  We propose a theory for modeling concepts that uses the
state-context-property 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 (see quant-ph/0402205)
