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 I: The structure of the sets of contexts and properties ispublished: pub subjects: cog-psy subjects: phil-mind subjects: comp-sci-art-intel full_text_status: public keywords: concept, conjunction, combination, context, entanglement, exemplar, mathematical model, prototype, potentiality, quantum, representation, state, structure 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. date: 2005 date_type: published publication: Kybernetes volume: 34 publisher: Emerald pagerange: 167-191 refereed: TRUE citation: Aerts, Diederik and Gabora, Liane (2005) A theory of concepts and their combinations I: The structure of the sets of contexts and properties. [Journal (Paginated)] document_url: http://cogprints.org/4770/1/hvf1.pdf