Abstract
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.
Highlights
Reference independence – the absence of influence of irrelevant alternatives on an agent’s decision outcome – is an important property of economic rationality, which in turn is one of the key concepts of microeconomic decision theory
To evaluate argumentation semantics from the perspective of economic rationality, we provide the definition of an argumentation-based decision function, which takes an argumentation framework and uses an argumentation semantics to determine exactly one set of arguments, which is returned as the decision result
As we show in [5], complete, preferred, semi-stable, grounded, ideal and eager semantics are weakly reference independent given normal, non-cyclic expansions that do not “add/change” attack sequences that originate from cycles; i.e., the extension-selecting approach to reference independence sequential argumentation can be realized with these semantics given severe constraints on the way an argumentation framework sequence is expanded
Summary
Reference independence – the absence of influence of irrelevant alternatives on an agent’s decision outcome – is an important property of economic rationality, which in turn is one of the key concepts of microeconomic decision theory. Let us highlight that by introducing approaches to ensure reference independence and (alternatively) cautious monotony, we enforce two principles that have their roots in highly influential principle-based approaches to reasoning and decisionmaking: i) reference independence reflects the consistent preference principle of the rational actor model, i.e. of formal (economic) rationality that a foundation of microeconomic theory, and game theory; ii) in contrast, cautious monotony reflects the idea that non-monotonic inference methods can be systematically constrained with respect to the conditions that need to be satisfied in order to allow for a violation of monotony [7]. Let us note that the focus of this paper is on generic, abstract argumentation-based approaches to ensuring reference independence and cautious monotony; approaches that use extensions of abstract argumentation, like preference-based [9] and value-based argumentation [12], are not presented.
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