A growing body of recent work in informal logic investigates the process of argumentation. Among other things, this work focuses on the ways in which individuals attempt to understand written or verbalised arguments in light of the fact that these are often presented in forms that are incomplete and unmarked. One of its aims is to develop general procedures for natural language argument recognition and reconstruction. Our aim here is to draw on this growing body of knowledge in informal logic in order to take preliminary steps towards developing an architecture for computer systems that are able to recognise and reconstruct natural language arguments. This architecture aims to structure research of an applied and computational nature that strives to implement linguistic systems of various sorts, and to analyse problems in a way that both yields manageable and relatively independent components and also highlights how implementations can interact with existing resources from natural language processing.