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TY - GEN ID - cogprints4771 UR - http://cogprints.org/4771/ A1 - Aerts, Diederik A1 - Gabora, Liane Y1 - 2005/// N2 - 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. PB - Emerald KW - concept KW - combination KW - conjunction KW - context KW - entanglement KW - exemplar KW - Hilbert space KW - mathematical model KW - prototype KW - potentiality KW - quantum KW - representation KW - state KW - structure TI - A theory of concepts and their combinations II: A Hilbert space representation SP - 192 AV - public EP - 221 ER -