Argumentation Theoretic Foundations for Abstract Dependence Networks

In this paper we show how to argue about agreements based on de- pendence. First, we introduce a formal theory of arguing about agreements by instantiating Dung’s abstract theory of argumentation with proposals for agree- ments represented as dependence networks. Second, we show that acceptable agreements are exchange based—satisfying the so-called do-ut-des principle— and not redundant. Third, to further decrease the number of proposals, we define a notion of minimal proposals. Roughly, all proposals can be split into a number of minimal sub-proposals such that if the proposal is acceptable, then its minimal sub-proposals are acceptable too. We show that minimal proposals satisfy the indecomposable do-ut-des property, i.e., they cannot be split into two nonempty sub-proposals with at most one shared agent.