Sarah Alice Gaggl

Answer-set programming encodings for argumentation frameworks

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.

ASPARTIX: Implementing Argumentation Frameworks Using Answer-Set Programming

The system ASPARTIX is a tool for computing acceptable extensions for a broad range of formalizations of Dungs argumentation framework and generalizations thereof. ASPARTIX relies on a fixed disjunctive datalog program which takes an instance of an argumentation framework as input, and uses the answer-set solver DLV for computing the type of extension specified by the user.

Methods for solving reasoning problems in abstract argumentation - A survey

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.

The Added Value of Argumentation

We discuss the value of argumentation in reaching agreements, based on its capability for dealing with conflicts and uncertainty. Logic-based models of argumentation have recently emerged as a key topic within Artificial Intelligence. Key reasons for the success of these models is that they are akin to human models of reasoning and debate, and their generalisation to frameworks for modelling dialogues. They therefore have the potential for bridging between human and machine reasoning in the presence of uncertainty and conflict. We provide an overview of a number of examples that bear witness to this potential, and that illustrate the added value of argumentation. These examples amount to methods and techniques for argumentation to aid machine reasoning (e.g. in the form of machine learning and belief functions) on the one hand and methods and techniques for argumentation to aid human reasoning (e.g. for various forms of decision making and deliberation and for the Web) on the other. We also identify a number of open challenges if this potential is to be realised, and in particular the need for benchmark libraries.

Making Use of Advances in Answer-Set Programming for Abstract Argumentation Systems

Dung’s famous abstract argumentation frameworks represent the core formalism for many problems and applications in the field of argumentation which significantly evolved within the last decade. Recent work in the field has thus focused on implementations for these frameworks, whereby one of the main approaches is to use Answer-Set Programming (ASP). While some of the argumentation semantics can be nicely expressed within the ASP language, others required rather cumbersome encoding techniques. Recent advances in ASP systems, in particular, the metasp optimization front-end for the ASP-package gringo/claspD provide direct commands to filter answer sets satisfying certain subset-minimality (or -maximality) constraints. This allows for much simpler encodings compared to the ones in standard ASP language. In this paper, we experimentally compare the original encodings (for the argumentation semantics based on preferred, semi-stable, and respectively, stage extensions) with new metasp encodings. Moreover, we provide novel encodings for the recently introduced resolution-based grounded semantics. Our experimental results indicate that the metasp approach works well in those cases where the complexity of the encoded problem is adequately mirrored within the metasp approach.

The cf2 argumentation semantics revisited

Abstract argumentation frameworks nowadays provide the most popular formal- ization of argumentation on a conceptual level. Numerous semantics for this paradigm have been proposed, whereby the cf2 semantics has shown to solve particular problems concerned with odd-length cycles in such frameworks. Due to the complicated definition of this semantics it has somehow been neglected in the literature. In this article, we introduce an alternative characterization of the cf2 semantics which, roughly speaking, avoids the recursive computation of sub-frameworks. This facilitates further investigation steps, like a complete complexity analysis. Furthermore, we show how the notion of strong equivalence can be characterized in terms of the cf2 semantics. In contrast to other semantics, it turns out that for the cf2 semantics strong equivalence coincides with syntactical equivalence. We make this particular behavior more explicit by defining a new property for argumenta- tion semantics, called the succinctness property. If a semantics satisfies the succinctness property, then for every framework F , all its attacks contribute to the evaluation of at least one framework F 0 containing F. We finally characterize strong equivalence also for the stage and the naive semantics. Together with known results these characterizations imply that none of the prominent semantics for abstract argumentation, except the cf2 semantics, satisfies the succinctness property.

Stage semantics and the SCC-recursive schema for argumentation semantics

Recently, stage and cf2 semantics for abstract argumentation attracted specific attention. By distancing from the notion of defense, they are capable to select arguments out of odd-length cycles. In case of cf2 semantics, the SCC-recursive schema guarantees that important evaluation criteria for argumentation semantics, like directionality, weakand CF -reinstatement, are fulfilled. Beside several desirable properties, both stage and cf2 semantics still have some drawbacks. The stage semantics does not satisfy the above mentioned evaluation criteria, whereas cf2 semantics produces some questionable results on frameworks with cycles of length ≥ 6. Therefore, we suggest to combine stage semantics with the SCC-recursive schema of cf2 semantics. The resulting stage2 semantics overcomes the problems regarding cf2 and stage semantics. We study properties of stage2 semantics and its relations to existing semantics, show that it fulfills the mentioned evaluation criteria, study strong equivalence for stage2 semantics, and provide a comprehensive complexity analysis of the associated reasoning problems. Besides the analysis of stage2 semantics we also complement existing complexity results for cf2 by an analysis of tractable fragments and fixed parameter tractability. Furthermore we provide answer-set programming (ASP) encodings for stage2 semantics and labeling-based algorithms for cf2 and stage2 semantics.

Reduction-Based Approaches to Implement Modgil's Extended Argumentation Frameworks

This paper reconsiders Modgils Extended Argumentation Frameworks EAFs that extend Dungs abstract argumentation frameworks by attacks on attacks. This allows to encode preferences directly in the framework and thus also to reason about the preferences themselves. As a first step to reduction-based approaches to implement EAFs, we give an alternative but equivalent characterization of acceptance in EAFs. Then we use this characterization to provide EAF encodings for answer set programming and propositional logic. Moreover, we address an open complexity question and the expressiveness of EAFs.

Towards a General Argumentation System based on Answer-Set Programming

Within the last years, especially since the work proposed by Dung in 1995, argumentation has emerged as a central issue in Artificial Intelligence. With the so called argumentation frameworks (AFs) it is possible to represent statements (arguments) together with a binary attack relation between them. The conflicts between the statements are solved on a semantical level by selecting acceptable sets of arguments. An increasing amount of data requires an automated computation of such solutions. Logic Programming in particular Answer-Set Programming (ASP) turned out to be adequate to solve problems associated to such AFs. In this work we use ASP to design a sophisticated system for the evaluation of several types of argumentation frameworks.

Intertranslatability of Labeling-Based Argumentation Semantics

Abstract Argumentation is a simple yet powerful formalism for modeling the human reasoning and argumentation process. Various semantics have been suggested with a view of arriving at coherent outcomes of the argumentation process. Two categories of semantics are well-known, extension-based semantics and labeling-based semantics. Translations between semantics are an important area of interest that enhance our understanding of the dynamics of various semantics and their structural and semantic interrelationship. The application of translations to extension-based semantics has been investigated in detail in the literature, however for labeling-based semantics which provide a more fine grained notion of acceptability such translations have not yet been studied. In this work, we fill this gab by investigating intertranslatability of labeling-based semantics. We show in which cases the existing results from the extension-based setting carry over to the labeling-based setting and we investigate intertranslatability between the three unique status semantics grounded, ideal and eager.