Trading properties and Alexandrov kernels for Boolean functions Original Research Article

Simple games correspond to monotonic Boolean functions, but their study is associated with a distinct set of intuitions and questions. We show how “trading properties” from simple games can be adapted to the nonmonotonic context, and how a number of these trading properties (some new and some old) are tied to each other via two kernel operations of the Alexandrov topology. These results provide an answer to a question of Peter Hammer about the relationship between the property referred to here as weak monotonicity and some better-known properties of Boolean functions.