Extension-based semantics of argumentation frameworks for agent interactions

Abstract

Argumentation plays an important part in human interaction, whether it is used for persuasion, negotiation or simply for sharing one's point of view on a certain topic. Even at the abstract level, choosing the acceptable arguments from a given set of conflicting arguments is a challenging problem, one that was given multiple solutions in the argumentation literature, in the form of argumentation semantics. An abstract argumentation framework is a directed graph that encodes the attacks between arguments. The content of the arguments is only used for deriving the attack relation and plays no further role in the abstract setting. Instead, the semantics are only defined based on the attacks between arguments. For example, one of the most intuitive constraints that can be imposed is that there should be no conflict between accepted arguments, but several other approaches are possible. On the other hand, it is difficult to say which of these constraints are the most appropriate. It is commonly agreed that there is no "best" argumentation semantics and that, instead, each of them has unique properties that make it more appropriate for some application domain or another. The first part of the thesis (Chapter 2 and Chapter 3) provides an extensive survey of existing argumentation semantics and their properties. In particular, the inclusion relations between semantics are captured in a map that can provide useful information for easily comparing novel semantics with existing ones. Such maps are augmented with argumentation frameworks that can distinguish between semantics, so as to exhibit their unique features. Argumentation frameworks and the Kripke models from modal logic are similar in the sense that they both give some meaning to a directed graph. This intuition has lead to the use of modal logic for describing argumentation semantics, first proposed by Davide Grossi in 2010. The second part of the thesis (Chapter 4 and Chapter 5) focuses on the modal definability of argumentation semantics using the global and converse modalities. We propose an algorithm that constructs models for satisfiable formulas, based on their normal form. Using this approach, we relate the formulas that describe argumentation semantics to properties that are satisfied by those semantics. This leads to a negative result showing that even a small set of properties cannot hold at the same time as modal definability. The last part of the thesis (Chapter 6) deals with the use of abstract argumentation in dynamic systems, for modeling the intentions and goals of agents, as well as the state of the environment where they are situated. The proposed model relies on the use of argumentation frameworks together with constraints on the acceptability of certain arguments. We show that the use of traditional extension-based semantics in this context is not appropriate and we propose a novel class of semantics, based on temporarily ignoring a set of arguments in order to satisfy the given constraints. Upon choosing an extension, the corresponding ignored set is to be attacked with new arguments, so as to bring about the desired extension. We use this approach to create a formal model of argumentation-based negotiation and we explain the use of the novel semantics as strategies for the agents.