Truth-tracking in collective reasoning systems is a core challenge in domains such as e-democracy, online deliberation, and citizen opinion polling. Our prior work introduced Opinion-Based Argumentation (OBA), a framework modeling both voting and argumentation, along with collective opinion semantics (COS) designed to select sets of arguments that are mutually coherent and aligned with agents' votes. In this paper, we first formally define the truth-tracking problem within OBA. We then introduce VAST, a comprehensive evaluation framework to systematically assess the epistemic adequacy of COS. Our empirical analysis, conducted using VAST, demonstrates substantial variation in their truth-tracking performance across diverse deliberative conditions.

Argumentation theory provides a formal framework to represent and analyse debates where participants propose arguments that attack or support others and assign scores expressing their opinions. Quantitative Bipolar Argumentation Frameworks model such debates by assigning initial weights to arguments and using semantics to compute final scores that reflect attackers’ and supporters’ influence. One of the major challenge is setting appropriate initial weights when debaters’ opinions are uncertain. In this paper, we introduce a formal approach to uncertainty propagation in Quantitative Bipolar argumentation frameworks by representing initial weights as belief mass functions over a discretized unit interval. We introduce two new propagation models: (i) an exact model that computes final mass functions by combining focal elements of initial weights with parent arguments via bipolar gradual semantics; (ii) a practical approximation that projects the exact mass onto a user-specified partition and reconstructs masses using the Moebius inverse. We prove mathematical properties of the projection and show that the baseline, while computationally efficient, can be overconfident by failing to preserve expectations. Our approximation reduces the exponential complexity of the exact model while satisfying Epistemic Cautiousness, yielding acceptability intervals that contain true theoretical expectations and balancing tractability with theoretical soundness.

This paper presents a comprehensive examination of human compliance with normative principles of argumentation across two experimental studies. The first study investigated whether fundamental argumentation principles such as anonymity, independence, void precedence, and maximality align with human reasoning. Additionally, it explored whether graph-based representations of arguments facilitate better understanding and adherence to these principles compared to textual representations of arguments alone and examined the role of individual cognitive differences in compliance with these principles. Our experiments revealed that graph-based representations significantly improved compliance with argumentation principles, particularly among individuals with higher cognitive reflection. The second study replicated and extended the first study’s findings, introducing new principles such as skeptical precedence and simple reinstatement, and explored the effects of presenting arguments solely in graphical form, as well as the impact of a short tutorial on argumentation theory. The study also assessed participants’ ability to perform graphical tasks and how this influenced their compliance with normative principles. Results partially replicated the first study’s findings, confirming that graphical representations enhance compliance, but also revealed that the effect does not generalize to the new principles. We found evidence that in the absence of a graphical representation, performing graphical tasks can improve compliance with principles; especially drawing the argumentation graph. Moreover, a brief tutorial significantly improved performance on several principles, indicating that even minimal instruction can enhance understanding and compliance. However, the difficulties observed with the simple reinstatement principle hint that the participants’ intuition about the notion of defense diverges significantly from that of the researchers and that more careful thoughts must be put in crafting them. These studies collectively suggest that while argumentation principles can be intuitive to some extent, their comprehension and application are significantly influenced by the instruction given as well as by graphical representations and processes used to obtain them. These findings have important implications for the design of future argumentation-based tools and our understanding of how to bridge human reasoning and formal argumentation.

Online deliberation platforms allow people to exchange their opinions around a specified issue and to vote on these opinions in order to reach a collective decision. Argumentation allows to structure and analyse user input for these platforms. A debate can be represented by a quantitative bipolar argumentation framework where votes on each argument of the debate are aggregated into an initial weight. One of the main challenges these platforms face is sparse voting i.e. participants vote on a few number of arguments, leading to an imbalance of the number of votes between the arguments. In this paper, we propose a methodology that handles sparse voting in online debates, by introducing imprecise quantitative bipolar argumentation frameworks that incorporate uncertainty on the initial weights. Specifically, we leverage votes on arguments to initialize weight intervals that represent the uncertainty on the initial weights, using the imprecise Dirichlet model. We use four state-of-the-art bipolar gradual semantics to generate a final acceptability interval on each argument and we introduce several properties to study the effect of these semantics on the uncertainty on each argument’s final evaluation. Our methodology allows for a more robust representation of argument strength in the presence of limited data.

