The Complexity of Repairing, Adjusting, and Aggregating of Extensions in Abstract Argumentation

We study the computational complexity of problems that arise in abstract argumentation in the context of dynamic argumentation, minimal change, and aggregation. In particular, we consider the following problems where always an argumentation framework F and a small positive integer k are given. - The Repair problem asks whether a given set of arguments can be modified into an extension by at most k elementary changes (i.e., the extension is of distance k from the given set). - The Adjust problem asks whether a given extension can be modified by at most k elementary changes into an extension that contains a specified argument. - The Center problem asks whether, given two extensions of distance k, whether there is a "center" extension that is a distance at most (k-1) from both given extensions. We study these problems in the framework of parameterized complexity, and take the distance k as the parameter. Our results covers several different semantics, including admissible, complete, preferred, semi-stable and stable semantics

Argumentation and graph properties

Argumentation theory is an area of interdisciplinary research that is suitable to characterise several diverse situations of reasoning and judgement in real world practices and challenges. In the discipline of Artificial Intelligence, argumentation is formalised by reasoning models based on building and evaluation of interacting arguments. In this argumentation framework, the semantics of acceptance plays a fundamental role in the argument evaluation process. The determination of accepted arguments under a given semantics (admissible, preferred, stable, etc.) can be a time-consuming and tedious (in number of steps) process. In this work we try to overcome this substantial process by providing a method to compute accepted arguments from an argumentation framework. The principle of this method is to combine mathematical properties (e.g. symmetry, asymmetry, strong connectivity and irreflexivity) of graphs built from the argumentation system to compute sets of accepted arguments. In this work, we combine several graph properties to provide three main propositions; one for identifying accepted arguments under the admissible, preferred semantics and the other to easily identify stable extension. The proofs of the suggested propositions are detailed and this is part of an approach designed to increase collaborative decision-making by improving the effectiveness of reasoning processes

Technical Communications of ICLP

Abstract Dynamic programming (DP) on tree decompositions is a well studied approach for solving hard problems efficiently. State-of-the-art implementations usually rely on tables for storing information, and algorithms specify how the tuples are manipulated during traversal of the decomposition. However, a major bottleneck of such table-based algorithms is relatively high memory consumption. The goal of the doctoral thesis herein discussed is to mitigate performance and memory shortcomings of such algorithms. The idea is to replace tables with an efficient data structure that no longer requires to enumerate intermediate results explicitly during the computation. To this end, Binary Decision Diagrams (BDDs) and related concepts are studied with respect to their applicability in this setting. Besides native support for efficient storage, from a conceptual point of view BDDs give rise to an alternative approach of how DP algorithms are specified. Instead of tuple-based manipulation operations, the algorithms are specified on a logical level, where sets of models can be conjointly updated. The goal of the thesis is to provide a general tool-set for problems that can be solved efficiently via DP on tree decompositions

Lower Bounds for QBFs of Bounded Treewidth

The problem of deciding the validity (QSAT) of quantified Boolean formulas (QBF) is a vivid research area in both theory and practice. In the field of parameterized algorithmics, the well-studied graph measure treewidth turned out to be a successful parameter. A well-known result by Chen in parameterized complexity is that QSAT when parameterized by the treewidth of the primal graph of the input formula together with the quantifier depth of the formula is fixed-parameter tractable. More precisely, the runtime of such an algorithm is polynomial in the formula size and exponential in the treewidth, where the exponential function in the treewidth is a tower, whose height is the quantifier depth. A natural question is whether one can significantly improve these results and decrease the tower while assuming the Exponential Time Hypothesis (ETH). In the last years, there has been a growing interest in the quest of establishing lower bounds under ETH, showing mostly problem-specific lower bounds up to the third level of the polynomial hierarchy. Still, an important question is to settle this as general as possible and to cover the whole polynomial hierarchy. In this work, we show lower bounds based on the ETH for arbitrary QBFs parameterized by treewidth (and quantifier depth). More formally, we establish lower bounds for QSAT and treewidth, namely, that under ETH there cannot be an algorithm that solves QSAT of quantifier depth i in runtime significantly better than i-fold exponential in the treewidth and polynomial in the input size. In doing so, we provide a versatile reduction technique to compress treewidth that encodes the essence of dynamic programming on arbitrary tree decompositions. Further, we describe a general methodology for a more fine-grained analysis of problems parameterized by treewidth that are at higher levels of the polynomial hierarchy

