ABAplus: Attack Reversal in Abstract and Structured Argumentation with Preferences

We present ABAplus, a system that implements reasoning with the argumentation formalism ABA+. ABA+ is a structured argumentation formalism that extends Assumption-Based Argumentation (ABA) with preferences and accounts for preferences via attack reversal. ABA+ also admits as instance Preference-based Argumentation which accounts for preferences by reversing attacks in abstract argumentation (AA). ABAplus readily implements attack reversal in both AA and ABAstyle structured argumentation. ABAplus affords computation, visualisation and comparison of extensions under five argumentation semantics. It is available both as a stand-alone system and as a web application

"Minimal defence": a refinement of the preferred semantics for argumentation frameworks

Dung's abstract framework for argumentation enables a study of the interactions between arguments based solely on an ``attack'' binary relation on the set of arguments. Various ways to solve conflicts between contradictory pieces of information have been proposed in the context of argumentation, nonmonotonic reasoning or logic programming, and can be captured by appropriate semantics within Dung's framework. A common feature of these semantics is that one can always maximize in some sense the set of acceptable arguments. We propose in this paper to extend Dung's framework in order to allow for the representation of what we call ``restricted'' arguments: these arguments should only be used if absolutely necessary, that is, in order to support other arguments that would otherwise be defeated. We modify Dung's preferred semantics accordingly: a set of arguments becomes acceptable only if it contains a minimum of restricted arguments, for a maximum of unrestricted arguments.Comment: 8 pages, 3 figure

A generalization of Dung's Abstract Framework for Argumentation:Arguing with Sets of Attacking Arguments

Abstract. One of the most widely studied systems of argumentation is the one described by Dung in a paper from 1995. Unfortunately, this framework does not allow for joint attacks on arguments, which we argue must be required of any truly abstract argumentation framework. A few frameworks can be said to allow for such interactions among arguments, but for various reasons we believe that these are inadequate for modelling argumentation systems with joint attacks. In this paper we propose a generalization of the framework of Dung, which allows for sets of arguments to attack other arguments. We extend the semantics associated with the original framework to this generalization, and prove that all results in the paper by Dung have an equivalent in this more abstract framework.

Preference in Abstract Argumentation

Consider an argument A that is attacked by an argument B, while A is preferred to B. Existing approaches will either ignore the attack or reverse it. In this paper we introduce a new reduction of preference and attack to defeat, based on the idea that in such a case, instead of ignoring the attack, the preference is ignored. We compare this new reduction with the two existing ones using a principle-based approach, for the four Dung semantics. The principle-based or axiomatic approach is a methodology to choose an argumentation semantics for a particular application, and to guide the search for new argumentation semantics. For this analysis, we also introduce a fourth reduction, and a semantics for preference-based argumentation based on extension selection. Our classification of twenty alternatives for preference-based abstract argumentation semantics using six principles suggests that our new reduction has some advantages over the existing ones, in the sense that if the set of preferences increases, the sets of accepted arguments increase as well

Semantics for Evidence-Based Argumentation

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