Résumé : We present a class of objects that denote proofs in classical propositional logic. The general definitions are in terms of a semiring of parameters. We discuss two concrete instances: With the Boolean semiring we get a theory of proof nets for classical logic, that comes with a geometric correctness criterion, a sequentialization theorem, and a strongly normalizing cut-elimination procedure. This allows us to build ``Boolean'' *-autonomous categories that are not posets. With the semiring of natural numbers, we obtain a sound semantics for classical logic, in which fewer proofs are identified. Though a ``real'' sequentialization theorem is missing, these proof nets have a grip on complexity issues, in particular the NP vs. co-NP problem. The strongly normalizing cut elimination procedure is closely related to the cut elimination process in the calculus of structures, and we also get a ``Boolean'' category.