How we designed winning algorithms for abstract argumentation and which insight we attained

In this paper we illustrate the design choices that led to the development of ArgSemSAT, the winner of the preferred semantics track at the 2017 International Competition on Computational Models of Arguments (ICCMA 2017), a biennial contest on problems associated to the Dung’s model of abstract argumentation frameworks, widely recognised as a fundamental reference in computational argumentation. The algorithms of ArgSemSAT are based on multiple calls to a SAT solver to compute complete labellings, and on encoding constraints to drive the search towards the solution of decision and enumeration problems. In this paper we focus on preferred semantics (and incidentally stable as well), one of the most popular and complex semantics for identifying acceptable arguments. We discuss our design methodology that includes a systematic exploration and empirical evaluation of labelling encodings, algorithmic variations and SAT solver choices. In designing the successful ArgSemSAT, we discover that: (1) there is a labelling encoding that appears to be universally better than other, logically equivalent ones; (2) composition of different techniques such as AllSAT and enumerating stable extensions when searching for preferred semantics brings advantages; (3) injecting domain specific knowledge in the algorithm design can lead to significant improvements

Système d'argumentation pour la collaboration en télémédecine

La télémédecine consiste en la pratique d’actes médicaux à distance par l’usage des nouvelles technologies de l’information et de la communication. Parmi ces actes médicaux, nous nous sommes intéressés à la téléexpertise qui est une sorte d’activité collaborative consistant aux recueils d’avis d’experts médicaux face à un problème de santé donné. Dans notre travail, nous avons fait le choix de modéliser ces activités collaboratives par le système d’argumentation de Dung basé sur des fondements mathématiques et qui permet d’illustrer les interactions entre les différentes parties prenantes et par la même occasion fournir des outils mathématiques de prises de décisions. Nous avons opté pour une modélisation sémantique avec des graphes conceptuels car l’un de nos objectifs est de garantir une interopérabilité sémantique. Cette modélisation peut inclure souvent des incohérences (mauvaises relations d’attaques dans le système d’argumentation) qui seront vérifiées par l’usage des contraintes en graphes conceptuels. Pour résoudre ces problèmes d’incohérences deux solutions majeures ont été proposées : (i) la pondération des arguments des différents professionnels de santé, (ii) la modélisation de quelques aspects de droit médical comme contraintes. Ce travail démontre une application informatique du raisonnement logique dans un cadre médical judiciaire où il apporte des éclairages sur la vérification d’information, l’argumentation et l’interaction. Il vise ainsi à garantir une bonne collaboration dans le but de se prémunir d’éventuelles conséquences financières et juridiques.Telemedicine involves the practice of medical procedures remotely through the use of new information and communications technology. Among these medical procedures, we looked at the tele-expertise which is a kind of collaborative activity consisting of collecting the opinions of medical experts facing a particular health problem. In our work, we have chosen to model these collaborative activities by Dung argumentation system based on mathematical foundations and illustrates the interactions between the different stakeholders and at the same time provides mathematical tools decisions. We opted for a semantic modeling with conceptual graphs as one of our objectives is to ensure semantic interoperability. This modeling can often include inconsistencies (poor relations of attacks in argumentation system) which will be verified by the use of constraints in conceptual graphs. To solve these inconsistency problems, two major solutions have been proposed : (i) the weight of the arguments of different health professionals, (ii) modeling some aspects of medical law as constraints. This work demonstrates a computer application of logical reasoning in a judicial medical setting where it sheds light on the verification of information, argumentation and interaction. It aims to ensure good cooperation in order to guard against possible financial and legal consequences