Cumulative arguments in artificial intelligence and informal logic

We define a new type of argument structure specifically for modeling cumulative arguments and then show how this structure is general enough to simulate linked and convergent arguments. Argumentation schemes are associated with argument weighing functions in this language, where the weight of an argument can depend on the status (labeling) of its premises in an argument graph. Several key examples are used to illustrate the modeling of cumulative arguments, as well as linked and convergent arguments, with this approach. One hypothesis suggested by the analysis of these examples is that cumulative arguments can be treated in the same way as what is called argument accrual in artificial intelligence.