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Voting on arguments in a debate is a natural approach for reaching a consensual decision. Despite this, there are few formal methods of abstract argumentation dealing with the use of votes in the process of selecting accepted arguments. We introduce the Opinion Based Argumentation (OBA) framework, where individuals can vote (or abstain) for or against arguments in a Dung argumentation framework. Our research aims to determine the most appropriate collective decisions within this framework. We propose a new semantics for this framework, called Collective Satisfaction Semantics (CSS), to evaluate the acceptability of arguments and study their properties. Additionally, we compare these semantics against alternative methods adapted from related literature to provide insights into their relative effectiveness.

Compensation is a strategy that a semantics may follow when it faces dilemmas between quality and quantity of attackers. It allows several weak attacks to compensate one strong attack. It is based on compensation degree, which is a tuple that indicates (i) to what extent an attack is weak and (ii) the number of weak attacks needed to compensate a strong one. Existing principles on compensation do not specify the parameters, thus it is unclear whether semantics satisfying them compensate at only one degree or several degrees, and which ones. This paper proposes a parameterised family of gradual semantics, which unifies multiple semantics that share some principles but differ in their strategy regarding solving dilemmas. Indeed, we show that the two semantics taking the extreme values of the parameter favour respectively quantity and quality, while all the remaining ones compensate at some degree. We define three classes of compensation degrees and show that the novel family is able to compensate at all of them while none of the existing gradual semantics does.

Abstract The issue of how a semantics should deal with self-attacking arguments was always a subject of debate among argumentation scholars. A consensus exists for extension-based semantics because those arguments are always rejected (as soon as the semantics in question respects conflict-freeness). In case of gradual semantics, the question is more complex, since other criteria are taken into account. In this paper, we check the impact of those arguments by using a principle-based approach. Principles like self-contradiction and strong self-contradiction prescribe how to deal with self-attacking arguments. We show that they are incompatible with the well-known equivalence principle (which is satisfied by almost all the existing gradual semantics), as well as with some other principles (e.g. counting). This incompatibility was not studied until now and the class of semantics satisfying self-contradiction is under-explored. In the present paper, we explore that class of semantics. We show links and incompatibilities between several principles. We define a new general oriented argumentation semantics that satisfies (strong) self-contradiction and a maximal number of compatible principles. We introduce an iterative algorithm to calculate our semantics and prove that it always converges. We also provide a characterization of our semantics. Finally, we experimentally show that our semantics is computationally efficient.

Gradual semantics with abstract argumentation provide each argument with a score reflecting its acceptability. Many different gradual semantics have been proposed in the literature, each following different principles and producing different argument rankings. A sub-class of such semantics, the so-called weighted semantics, takes, in addition to the graph structure, an initial set of weights over the arguments as input, with these weights affecting the resultant argument ranking. In this work, we consider the inverse problem over such weighted semantics. That is, given an argumentation framework and a desired argument ranking, we ask whether there exist initial weights such that a particular semantics produces the given ranking. The contribution of this paper are: (1) an algorithm to answer this problem, (2) a characterisation of the properties that a gradual semantics must satisfy for the algorithm to operate, and (3) an empirical evaluation of the proposed algorithm.

An argumentation framework is a pair made of a graph and a semantics. The nodes and the edges of the graph represent respectively arguments and relations (e.g., attacks, supports) between arguments while the semantics evaluates the strength of each argument of the graph. This paper investigates gradual semantics dealing with weighted graphs, a family of graphs where each argument has an initial weight and may be attacked by other arguments. It contains four contributions. The first consists of laying the foundations of gradual semantics by proposing key principles on which evaluation of argument strength may be based. Foundations are important not only for a better understanding of the evaluation process in general, but also for clarifying the basic assumptions underlying semantics, for comparing different (families of) semantics, and for identifying families of semantics that have not been explored yet. The second contribution consists of providing a formal analysis and a comprehensive comparison of the semantics that have been defined in the literature for evaluating arguments in weighted graphs. As a third contribution, the paper proposes three novel semantics and shows which principles they satisfy. The last contribution is the implementation and empirical evaluation of the three novel semantics. We show that the three semantics are very efficient in that they compute the strengths of arguments in less than 20 iterations and in a very short time. This holds even for very large graphs, meaning that the three semantics scale very well.

Argumentation is a process of evaluating and comparing sets of arguments. Ranking-based semantics received a lot of attention recently. All of the semantics introduced so far are applicable to binary attack relations. In this paper, we study a more general case when sets of arguments can jointly attack an argument. We generalise existing postulates for ranking-based semantics to fit this framework, define a general variant of h-categoriser, prove that it converges for every argumentation framework and study the postulates it satisfies. We also study the link between binary and hypergraph version of h-categoriser.

