Answer-set programming encodings for argumentation frameworks

Abstract

Answer-set programming (ASP) has emerged as a declarative programming paradigm where problems are encoded as logic programs, such that the so-called answer sets of theses programs represent the solutions of the encoded problem. The efficiency of the latest ASP solvers reached a state that makes them applicable for problems of practical importance. Consequently, problems from many different areas, including diagnosis, data integration, and graph theory, have been successfully tackled via ASP. In this work, we present such ASP-encodings for problems associated to abstract argumentation frameworks (AFs) and generalisations thereof. Our encodings are formulated as fixed queries, such that the input is the only part depending on the actual AF to process. We illustrate the functioning of this approach, which is underlying a new argumentation system called ASPARTIX in detail and show its adequacy in terms of computational complexity.Keywords: abstract argumentation frameworks; answer-set programming; implementation MotivationIn Artificial Intelligence (AI), the area of argumentation (the survey by Bench-Capon and Dunne (2007) gives an excellent overview) has become one of the central issues during the last decade. Argumentation provides a formal treatment for reasoning problems arising in a number of applications fields, including Multi-Agent Systems and Law Research. In a nutshell, the so-called abstract argumentation frameworks (AFs) formalise statements together with a relation denoting rebuttals between them, such that the semantics gives an abstract handle to solve the inherent conflicts between statements by selecting admissible subsets of them. The reasoning underlying such AFs turned out to be a very general principle capturing many other important formalisms from the areas of AI and knowledge representation.The increasing interest in argumentation led to numerous proposals for formalisations of argumentation. These approaches differ in many aspects. First, there are several ways as to how "admissibility" of a subset of statements can be defined; second, the notion of rebuttal has different meanings (or even additional relationships between statements are taken into account); finally, statements are augmented with priorities, such that the semantics yields those admissible sets which contain statements of higher priority. Thus, in order to compare these different proposals, it is desirable to have a system at hand, which is capable of dealing with a large number of argumentation semantics.Argumentation problems are, in general, intractable; for instance, deciding if an argument is contained in some preferred extension is known to be NP-complete. Therefore, developing dedicated algorithms for the different reasoning problems is non-trivial. A promising way to implement such systems is to use a reduction method, where the given problem is translated into another language, for which sophisticated systems already exist.

Senses of ‘argument’ in instantiated argumentation frameworks

“…They also thank the ASPARTIX research group (Egly, Alice Gaggl, and Woltran, 2010) for their useful web application which has been widely used for this research. The authors appreciate the comments from reviewers and conference participants.…”

Encoding Argument Graphs in Logic

“…Further work by different authors following the same idea was published later, e.g. [3][4][5][6][7]. However, all these approaches were devoted to specific cases in the sense that for each semantics, a dedicated encoding was proposed from scratch.…”

Argumentation frameworks as constraint satisfaction problems

“…In [18] an implementation of Dung's semantics using answer set programming (ASP) has been provided. Thus, it is complementary to our work.…”

“…The results are a bit disappointing since they show that the most important decision problems (like for instance testing whether a framework has a stable set of arguments) are costly. Some algorithms that compute extensions under some semantics have been developed, for instance in [8,11,18].…”