Adpositional Argumentation (AdArg) is a new method for annotating argumentative discourse that represents linguistic and pragmatic information in argumentative adpositional trees. In this paper, we explain how the representation of claims and individual arguments provide the building blocks for more complex argumentation structures. We illustrate the abstract trees representing the systematic possibilities of a claim (one statement), minimal argument (one conclusion, one premise), convergent argumentation (one conclusion, multiple premises), as well as serial argumentation, when the same linguistic material plays the double role of the premise of a given argument and the conclusion of a subargument
