Faithful Modeling of Product Lines with Kripke Structures and Modal Logic

Software product lines are now an established framework for software design. They are specified by special diagrams called feature models. For formal analysis, the latter are usually encoded by Boolean propositional theories. We discuss a major deficiency of this semantics, and show that it can be fixed by considering a product to be an instantiation process rather than its final result. We call intermediate states of this process partial products, and argue that what a feature model really defines is a poset of its partial products. We argue that such structures can be viewed as special Kripke structure that we call partial product Kripke structures, ppKS. To specify these Kripke structures, we propose a CTL-based logic, called partial product CTL, ppCTL. We show how to represent a feature model M by a ppCTL theory ML(M) (ML stands for modal logic) such that any ppKS satisfying the theory is equal to the partial product line determined by M. Hence, ML(M) can be considered a sound and complete representation of M. We also discuss several applications of the modal logic view in feature modeling, including refactoring of feature models