An important tool for scientific study in any field is a formal language in which the phenomena can be described and hypotheses formulated. In this book a formal notation is developed for the description of the cognitive structure of arguments. The analyses based on this notation are more fine-grained than the analyses in previous attempts, and they are applicable not only to arguments but to all types of moves in a discourse. Further, the notational system provides a basis for the description of relations between arguments and the structure of the discourse as a whole. In the final chapter, some empirical studies of retention of arguments in memory and of precis writing are reported, based on hypotheses formulated in terms of the notational system.