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.

Efficient computation of hard reasoning tasks is a key issue in abstract argumentation. One recent approach is to define approximate algorithms, i.e. methods that provide an answer that may not always be correct, but outperform the exact algorithms regarding the computation runtime. One such approach proposes to use the grounded semantics, which is polynomially computable, as a starting point for determining whether arguments are (credulously or skeptically) accepted with respect to various other extension-based semantics. In this paper, we push further this idea by defining a general family of approaches to evaluate the acceptability of arguments which are not in the grounded extension, neither attacked by it. These approaches rely on gradual semantics to evaluate these arguments. We also propose an approach using an heuristic based on the number of arguments attacked by or attacking an argument, and we show that this last approach, although seemingly different, is actually also an instance of our general family of approaches based on gradual semantics. We have implemented our approaches and provided an empirical study in which we discuss the results and compare our approach with the state-of-the-art approximate algorithms.

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.

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.

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.

Argumentation is a process of evaluating and comparing a set of arguments. A way to compare them consists in using a ranking-based semantics which rank-order arguments from the most to the least acceptable ones. Recently, a number of such semantics have been pro- posed independently, often associated with some desirable properties. However, there is no comparative study which takes a broader perspective. This is what we propose in this work. We provide a general comparison of all these semantics with respect to the proposed proper- ties. That allows to underline the differences of behavior between the existing semantics.

Argumentation is based on the exchange and the evaluation of interacting arguments. Unlike Dung's theory where arguments are either accepted or rejected, ranking-based semantics rank-order arguments from the most to the least acceptable ones. We propose in this work six new ranking-based semantics. We argue that, contrarily to existing ranking semantics in the literature, that focus on evaluating attacks and defenses only, it is reasonable to give a prominent role to non-attacked arguments, as it is the case in standard Dung's semantics. Our six semantics are based on the propagation of the weight of each argument to its neighbors, where the weight of non-attacked arguments is greater than the attacked ones.

Possibilistic networks are belief graphical models based on possibility theory. This paper deals with a special kind of possibilistic networks called three-valued possibilistic networks where only three possibility levels are used to encode uncertain information. The paper analyzes different semantics of three-valued networks and provides precise relationships relating the different semantics. More precisely, the paper analyzes two categories of methods for deriving a three-valued joint possibility distribution from a three-valued possibilistic network. The first category of methods is based on viewing a three-valued possibilistic network as a family of compatible networks and defining combination rules for deriving the three-valued joint distribution. The second category is based on three-valued chain rules using three-valued operators inspired from some three-valued logics. Finally, the paper shows that the inference using the well-known junction tree algorithm can only be extended for some three-valued chain rules.