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Contextualizing concepts using a mathematical generalization of the quantum formalism

Gabora, Liane and Aerts, Diederik (2002) Contextualizing concepts using a mathematical generalization of the quantum formalism. [Journal (Paginated)]

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Abstract

We outline the rationale and preliminary results of using the State Context Property (SCOP) formalism, originally developed as a generalization of quantum mechanics, to describe the contextual manner in which concepts are evoked, used, and combined to generate meaning. The quantum formalism was developed to cope with problems arising in the description of (1) the measurement process, and (2) the generation of new states with new properties when particles become entangled. Similar problems arising with concepts motivated the formal treatment introduced here. Concepts are viewed not as fixed representations, but entities existing in states of potentiality that require interaction with a context---a stimulus or another concept---to `collapse' to observable form as an exemplar, prototype, or other (possibly imaginary) instance. The stimulus situation plays the role of the measurement in physics, acting as context that induces a change of the cognitive state from superposition state to collapsed state. The collapsed state is more likely to consist of a conjunction of concepts for associative than analytic thought because more stimulus or concept properties take part in the collapse. We provide two contextual measures of conceptual distance---one using collapse probabilities and the other weighted properties---and show how they can be applied to conjunctions using the pet fish problem.

Item Type:Journal (Paginated)
Keywords:analytical thought, associative thought, collapse, concept, conjunction, context, entanlement, exemplar, mathematical model, prototype, potentiality, quantum, representation, state, structure
Subjects:Psychology > Cognitive Psychology
Philosophy > Philosophy of Mind
Computer Science > Artificial Intelligence
ID Code:2725
Deposited By:Gabora, Dr. Liane
Deposited On:09 Feb 2004
Last Modified:11 Mar 2011 08:55

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