Following the framework proposed by Besnard and Hunter for argumentation, this paper aims to propose a logical tool for the generation of new arguments when two formal agents have to face their respective knowledge. The following notions are addressed: the behaviour of an agent facing an argument, the answer of an agent in front of a set of formulas, and relations among arguments. X-logics, a nonmonotonic extension of classical propositional logic proposed by Siegel and Forget, is used as the background formalism for representing the reasoning of the agents on arguments.