Within the last decade, abstract argumentation has emerged as a central field in Artificial Intelligence. Besides providing a core formalism for many advanced argumentation systems, abstract argumentation has also served to capture several non-monotonic logics and other AI related principles. Although the idea of abstract argumentation is appealingly simple, several reasoning problems in this formalism exhibit high computational complexity. This calls for advanced techniques when it comes to implementation issues, a challenge which has been recently faced from different angles. In this survey, we give an overview on different methods for solving reasoning problems in abstract argumentation and compare their particular features. Moreover, we highlight available state-of-the-art systems for abstract argumentation, which put these methods to practice.

Answer Set Programming is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, PDDL and many others. Since its first informal editions, ASP systems are compared in the nowadays customary ASP Competition. The fourth ASP Competition, held in 2012/2013, is the sequel to previous editions and it was jointly organized by University of Calabria (Italy) and the Vienna University of Technology (Austria). Participants competed on a selected collection of benchmark problems, taken from a variety of research areas and real world applications. The Competition featured two tracks: the Model& Solve Track, held on an open problem encoding, on an open language basis, and open to any kind of system based on a declarative specification paradigm; and the System Track, held on the basis of fixed, public problem encodings, written in a standard ASP language.

Many problems from the area of AI have been shown tractable for bounded treewidth. In order to put such results into practice, quite involved dynamic programming (DP) algorithms on tree decompositions have to be designed and implemented. These algorithms typically show recurring patterns that call for tasks like subset-minimization. In this paper we present D-FLATˆ2, a system that allows one to obtain DP algorithms (specified in ASP) from simpler principles, where the DP formalization of subset-minimization is performed automatically. We illustrate the method at work by providing several DP algorithms-given in form of ASP programs-that are more space-efficient than existing solutions, while featuring improved readability, reuse and therefore maintainability of ASP code. Experiments show that our approach also yields a significant improvement in runtime performance.

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The notion of secure sets is a rather new concept in the area of graph theory. Applied to social network analysis, the goal is to identify groups of entities that can repel any attack or influence from the outside. In this article, we tackle this problem by utilizing Answer Set Programming (ASP). It is known that verifying whether a set is secure in a graph is already co-NP-hard. Therefore, the problem of enumerating all secure sets is challenging for ASP and its systems. In particular, encodings for this problem seem to require disjunction and also recursive aggregates. Here, we provide such encodings and analyse their performance using the Clingo system. Furthermore, we study several problem variants, including multiple secure or insecure sets, and weighted graphs.