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 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 précis writing are reported, based on hypotheses formulated in terms of the notational system.