We present a generalization of Dung's theory of argumentation enabling to take account for some additional constraints on the admissible sets of arguments, expressed as a propositional formula over the set of arguments. We point out several semantics for such constrained argumentation frameworks, and compare the corresponding inference relations w.r.t. cautiousness. We show that our setting encompasses some previous approaches based on Dung's theory as specific cases. We also investigate the complexity issue for the inference relations in the extended setting. Interestingly, we show that our generalization does not lead to a complexity shift w.r.t. inference for several semantics.