  We introduce a novel framework, the theory of Cartesian frames (CF), that
gives powerful tools for manipulating sets of acts. The CF framework takes as
its most fundamental building block that an agent can freely choose from a set
of available actions. The framework uses the mathematics of Chu spaces to
develop a calculus of those sets of actions, how those actions change at
various levels of description, and how different agents' actions can combine
when agents work in concert. We discuss how this framework might provide an
illuminating perspective on issues in decision theory and formal epistemology.
