  The concept of complementarity in combination with a non-Boolean calculus of
propositions refers to a pivotal feature of quantum systems which has long been
regarded as a key to their distinction from classical systems. But a
non-Boolean logic of complementary features may also apply to classical
systems, if their states and observables are defined by partitions of a
classical state space. If these partitions do not satisfy certain stability
criteria, complementary observables and non-Boolean propositional lattices may
be the consequence. This is especially the case for non-generating partitions
of nonlinear dynamical systems. We show how this can be understood in more
detail and indicate some challenging consequences for systems outside quantum
physics, including mental processes.
