 
Summary: Published as: Aerts, D., Coecke, B., Durt, T. and Valckenborgh, F., 1997, "Quantum,
classical and intermediate I: a model on the PoincarŽe sphere", Tatra Mt. Math. Publ., 10,
241.
Quantum, Classical and Intermediate II : the Vanishing Vector Space Structure.
Diederik Aerts*, Bob Coecke
, Thomas Durt
and Frank Valckenborgh
TENA , Free University of Brussels,
Pleinlaan 2, B1050 Brussels, Belgium.
Abstract. We put forward an approach where physical entities are described by the
set of their states, and the set of their relevant experiments. In this framework we will
study a general entity that is neither quantum nor classical. We show that the collection
of eigenstate sets forms a closure structure on the set of states. We also illustrate this
framework on a concrete physical example, the example. this leads us to a model for a
continuous evolution from the linear closure in vector space to the standard topological
closure.
1. Introduction.
It is well known that classical theories and quantum theories are structurally completely dif
ferent (Boolean versus nonBoolean, commutative versus noncommutative, Kolmogorovian
versus nonKolmogorovian). In the field of the more general approaches (lattice theories, *al
