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We propose a theory for modeling concepts that uses the statecontextproperty 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.
 http://repositories.cdlib.org/postprints/537

Aerts
Diederik

Gabora
Liane

Riegler
Alexander
pub
concept, conjunction, combination, context, entanglement, exemplar, mathematical model, prototype, potentiality, quantum, representation, state, structure
167191
TRUE
Kybernetes
Emerald
TRUE
 cogpsy
 philmind
 compsciartintel
A theory of concepts and their combinations I: The structure of the sets of contexts and properties
34
published
2005
public