In this paper, we propose the task of argument explicitation, a task that makes the structure of a natural language argument explicit, as well as the background knowledge the argument is built on, in the form of implicit premises or contextual knowledge. The purpose of argument explicitation is to support the understanding of an argument by providing users with an end-to-end analysis that offers a critical assessment of arguments including identification of argument weaknesses. Besides, the results of the argument explicitation process can be used by machines to retrieve similar arguments as well as counter-arguments. We propose a framework for argumentation mining sub-tasks that by now have mostly been treated separately in the literature....