Ensuring reference independence and cautious monotony in abstract argumentation

In the symbolic artificial intelligence community, abstract argumentation with its semantics, i.e. approaches for defining sets of valid conclusions (extensions) that can be derived from argumentation graphs, is considered a promising method for non-monotonic reasoning. However, from a sequential perspective, abstract argumentation-based decision-making processes typically do not guarantee an alignment with common formal notions to assess consistency; in particular, abstract argumentation can, in itself, not enforce the satisfaction of relational principles such as reference independence (based on a key principle of microeconomic theory) and cautious monotony. In this paper, we address this issue by introducing different approaches to ensuring reference independence and cautious monotony in sequential argumentation: a reductionist, an expansionist, and an extension-selecting approach. The first two approaches are generically applicable, but may require comprehensive changes to the corresponding argumentation framework. In contrast, the latter approach guarantees that an extension of the corresponding argumentation framework can be selected to satisfy the relational principle by requiring that the used argumentation semantics is weakly reference independent or weakly cautiously monotonous, respectively, and also satisfies some additional straightforward principles. To highlight the relevance of the approach, we illustrate how the extension-selecting approach to reference independent argumentation can be applied to model (boundedly) rational economic decision-making.