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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
E-Mail: diraerts@vub.ac.be
Liane Gabora
Center Leo Apostel for Interdisciplinary Studies
Vrije Universiteit Brussel and Department of Psychology
University of California, Berkeley, CA 94720-1650, USA
E-Mail: liane@berkeley.edu
Abstract
We propose a theory for modeling concepts that uses the state-context-property 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
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