 
Summary: A Theory of Concepts and Their Combinations I:
The Structure of the Sets of Contexts and Properties
Diederik Aerts
Center Leo Apostel for Interdisciplinary Studies
Department of Mathematics and Department of Psychology
Vrije Universiteit Brussel, 1160 Brussels, Belgium
EMail: diraerts@vub.ac.be
Liane Gabora
Center Leo Apostel for Interdisciplinary Studies
Vrije Universiteit Brussel and Department of Psychology
University of California, Berkeley, CA 947201650, USA
EMail: liane@berkeley.edu
Abstract
We propose a theory for modeling concepts that uses the statecontextproperty theory (SCOP), a gener
alization 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 orthocomple
mented lattice. The structural study in this article is a preparation for a numerical mathematical theory of
