Exploiting Parallelism for Hard Problems in Abstract Argumentation

Abstract argumentation framework (AF) is a unifying framework able to encompass a variety of nonmonotonic reasoning approaches, logic programming and computational argumentation. Yet, efficient approaches for most of the decision and enumeration problems associated to AF s are missing, thus potentially limiting the efficacy of argumentation-based approaches in real domains. In this paper, we present an algorithm for enumerating the preferred extensions of abstract argumentation frameworks which exploits parallel computation. To this purpose, the SCC-recursive semantics definition schema is adopted, where extensions are defined at the level of specific sub-frameworks. The algorithm shows significant performance improvements in large frameworks, in terms of number of solutions found and speedup

Counting Complexity for Reasoning in Abstract Argumentation

In this paper, we consider counting and projected model counting of extensions in abstract argumentation for various semantics. When asking for projected counts we are interested in counting the number of extensions of a given argumentation framework while multiple extensions that are identical when restricted to the projected arguments count as only one projected extension. We establish classical complexity results and parameterized complexity results when the problems are parameterized by treewidth of the undirected argumentation graph. To obtain upper bounds for counting projected extensions, we introduce novel algorithms that exploit small treewidth of the undirected argumentation graph of the input instance by dynamic programming (DP). Our algorithms run in time double or triple exponential in the treewidth depending on the considered semantics. Finally, we take the exponential time hypothesis (ETH) into account and establish lower bounds of bounded treewidth algorithms for counting extensions and projected extension.Comment: Extended version of a paper published at AAAI-1

Preservation of Semantic Properties during the Aggregation of Abstract Argumentation Frameworks

An abstract argumentation framework can be used to model the argumentative stance of an agent at a high level of abstraction, by indicating for every pair of arguments that is being considered in a debate whether the first attacks the second. When modelling a group of agents engaged in a debate, we may wish to aggregate their individual argumentation frameworks to obtain a single such framework that reflects the consensus of the group. Even when agents disagree on many details, there may well be high-level agreement on important semantic properties, such as the acceptability of a given argument. Using techniques from social choice theory, we analyse under what circumstances such semantic properties agreed upon by the individual agents can be preserved under aggregation.Comment: In Proceedings TARK 2017, arXiv:1707.0825

"Minimal defence": a refinement of the preferred semantics for argumentation frameworks

Dung's abstract framework for argumentation enables a study of the interactions between arguments based solely on an ``attack'' binary relation on the set of arguments. Various ways to solve conflicts between contradictory pieces of information have been proposed in the context of argumentation, nonmonotonic reasoning or logic programming, and can be captured by appropriate semantics within Dung's framework. A common feature of these semantics is that one can always maximize in some sense the set of acceptable arguments. We propose in this paper to extend Dung's framework in order to allow for the representation of what we call ``restricted'' arguments: these arguments should only be used if absolutely necessary, that is, in order to support other arguments that would otherwise be defeated. We modify Dung's preferred semantics accordingly: a set of arguments becomes acceptable only if it contains a minimum of restricted arguments, for a maximum of unrestricted arguments.Comment: 8 pages, 3 figure

Enumeration of Preferred Extensions in Almost Oriented Digraphs

In this paper, we present enumeration algorithms to list all preferred extensions of an argumentation framework. This task is equivalent to enumerating all maximal semikernels of a directed graph. For directed graphs on n vertices, all preferred extensions can be enumerated in O^*(3^{n/3}) time and there are directed graphs with Omega(3^{n/3}) preferred extensions. We give faster enumeration algorithms for directed graphs with at most 0.8004 * n vertices occurring in 2-cycles. In particular, for oriented graphs (digraphs with no 2-cycles) one of our algorithms runs in time O(1.2321^n), and we show that there are oriented graphs with Omega(3^{n/6}) > Omega(1.2009^n) preferred extensions. A combination of three algorithms leads to the fastest enumeration times for various proportions of the number of vertices in 2-cycles. The most innovative one is a new 2-stage sampling algorithm, combined with a new parameterized enumeration algorithm, analyzed with a combination of the recent monotone local search technique (STOC 2016) and an extension thereof (ICALP 2017)

Improved Answer-Set Programming Encodings for Abstract Argumentation

The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor. In this paper, we present new encodings for three prominent argumentation semantics using the concept of conditional literals in disjunctions as provided by the ASP-system clingo. Our new encodings are not only more succinct than previous versions, but also outperform them on standard benchmarks.Comment: To appear in Theory and Practice of Logic Programming (TPLP), Proceedings of ICLP 201

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

Argumentation Frameworks Features: an Initial Study

Semantics extensions are the outcome of the argumentation reasoning process: enumerating them is generally an intractable problem. For preferred semantics two efficient algorithms have been recently proposed, PrefSAT and SCC-P, with significant runtime variations. This preliminary work aims at investigating the reasons (argumentation framework features) for such variations. Remarkably, we observed that few features have a strong impact, and those exploited by the most performing algorithm are not the most relevant