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A theory of concepts and their combinations II: A Hilbert space representation

Aerts, Diederik and Gabora, Liane (2005) A theory of concepts and their combinations II: A Hilbert space representation. [Journal (Paginated)]

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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.

Item Type:Journal (Paginated)
Keywords:concept, combination, conjunction, context, entanglement, exemplar, Hilbert space, mathematical model, prototype, potentiality, quantum, representation, state, structure
Subjects:Psychology > Cognitive Psychology
Philosophy > Philosophy of Mind
Computer Science > Artificial Intelligence
ID Code:4771
Deposited By:Gabora, Dr. Liane
Deposited On:16 Mar 2006
Last Modified:11 Mar 2011 08:56

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