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.

Recently, Strength-based Argumentation Frameworks (StrAFs) have been proposed to model situations where some quantitative strength is associated with arguments. In this setting, the notion of accrual corresponds to sets of arguments that collectively attack an argument. Some semantics have already been defined, which are sensitive to the existence of accruals that collectively defeat their target, while their individual elements cannot. However, until now, only the surface of this framework and semantics have been studied. Indeed, the existing literature focuses on the adaptation of the stable semantics to StrAFs. In this paper, we push forward the study and investigate the adaptation of admissibility-based semantics. Especially, we show that the strong admissibility defined in the literature does not satisfy a desirable property, namely Dung’s fundamental lemma. We therefore propose an alternative definition that induces semantics that behave as expected. We then study computational issues for these new semantics, in particular we show that complexity of reasoning is similar to the complexity of the corresponding decision problems for standard argumentation frameworks in almost all cases. We then propose a translation in pseudo-Boolean constraints for computing (strong and weak) extensions. We conclude with an experimental evaluation of our approach which shows in particular that it scales up well for solving the problem of providing one extension as well as enumerating them all.

Preference-based argumentation and ranking semantics are two important research topics in the computational argumentation literature. Surprisingly, no study investigates to what extent preferences over arguments and ranking semantics can interact. This paper fills the gap between the relative priorities that one can express and the evaluation of arguments individual acceptability. More precisely, we propose a natural principle that should be satisfied by a ranking semantics for Preference-based Argumentation Frameworks. We show that although existing semantics do not satisfy this desirable principle, they can be used to define new ranking semantics that exhibit the expected behavior. Finally, we discuss an application of these semantics to the modeling of human reasoning.

We review a recently introduced model in which each of a number of agents is endowed with an abstract argumentation framework reflecting her individual views regarding a given set of arguments. A question arising in this context is whether the diversity of views observed in such a situation is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual information and, second, the personal preferences of the agent concerned. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. This is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

Different agents may have different points of view. Following a popular approach in the artificial intelligence literature, this can be modeled by means of different abstract argumentation frameworks, each consisting of a set of arguments the agent is contemplating and a binary attack-relation between them. A question arising in this context is whether the diversity of views observed in such a profile of argumentation frameworks is consistent with the assumption that every individual argumentation framework is induced by a combination of, first, some basic factual attack-relation between the arguments and, second, the personal preferences of the agent concerned regarding the moral or social values the arguments under scrutiny relate to. We treat this question of rationalisability of a profile as an algorithmic problem and identify tractable and intractable cases. In doing so, we distinguish different constraints on admissible rationalisations, e.g., concerning the types of preferences used or the number of distinct values involved. We also distinguish two different semantics for rationalisability, which differ in the assumptions made on how agents treat attacks between arguments they do not report. This research agenda, bringing together ideas from abstract argumentation and social choice, is useful for understanding what types of profiles can reasonably be expected to occur in a multiagent system.

Possibilistic logic is a well-known framework for dealing with uncertainty and reasoning under inconsistent knowledge bases. Standard possibilistic logic expressions are propositional logic formulas associated with positive real degrees belonging to [0,1]. However, in practice it may be difficult for an expert to provide exact degrees associated with formulas of a knowledge base. This paper proposes a flexible representation of uncertain information where the weights associated with formulas are in the form of intervals. We first study a framework for reasoning with interval-based possibilistic knowledge bases by extending main concepts of possibilistic logic such as the ones of necessity and possibility measures. We then provide a characterization of an interval-based possibilistic logic base by means of a concept of compatible standard possibilistic logic bases. We show that intervalbased possibilistic logic extends possibilistic logic in the case where all intervals are singletons. Lastly, we provide computational complexity results of deriving plausible conclusions from interval-based possibilistic bases and we show that the flexibility in representing uncertain information is handled without extra computational costs.

In the last decade, several approaches have been proposed for merging multiple and potentially conflicting pieces of information. Egalitarian fusion modes pick solutions that minimize the local dissatisfaction of each source (agent, expert), which is involved in the fusion process. When pieces of information to merge are prioritized, or ranked, most existing approaches assume that these priority degrees are commensurable, namely sources are assumed to share the same meaning of uncertainty scales. This article provides useful strategies for an egalitarian fusion of incommensurable ranked belief bases under constraints. In particular, it focuses on Max-based merging operators, and proposes a merging operator that allows to aggregate a set of ranked belief bases E. This operator is based on the concept of compatible scales. We provide three equivalent characterizations of this operator. The first one shows that Max-based merging of incommensurable belief bases can also be defined in terms of a Pareto-like ordering on possible worlds, denominated SMP ordering. The second one is based on the notion of compatible rankings defined on finite scales. The third one is only based on total pre-orders induced by ranked bases to merge. The last part of the article analyses rational postulates satisfied by our merging operator and compare it with some related works.

Recently, several approaches have been proposed to merge possibly contradictory belief bases. This paper focuses on max-based merging operators applied to incommensurable ranked belief bases. We first propose a characterization of a result of merging using Pareto-like ordering on a set of possible solutions. Then we propose two equivalent ways to recover the result of merging. The first one is based on the notion of compatible rankings defined on finite scales. The second one is only based on total pre-orders induced by ranked bases to merge.