Abstract: The relationship between feature modules and feature interactions is not well-understood. To explain classic examples of feature interaction, we show that features are not only composed sequentially, but also by cross-product and interaction operations that heretofore were implicit in the literature. Using the CIDE tool as our starting point, we (a) present a formal model of these operations, (b) show how it connects and explains previously unrelated results in Feature Oriented Software Development (FOSD), and (c) describe a tool, based on our formalism, that demonstrates how changes in composed documents can be back-propagated to their original feature module definitions, thereby improving FOSD tooling.