Logic-based argumentation is a well-known approach for reasoning with inconsistent logic knowledge bases.Such frameworks have been shown to suffer from a major practical drawback consisting of a large number of arguments and attacks.To address this issue, we provide an argumentation framework that considers sets of attacking arguments and provide a theoretical analysis of the new framework with respect to its syntactic and semantic properties.We provide a tool for generating such argumentation frameworks from a Datalog knowledge base and study their characteristics.

Bipolar argumentation studies argumentation graphs where attacks are combined with another relation between arguments. Many kind of relations (e.g. deductive support, evidential support, necessities etc.) have been defined and investigated from a Dung semantics perspective. We place ourselves in the context of argumentation systems with necessities and provide the first study to investigate ranking semantics in this setting. To this end, we (1) provide a set of postulates specifically designed for necessities and (2) propose the first ranking-based semantics in the literature to be shown to respect these postulates.

When one wants to draw non-trivial inferences from an inconsistent belief base, a very natural approach is to take advantage of the maximal consistent subsets of the base. But few inference relations from maximal consistent subsets exist. In this paper we point out new such relations based on selection of some of the maximal consistent subsets, leading thus to inference relations with a stronger inferential power. The selection process must obey some principles to ensure that it leads to an inference relation which is rational. We define a general class of monotonic selection relations for comparing maximal consistent sets. And we show that it corresponds to the class of rational inference relations.

In this demonstration extended abstract we present a workflow of how to generate a benchmark for logical argumentation graphs issued from knowledge bases expressed using existential rules.

To address the needs of the EU NoAW project, in this paper we solve the problem of efficiently generating the argumentation graphs from knowledge bases expressed using existential rules. For the knowledge bases without rules, we provide a methodology that allows to optimise the generation of argumentation graphs. For knowledge bases with rules, we show how to filter out a large number of arguments and reduce the number of attacks.

To address the needs of the EU NoAW project, in this paper we introduce a new modular framework that generates viewpoints (i.e. extensions) based on ranking argumentation semantics by considering a selection function, a ranking on arguments and a lifting function as its input parameters. We study the different combinations of the input parameters and introduce a set of postulates investigated for the framework's different classes of output.

In this paper, we place ourselves in the Ontology Based Data Access (OBDA) setting and investigate reasoning with inconsistent existential rules knowledge bases. We use the notion of inconsistency measures on sets of facts to rank and filter repairs. We propose a generic framework to answer queries by using the best repairs and study productivity and properties of such a framework.

In this paper, we study the problem of aggregation of Dung’s abstract argumentation frameworks (AFs). An argumentation framework allows the representation of conflictual agent’s beliefs by using a set of arguments and interactions between them (i.e. attack or non-attack). One AF per agent can be used to represent the beliefs of a group of agents. The aggregation process aims to represent the beliefs of this group by solving the potential conflicts between them. Some aggregation operators were defined, and more recently, some rationality properties for this process were introduced. In this work, we study the existing operators as well as some new ones, which we define in light of the proposed properties. We highlight the fact that existing operators do not satisfy a lot of properties. The conclusions are that on one hand none of the existing operators seem fully satisfactory, but on the other hand some of the properties proposed so far seem too demanding.

The paper studies semantics that evaluate arguments in argumentation graphs, where each argument has a basic strength, and may be attacked by other arguments. It starts by defining a set of principles, each of which is a property that a semantics could satisfy. It provides the first formal analysis and comparison of existing semantics. Finally, it defines three novel semantics that satisfy more principles than existing ones.

In an argumentation setting, a semantics evaluates the overall acceptability of arguments. Consequently, it reveals the global loss incurred by each argument due to attacks. However, it does not say anything on the contribution of each attack to that loss. This paper introduces the novel concept of contribution measure which evaluates those contributions. It starts by defining a set of axioms that a reasonable measure would satisfy, then shows that the Shapley value is the unique measure that satisfies them. Finally, it investigates the properties of the latter under existing semantics.

One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in the same agenda. Independence, although considered a desirable property, is too strong, because together with mild additional conditions it implies dictatorship. We propose here a weakening of independence, named agenda separability: a judgment aggregation rule satisfies it if, whenever the agenda is composed of several independent sub-agendas, the resulting collective judgment sets can be computed separately for each sub-agenda and then put together. We show that this property is discriminant, in the sense that among judgment aggregation rules so far studied in the literature, some satisfy it and some do not. We briefly discuss the implications of agenda separability on the computation of judgment aggregation rules.

In 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.

One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in the same agenda. Independence is a desirable property for various reasons, but unfortunately it is too strong, as, together with mild additional conditions, it implies dictatorship. We propose here a weakening of independence, named agenda separability and show that this property is discriminant, i.e., some judgment aggregation rules satisfy it, others do not.

