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--- abstract: "The sets of contexts and properties of a concept are embedded in the complex Hilbert space of quantum mechanics. States are unit vectors or density operators, and contexts and properties are orthogonal projections. The way calculations are done in Hilbert space makes it possible to model how context influences the state of a concept. Moreover, a solution to the combination of concepts is proposed. Using the tensor product, a procedure for describing combined concepts is elaborated, providing a natural solution to the pet fish problem. This procedure allows the modeling of an arbitrary number of combined concepts. By way of example, a model for a simple sentence containing a subject, a predicate and an object, is presented. \n" altloc: - http://repositories.cdlib.org/postprints/538 chapter: ~ commentary: ~ commref: ~ confdates: ~ conference: ~ confloc: ~ 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: disk0/00/00/47/71 edit_lock_since: ~ edit_lock_until: ~ edit_lock_user: ~ editors_id: [] editors_name: - family: Riegler given: Alexander honourific: '' lineage: '' eprint_status: archive eprintid: 4771 fileinfo: /style/images/fileicons/application_pdf.png;/4771/1/hvf2.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, combination, conjunction, context, entanglement, exemplar, Hilbert space, mathematical model, prototype, potentiality, quantum, representation, state, structure' lastmod: 2011-03-11 08:56:21 latitude: ~ longitude: ~ metadata_visibility: show note: ~ number: ~ pagerange: 192-221 pubdom: TRUE publication: Kybernetes publisher: Emerald refereed: TRUE referencetext: ~ relation_type: [] relation_uri: [] reportno: ~ rev_number: 12 series: ~ source: ~ status_changed: 2007-09-12 17:02:22 subjects: - cog-psy - phil-mind - comp-sci-art-intel succeeds: ~ suggestions: ~ sword_depositor: ~ sword_slug: ~ thesistype: ~ title: 'A theory of concepts and their combinations II: A Hilbert space representation' type: journalp userid: 352 volume: 34