is a complete orthocomplemented lattice. The structural study in this article is a preparation for a numerical mathematical theory of concepts in the Hilbert space of quantum mechanics that allows the description of the combination of concepts."
altloc:
  - http://repositories.cdlib.org/postprints/537
chapter: ~
commentary: ~
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conference: ~
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contact_email: ~
creators_id: []
creators_name:
  - family: Aerts
    given: Diederik
    honourific: ''
    lineage: ''
  - family: Gabora
    given: Liane
    honourific: ''
    lineage: ''
date: 2005
date_type: published
datestamp: 2006-03-16
department: ~
dir: disk0/00/00/47/70
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editors_id: []
editors_name:
  - family: Riegler
    given: Alexander
    honourific: ''
    lineage: ''
eprint_status: archive
eprintid: 4770
fileinfo: /style/images/fileicons/application_pdf.png;/4770/1/hvf1.pdf
full_text_status: public
importid: ~
institution: ~
isbn: ~
ispublished: pub
issn: ~
item_issues_comment: []
item_issues_count: 0
item_issues_description: []
item_issues_id: []
item_issues_reported_by: []
item_issues_resolved_by: []
item_issues_status: []
item_issues_timestamp: []
item_issues_type: []
keywords: 'concept, conjunction, combination, context, entanglement, exemplar, mathematical model, prototype, potentiality, quantum, representation, state, structure'
lastmod: 2011-03-11 08:56:21
latitude: ~
longitude: ~
metadata_visibility: show
note: ~
number: ~
pagerange: 167-191
pubdom: TRUE
publication: Kybernetes
publisher: Emerald
refereed: TRUE
referencetext: ~
relation_type: []
relation_uri: []
reportno: ~
rev_number: 12
series: ~
source: ~
status_changed: 2007-09-12 17:02:21
subjects:
  - cog-psy
  - phil-mind
  - comp-sci-art-intel
succeeds: ~
suggestions: ~
sword_depositor: ~
sword_slug: ~
thesistype: ~
title: "A theory of concepts and their combinations I: The structure of the sets of contexts and properties\n"
type: journalp
userid: 352
volume: 34
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