Online social platforms, e-commerce sites and technical fora support the unfolding of informal exchanges, e.g. debates or discussions, that may be topic-driven or serendipitous. We outline a methodology for analysing these exchanges in computational argumentation terms, thus allowing a formal assessment of the dialectical validity of the positions debated in or emerging from the exchanges. Our methodology allows users to be engaged in this formal analysis and the assessment, within a dynamic process where comments, opinions, objections, as well as links connecting them, can all be contributed by users.