Martin Caminada

Review: an introduction to argumentation semantics

This paper presents an overview on the state of the art of semantics for abstract argumentation, covering both some of the most influential literature proposals and some general issues concerning semantics definition and evaluation. As to the former point, the paper reviews Dungs original notions of complete, grounded, preferred, and stable semantics, as well as subsequently proposed notions like semi-stable, ideal, stage, and CF2 semantics, considering both the extension-based and the labelling-based approaches with respect to their definitions. As to the latter point, the paper presents an extensive set of general properties for semantics evaluation and analyzes the notions of argument justification and skepticism. The final part of the paper is focused on the discussion of some relationships between semantics properties and domain-specific requirements.

A Logical Account of Formal Argumentation

In the current paper, we re-examine how abstract argumentation can be formulated in terms of labellings, and how the resulting theory can be applied in the field of modal logic. In particular, we are able to express the (complete) extensions of an argumentation framework as models of a set of modal logic formulas that represents the argumentation framework. Using this approach, it becomes possible to define the grounded extension in terms of modal logic entailment.

On judgment aggregation in abstract argumentation

Judgment aggregation is a field in which individuals are required to vote for or against a certain decision (the conclusion) while providing reasons for their choice. The reasons and the conclusion are logically connected propositions. The problem is how a collective judgment on logically interconnected propositions can be defined from individual judgments on the same propositions. It turns out that, despite the fact that the individuals are logically consistent, the aggregation of their judgments may lead to an inconsistent group outcome, where the reasons do not support the conclusion. However, in this paper we claim that collective irrationality should not be the only worry of judgment aggregation. For example, judgment aggregation would not reject a consistent combination of reasons and conclusion that no member voted for. In our view this may not be a desirable solution. This motivates our research about when a social outcome is ‘compatible’ with the individuals’ judgments. The key notion that we want to capture is that any individual member has to be able to defend the collective decision. This is guaranteed when the group outcome is compatible with its members views. Judgment aggregation problems are usually studied using classical propositional logic. However, for our analysis we use an argumentation approach to judgment aggregation problems. Indeed the question of how individual evaluations can be combined into a collective one can also be addressed in abstract argumentation. We introduce three aggregation operators that satisfy the condition above, and we offer two definitions of compatibility. Not only does our proposal satisfy a good number of standard judgment aggregation postulates, but it also avoids the problem of individual members of a group having to become committed to a group judgment that is in conflict with their own individual positions.

An Algorithm for Computing Semi-stable Semantics

The semi-stable semantics for formal argumentation has been introduced as a way of approximating stable semantics in situations where no stable extensions exist. Semi-stable semantics can be located between stable semantics and preferred semantics in the sense that every stable extension is a semi-stable extension and every semi-stable extension is a preferred extension. Moreover, in situations where at least one stable extension exists, the semi-stable extensions are equal to the stable extensions. In this paper we provide an outline of an algorithm for computing the semi-stable extensions, given an argumentation framework. We show that with a few modifications, the algorithm can also be used for computing stable and preferred semantics.

A labelling approach for ideal and stage semantics

In this document, we describe the concepts of ideal semantics and stage semantics for abstract argumentation in terms of argument labellings. The difference between the traditional extensions approach and the labelling approach is that where the former only identifies the sets of accepted arguments, the latter also identifies the rejected arguments as well as the arguments that are neither accepted nor rejected. So far, the labellings approach has been successfully applied to complete, grounded, preferred, stable and semi-stable semantics, as well as to the concept of admissibility. In the current paper, we continue this line of research by showing that ideal semantics and stage semantics can also be described in terms of argument labellings.

Preferred semantics as socratic discussion

n abstract argumentation theory, preferred semantics has become one of the most popular approaches for determining the sets of arguments that can collectively be accepted. However, the description of preferred semantics, as it was originally stated by Dung, has a mainly technical and mathematical nature, making it difficult for lay persons to understand what the concept of preferred semantics is essentially about. In the current article, we aim to bridge the gap between mathematics and philosophy by providing a reformulation of (credulous) preferred semantics in terms of Socratic discussion. In order to do so, we first provide a (semi-)formal treatment of some of the concepts in Socratic dialogue.

A QBF-based formalization of abstract argumentation semantics

We introduce a unified logical theory, based on signed theories and Quantified Boolean Formulas (QBFs) that can serve as the basis for representing and computing various argumentation-based decision problems. It is shown that within our framework we are able to model, in a simple and modular way, a wide range of semantics for abstract argumentation theory. This includes complete, grounded, preferred, stable, semi-stable, stage, ideal and eager semantics. Furthermore, our approach is purely logical, making for instance decision problems like skeptical and credulous acceptance of arguments simply a matter of entailment and satisfiability checking. The latter may be verified by off-the-shelf QBF-solvers.

A logical account of lying

This paper aims at providing a formal account of lying - a dishonest attitude of human beings. We first formulate lying under propositional modal logic and present basic properties for it. We then investigate why one engages in lying and how one reasons about lying. We distinguish between offensive and defensive lies, or deductive and abductive lies, based on intention behind the act. We also study two weak forms of dishonesty, bullshit and deception, and provide their logical features in contrast to lying. We finally argue dishonesty postulates that agents should try to satisfy for both moral and self-interested reasons.

An Algorithm for Stage Semantics

In the current paper, we re-examine the concept of stage semantics, which is one of the oldest semantics for abstract argumentation. Using a formal treatment of its properties, we explain how the intuition behind stage semantics differs from the intuition behind the admissibility based semantics that most scholars in argumentation theory are familiar with. We then provide a labelling-based algorithm for computing all stage extensions, based on earlier algorithms for computing all preferred, stable and semi-stable extensions.

Manipulation in group argument evaluation

Given an argumentation framework and a group of agents, the individuals may have divergent opinions on the status of the arguments. If the group needs to reach a common position on the argumentation framework, the question is how the individual evaluations can be mapped into a collective one. This problem has been recently investigated in 1]. In this paper, we study under which conditions these operators are Pareto optimal and whether they are manipulable.