Dung’s abstract argumentation theory can be seen as a general framework for non-monotonic reasoning. An important question is then: what is the class of logics that can be subsumed as instantiations of this theory? The goal of this paper is to identify and study the large class of logic-based instantiations of Dung’s theory which correspond to the maxi-consistent operator, i.e. to the function which returns maximal consistent subsets of an inconsistent knowledge base. In other words, we study the class of instantiations where very extension of the argumentation system corresponds to exactly one maximal consistent subset of the knowledge base. We show that an attack relation belonging to this class must be conflict-dependent, must not be valid, must not be conflict-complete, must not be symmetric etc. Then, we show that some attack relations serve as lower or upper bounds of the class (e.g. if an attack relation contains canonical undercut then it is not a member of this class). By using our results, we show for all existing attack relations whether or not they belong to this class. We also define new attack relations which are members of this class. Finally, we interpret our results and discuss more general questions, like: what is the added value of argumentation in such a setting? We believe that this work is a first step towards achieving our long-term goal, which is to better understand the role of argumentation and, particularly, the expressivity of logic-based instantiations of Dung-style argumentation frameworks.

“The Synergy” is an on-line collaborative argument-based decision making platform. Our goal is to create a system allowing for both user-driven (the users themselves can vote “for” and “against” any particular option) and machine-driven (the system can propose an order of options based on the arguments provided by users) decision making. For the second option, we implemented existing and newly developed decision-making criteria. The basic concepts of our system are an option, a goal and an argument. An argument links an option with a goal. It can be in favour of or against an option and it can be attached a probability measure, which we believe is necessary for representing numerous scenarios in decision making under uncertainty. Our long term goal is to have pre-made answers for some general decisions: like Wikipedia collects data, we will collect PROS and CONS of possible decisions.

This article proposes an abstract framework for argumentation-based negotiation in which the impact of exchanging arguments on agents' theories is formally described, the different types of solutions in negotiation are investigated, and the added value of argumentation in negotiation dialogues is analysed. We study when, how and to which extent an exchange of arguments can be beneficial in negotiation. The results show that argumentation can improve the quality of an outcome but never decrease it.

Decision making is usually based on the comparative evaluation of different options by means of a decision criterion. Recently, the qualitative pessimistic criterion was articulated in terms of a four-step argumentation process: (i) to build arguments in favour/against each option, (ii) to compare and evaluate those arguments, (iii) to assign a status for each option, and (iv) to rank order the options on the basis of their status. Thus, the argumentative counter-part of the pessimistic criterion provides not only the ‘best’ option to the user but also the reasons justifying this recommendation. The aim of this article is to study the dynamics of this argumentation model. The idea is to study how the ordering on options changes in light of a new argument. For this purpose, we study under which conditions an option may change its status, and under which conditions the new argument has no impact on the status of options, and consequently, on the ordering. This amounts to study how the acceptability of arguments evolves when the decision system is extended by new arguments. In the article, we focus on two acceptability semantics the skeptical grounded semantics and the credulous preferred semantics.

We are interested by argumentation systems which build their arguments from a propositional knowledge base (KB), and evaluate them using Dung's acceptability semantics. We start by showing that such systems are infinite, i.e. from a finite KB, an infinite set of arguments and an infinite set of attacks among them are generated. While the construction of arguments under propositional logic is costly even in the finite case, the fact that those systems are infinite makes them completely useless. Then, we provide a procedure which, given an argumentation system, computes its finite sub-system, called core. A core considers a finite subset of arguments and a finite subset of attacks, and returns all the results of the original system. This means that a finite subset of arguments is sufficient to draw all the expected conclusions from a KB.

An argumentation system consists mainly of a set of interacting arguments and a semantics for evaluating them. In this paper, we study when two argumentation systems are equivalent. We focus on argumentation systems defined around a Tarskian logic. We propose different equivalence criteria, study their links and finally show under which conditions two systems are equivalent wrt each of the proposed criteria.

Different proposals have been made in the literature for refining Dung's argumentation framework by preferences between arguments. The idea is to ignore an attack if the attacked argument is stronger than its attacker. Acceptability semantics are then applied on the remaining attacks. Unfortunately, these proposals may return some unintended results, in particular, when the attack relation is asymmetric.

The aim of this paper is to study how preferences, which are used to model intrinsic strengths of arguments, can be used in argumentation. We show that they play two roles: i) to repair the attack relation between arguments, and ii) to refine the evaluation of arguments. Then, we point out that the existing approaches for preference-based argumentation model only the first role. They may also return non conflict-free extensions. We propose a general framework that overcomes those limitations.