Assessing the strength of arguments is essential for determining the outcomes of any argument-based system. A wide range of semantics has been proposed in the literature. These take as input a set of arguments—each assigned a basic weight and potentially subject to attacks from others—and compute a single strength value for each argument. Despite the diversity of argument types (or schemes), existing semantics apply uniform evaluation criteria across all arguments. In this paper, we advocate for type-dependent evaluations, acknowledging that the impact of attacks can vary across types. Given that many argument-based systems involve heterogeneous types of arguments, we propose a broad family of hybrid semantics that combine distinct base semantics, each tailored to specific argument types. We investigate their theoretical properties, present concrete instances within this family, and examine their computational complexity.

International audience

This paper investigates complex argumentation settings, called weighted higher-order argumentation frameworks (wHO-AFs), where both arguments and attacks carry initial weights and may be subject to attacks from arguments. It focuses on developing gradual semantics capable of rationally evaluating these elements by assigning each argument and attack a numerical value, representing their respective degrees of acceptance and seriousness. The contributions of the paper are five-fold: i) It identifies key technical challenges for semantics in wHO-AFs, such as handling the distinction between arguments and attacks, and determining how their values should be combined. To address these challenges, the paper introduces a set of guiding principles that capture various semantic strategies. ii) It introduces a broad family of semantics that treat arguments and attacks uniformly, evaluating them in the same way. This family encompasses both semantics inspired by extension-based approaches and those that are purely gradual. iii) It defines a second extensive family of semantics that differentiate between arguments and attacks. This includes instances where a single function evaluates both types of elements, as well as hybrid variants that apply distinct evaluation functions to arguments and attacks. iv) It offers a formal analysis and comprehensive comparison of the resulting diverse semantics. v) It presents an empirical evaluation of these semantics. The results are promising as they show that the values of all elements can be computed in fewer than 20 iterations, even for large frameworks, while maintaining very low runtime. The paper ultimately delivers a catalogue of semantics, each offering distinct formal properties and behaviors, contributing a flexible toolkit for reasoning in rich argumentative contexts.

Abstract Argumentation has become an essential tool in AI, allowing the representation of knowledge with only a set of arguments and a binary relation between arguments, the attack relation. Since the seminal work presented in 1995 by Dung, many extensions have been proposed in order to enrich this very simple framework by the addition of a second type of interaction, the support relation, and by the use of higher-order or collective interactions. In parallel, several links have been exhibited and studied between Logics and Abstract Argumentation, showing that these two domains are closely interrelated. Among these works, one can find several logical encodings of abstract argumentation frameworks. Nevertheless, these encodings are very often built ad hoc and only for some given frameworks. The aim of this paper is to propose a generic logical encoding covering several families of abstract argumentation frameworks, from Dung’s framework to the most enriched framework using higher-order and collective evidential supports and attacks.

Abstract In our paper [17], we have proposed a logical encoding of argumentation frameworks with higher-order interactions (i.e. attacks or supports whose targets are arguments or other attacks or supports) with an evidential interpretation for supports, such frameworks are called REBAF. With this encoding, we are able to characterize the semantics of REBAF under the form of specific logical models. Nevertheless, this encoding has two important drawbacks: first, the handling of support cycles has some weaknesses, and second, the collective interactions (i.e. attacks or supports whose source is a set of arguments and not only one argument) are not taken into account. The present paper proposes an improvement of this encoding for solving these drawbacks. Moreover, we also extend this proposal to another kind of Higher-Order Bipolar Argumentation Framework, the RAFN, in which supports are interpreted as necessity.

Computation and decision problems related to argumentation frameworks with higher-order attacks have not received a lot of attention so far. This paper is a step towards these issues: first, it provides a labelling counterpart for the structure semantics of Recursive Argumentation Frameworks (RAF); second, it investigates the complexity of decision problems associated with RAF. This investigation shows that, for the higher expressiveness offered by these enriched systems, the complexity is the same as for classical argumentation frameworks. As a side contribution, a new semantics for RAF, the semi-stable semantics, and a new process for translating RAF into Argumentation Frameworks without higher-order attacks (AF), are introduced.

In this paper, we propose a generalisation of Dung's abstract argumentation framework that allows representing higher-order attacks and supports, that is attacks or supports whose targets are other attacks or supports. We follow the necessary interpretation of the support, based on the intuition that the acceptance of an argument requires the acceptance of each supporter. We propose semantics accounting for acceptability of arguments and validity of interactions, where the standard notion of extension is replaced by a triple of a set of arguments, a set of attacks and a set of supports. Our framework is a conservative generalisation of Argumentation Frameworks with Necessities (AFN). When supports are ignored, Argumentation Frameworks with Recursive Attacks are recovered.

We propose a logical encoding of extended abstract argumentation frameworks, that is frameworks with higher-order attacks (i.e. attacks whose targets are other attacks). Our purpose is to separate the logical expression of the meaning of an attack (simple or higher-order) from the logical expression of acceptability semantics. We consider semantics which specify the conditions under which the arguments (resp. the attacks) are considered as accepted, directly on the extended framework, without translating the original framework into a Dung's argumentation framework. We characterize the output of a given framework in logical terms (namely as particular models of a logical theory). Our proposal applies to the particular case of Dung's frameworks, enabling to recover standard extensions.

International audience

GRAFIX is a graphical tool for handling abstract argumentation graphs. GRAFIX allows the edition and the presentation of argumentation graphs (or sets of graphs), and the execution of some “predefined treatments” (called “server treatments”) on the current graph(s) such as, for instance, computing various acceptability semantics, or computing the strength of arguments. GRAFIX also allows the user to introduce her own treatments (“client treatments”).

