A Proposal to Embed the In Dubio Pro Reo Principle into Abstract Argumentation Semantics based on Topological Ordering and Undecidedness Propagation

Abstract. In this paper we discuss how the in dubio pro reo principle and the corresponding standard of proof beyond reasonable doubt can be modelled in abstract argumentation. The in dubio pro reo principle protects arguments against attacks from doubtful arguments. We identify doubtful arguments with a subset of undecided arguments, called active undecided arguments, consisting of cyclic arguments responsible for generating the undecided situation. We obtain the standard of proof beyond reasonable doubt by imposing that attacks from doubtful undecided arguments are not enough to change the acceptability status of an attacked argument (the reo). The resulting semantics, called SCCvoid semantics, are defined using a SCC-recursive schema. The semantics are conflict-free, non-admissible (in Dung’s sense), but employing a more relaxed defence-based notion of admissibility; they allow reinstatement and they accept credulously what the corresponding complete semantics accepts at least credulously

SCF2 - an Argumentation Semantics for Rational Human Judgments on Argument Acceptability

In abstract argumentation theory, many argumentation semantics have been proposed for evaluating argumentation frameworks. This paper is based on the following research question: Which semantics corresponds well to what humans consider a rational judgment on the acceptability of arguments? There are two systematic ways to approach this research question: A normative perspective is provided by the principle-based approach, in which semantics are evaluated based on their satisfaction of various normatively desirable principles. A descriptive perspective is provided by the empirical approach, in which cognitive studies are conducted to determine which semantics best predicts human judgments about arguments. In this paper, we combine both approaches to motivate a new argumentation semantics called SCF2. For this purpose, we introduce and motivate two new principles and show that no semantics from the literature satisfies both of them. We define SCF2 and prove that it satisfies both new principles. Furthermore, we discuss findings of a recent empirical cognitive study that provide additional support to SCF2

Beyond reasonable doubt: a proposal for undecidedness blocking in abstract argumentation

In Dung’s abstract semantics, the label undecided is always propagated from the attacker to the attacked argument, unless the latter is also attacked by an accepted argument. In this work we propose undecidedness blocking abstract argumentation semantics where the undecided label is confined to the strong connected component where it was generated and it is not propagated to the other parts of the argumentation graph. We show how undecidedness blocking is a fundamental reasoning pattern absent in abstract argumentation but present in similar fashion in the ambiguity blocking semantics of Defeasible logic, in the beyond reasonable doubt legal principle or when someone gives someone else the benefit of the doubt. The resulting semantics, called SCC-void semantics, are defined using an SCC-recursive schema. The semantics are conflict-free and non-admissible, but they incorporate a more relaxed defence-based notion of admissibility. They allow reinstatement and they credulously accept what the corresponding Dung’s complete semantics accepts at least credulously

Argumentation Label Functions - Technical Report

An important approach to abstract argumentation is the labeling-based approach, in which one makes use of labelings that assign to each argument one of three labels: in, out or und. In this paper, we address the question, which of the twenty-seven functions from the set of labels to the set of labels can be represented by an argumentation framework. We prove that in preferred, complete and grounded semantics, eleven labeling functions can be represented in this way while sixteen labeling functions cannot be represented by any argumentation framework. We show how this analysis of labeling functions can be applied to prove an impossibility result: Argumentation frameworks extended with a certain kind of weak attack relation cannot be flattened to the standard Dung argumentation frameworks

A general schema for generating argumentation semantics from logic programming semantics

In this paper, by considering the idea that argumentation semantics can be viewed as a special form of logic programming semantics with negation as failure, we show that any logic programming semantics as the stable model semantics, the minimal models, etc., can define candidate argumentation semantics. These new argumentation semantics will overcome some of the problems of the Dung's argumentation semantics that have been discussed in the literature. The new argumentation semantics are based on a new recursive framework for logic programming semantics. This framework generalizes any logic programming semantics in order to build logic programming semantics which are always defined, satisfy the property of relevance and agree with the stable semantics for the class of stratified programs.Postprint (published version

Abstract and Concrete Decision Graphs for Choosing Extensions of Argumentation Frameworks - Technical Report

Most argumentation semantics allow for multiple extensions, which raises the question of how to choose among extensions. We propose to study this question as a decision problem. Inspired by decision trees commonly used in economics, we introduce the notion of a decision graph for deciding between the multiple extensions of a given AF in a given semantics. We distinguish between abstract decision graphs and concrete instantiations thereof. Inspired by the principle-based approach to argumentation, we formulate two principles that mappings from argumentation frameworks to decision graphs should satisfy, the principle of decision-graph directionality and the one of directional decision-making. We then propose a concrete instantiation of decision graphs, which satisfies one of these principles. Finally, we discuss the potential for further research based on this novel methodology

A Plausibility Semantics for Abstract Argumentation Frameworks

We propose and investigate a simple ranking-measure-based extension semantics for abstract argumentation frameworks based on their generic instantiation by default knowledge bases and the ranking construction semantics for default reasoning. In this context, we consider the path from structured to logical to shallow semantic instantiations. The resulting well-justified JZ-extension semantics diverges from more traditional approaches.Comment: Proceedings of the 15th International Workshop on Non-Monotonic Reasoning (NMR 2014). This is an improved and extended version of the author's ECSQARU 2013 pape

The Principle-Based Approach to Abstract Argumentation 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. This article gives a complete classification of the fifteen main alternatives for argumentation semantics using the twenty-seven main principles discussed in the literature on abstract argumentation, extending Baroni and Giacomin’s original classification with other semantics and principles proposed in the literature. It also lays the foundations for a study of representation and (im)possibility results for abstract argumentation, and for a principle-based approach for extended argumentation such as bipolar frameworks, preference-based frameworks, abstract dialectical frameworks, weighted frameworks, and input/output frameworks