creators_name: Aerts, Diederik creators_name: Gabora, Liane editors_name: Riegler, Alexander type: journalp datestamp: 2006-03-16 lastmod: 2011-03-11 08:56:21 metadata_visibility: show title: A theory of concepts and their combinations II: A Hilbert space representation ispublished: pub subjects: cog-psy subjects: phil-mind subjects: comp-sci-art-intel full_text_status: public keywords: concept, combination, conjunction, context, entanglement, exemplar, Hilbert space, mathematical model, prototype, potentiality, quantum, representation, state, structure 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. date: 2005 date_type: published publication: Kybernetes volume: 34 publisher: Emerald pagerange: 192-221 refereed: TRUE citation: Aerts, Diederik and Gabora, Liane (2005) A theory of concepts and their combinations II: A Hilbert space representation. [Journal (Paginated)] document_url: http://cogprints.org/4771/1/hvf2.pdf