Abstract Projection can be seem as a unifying concept that underlies inference in logic and consistency maintenance in constraint programming. This perspective allows one to import projection methods into both areas, resulting in deeper insight as well as faster solution methods. We show that inference in propositional logic can be achieved by Benders decomposition, an optimization method based on projection. In constraint programming, viewing consistency maintenance as projection suggests a new but natural concept of consistency that is achieved by projection onto a subset of variables. We show how to solve this combinatorial projection problem for some global constraints frequently used in constraint programming. The resulting projections are useful when propagated through decision diagrams rather than the traditional domain store.