  We elaborate a theory for the modeling of concepts using the mathematical
structure of quantum mechanics. Concepts are represented by vectors in the
complex Hilbert space of quantum mechanics and membership weights of items are
modeled by quantum weights calculated following the quantum rules. We apply
this theory to model the disjunction of concepts and show that experimental
data of membership weights of items with respect to the disjunction of concepts
can be modeled accurately. It is the quantum effects of interference and
superposition, combined with an effect of context, that are at the origin of
the effects of overextension and underextension observed as deviations from a
classical use of the disjunction. We put forward a graphical explanation of the
effects of overextension and underextension by interpreting the quantum model
applied to the modeling of the disjunction of concepts.
