TY - GEN ID - cogprints4770 UR - http://cogprints.org/4770/ A1 - Aerts, Diederik A1 - Gabora, Liane Y1 - 2005/// N2 - 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. PB - Emerald KW - concept KW - conjunction KW - combination KW - context KW - entanglement KW - exemplar KW - mathematical model KW - prototype KW - potentiality KW - quantum KW - representation KW - state KW - structure TI - A theory of concepts and their combinations I: The structure of the sets of contexts and properties SP - 167 AV - public EP - 191 ER -