The purpose of this paper is to describe some results of the LELIE project, that are a contribution of Artificial Intelligence to a special domain: the analysis of the risks due to poorly written technical documents. This is a multidisciplinary contribution since it combines natural language processing with logical satisfiability checking. This paper explains how satisfiability checking can be used for detecting inconsistencies, redundancy and incompleteness in procedural texts and describes the part of the implemented tool that produces the logical translation of technical texts and realizes the checkings.

This paper defines a new framework for dynamics in argumentation. In this framework, an agent can change an argumentation system (the target system) in order to achieve some desired goal. Changes consist in addition/removal of arguments or attacks between arguments and are constrained by theagent's knowledge encoded by another argumentation system. We present a software that computes the possible change operations for a given agent on a given target argumentation system in order to achieve some given goal.

Dung's argumentation framework has been extended to consider preferences over arguments or over attacks, in a qualitative or in a quantitative way. In this paper, we investigate the relationships between preferences over arguments and preferences over attacks. We give conditions on the definition of preferences over attacks from preferences over arguments. Following these principles, we propose different instantiations of an AFvs (argumentation framework with attacks of various strength), when preferences over arguments are available. Our proposal is compared to existing work, particularly regarding the conditions in which the defence holds.

In this paper, we address the problem of merging argumentation systems (AS) in a multi-agent setting. Each agent's system may be built from different sets of arguments and/or different interactions between these arguments. The merging process must lead to solve conflicts between the agents and to identify ASs representing the knowledge of the group of agents. Previous work [6] has proposed a two-step merging process in which conflicts about an interaction result in a new kind of interaction, called ignorance. However, this merging process is computationally expensive, and does not provide a single resulting AS. We propose a novel approach to overcome these limitations by introducing a refinement of the ignorance relation under the form of a weighted attack. Our merging process takes only one step and provides a single weighted AS, which is easy to compute.

We consider argumentation systems with several attack relations of different strength. We focus on the impact of various strength attacks on the semantics of such systems. First, we refine the classical notion of defence, by comparing the strength of an attack with the strength of a counter-attack. Then, we propose different ways to compare defenders, and sets of defenders. That enables us to define admissible sets offering a best defence for their elements.

We consider argumentation systems taking into account several attack relations of different strength. We focus on the impact of various strength attacks on the semantics of such systems, and particularly on the decision problem of credulous acceptance: namely, focussing on one particular argument, a classical issue is to compute a proof, under the form of an admissible set containing this argument. Taking into account attacks of various strength leads to search for the best proofs.

Bipolar argumentation frameworks enable to represent two kinds of interaction between arguments: support and conflict. In this paper, we turn a bipolar argumentation framework into a meta-argumentation framework where conflicts occur between sets of arguments, characterized as coalitions of supporting arguments. So, Dung's well-known semantics can be used on this meta-argumentation framework to select the acceptable arguments. © 2009 Wiley Periodicals, Inc.

In this paper, we address the problem of change in an abstract argumentation system. We focus on a particular change: the addition of a new argument which interacts with previous arguments. We study the impact of such an addition on the outcome of the argumentation system, more particularly on the set of its extensions. Several properties for this change operation are defined by comparing the new set of extensions to the initial one, these properties are called structural when the comparisons are based on set-cardinality or set-inclusion relations. Several other properties are proposed where comparisons are based on the status of some particular arguments: the accepted arguments; these properties refer to the evolution of this status during the change, e.g., Monotony and Priority to Recency. All these properties may be more or less desirable according to specific applications. They are studied under two particular semantics: the grounded and preferred semantics.

There already exist some links between argumentation and game theory. For instance, dynamic games can be used for simulating interactions between agents in an argumentation process. In this paper, we establish a new link between these domains in a static framework: we show how an argumentation framework can be translated into a CP-Boolean game and how this translation can be used for computing extensions of argumentation semantics. We give formal algorithms to do so.

In this article, we propose a survey of the use of bipolarity in argumentation frameworks. On the one hand, the notion of bipolarity relies on the presence of two kinds of entities that have a diametrically opposed nature and that represent repellent forces (a positive entity and a negative entity). The notion exists in various domains (for example with the representation of preferences in artificial intelligence, or in cognitive psychology). On the other hand, argumentation process is a promising approach for reasoning, based on the construction and the comparison of arguments. It follows five steps: building the arguments, defining the interactions between these arguments, valuating the arguments, selecting the most acceptable arguments and, finally, drawing a conclusion. Using the nomenclature proposed by Dubois and Prade, this article shows on various applications, and with some formal definitions, that bipolarity appears in argumentation (in some cases if not always) and can be used in each step of this process under different forms. © 2008 Wiley Periodicals, Inc.

Argumentation is based on the exchange and valuation of interacting arguments, followed by the selection of the most acceptable of them (for example, in order to take a decision, to make a choice). Starting from the framework proposed by Dung in 1995, our purpose is to introduce 'graduality' in the selection of the best arguments, i.e., to be able to partition the set of the arguments in more than the two usual subsets of 'selected' and 'non-selected' arguments in order to represent different levels of selection. Our basic idea is that an argument is all the more acceptable if it can be preferred to its attackers. First, we discuss general principles underlying a 'gradual' valuation of arguments based on their interactions. Following these principles, we define several valuation models for an abstract argumentation system. Then, we introduce 'graduality' in the concept of acceptability of arguments. We propose new acceptability classes and a refinement of existing classes taking advantage of an available 'gradual' valuation.