On the Complexity of Determining Defeat Relations Consistent with Abstract Argumentation Semantics

Typically in abstract argumentation, one starts with arguments and a defeat relation, and applies some semantics in order to determine the acceptability status of the arguments. We consider the converse case where we have knowledge of the acceptability status of arguments and want to identify a defeat relation that is consistent with the known acceptability data – the σ-consistency problem. Focusing on complete semantics as underpinning the majority of the major semantic types, we show that the complexity of determining a defeat relation that is consistent with some set of acceptability data is highly dependent on how the data is labelled. The extension-based 2-valued σ-consistency problem for complete semantics is revealed as NP-complete, whereas the labelling-based 3-valued σ-consistency problem is solvable within polynomial time. We then present an informal discussion on application to grounded, stable, and preferred semantics.</jats:p

On the Complexity of Determining Defeat Relations Consistent with Abstract Argumentation Semantics

Presented at Computational Models of Argument Proceedings of COMMA 2022 ((9th International Conference on Computational Models of Argument COMMA 2022, Cardiff, UK, 14-16 September, 2022) Available at https://ebooks.iospress.nl/ISBN/978-1-64368-306-5Copyright 2022 The authors and IOS Press. Typically in abstract argumentation, one starts with arguments and a defeat relation, and applies some semantics in order to determine the acceptability status of the arguments. We consider the converse case where we have knowledge of the acceptability status of arguments and want to identify a defeat relation that is consistent with the known acceptability data – the σ-consistency problem. Focusing on complete semantics as underpinning the majority of the major semantic types, we show that the complexity of determining a defeat relation that is consistent with some set of acceptability data is highly dependent on how the data is labelled. The extension-based 2-valued σ-consistency problem for complete semantics is revealed as NP-complete, whereas the labelling-based 3-valued σ-consistency problem is solvable within polynomial time. We then present an informal discussion on application to grounded, stable, and preferred semantics

Investigating subclasses of abstract dialectical frameworks

Dialectical frameworks (ADFs) are generalizations of Dung argumentation frameworks where arbitrary relationships among arguments can be formalized. This additional expressibility comes with the price of higher computational complexity, thus an understanding of potentially easier subclasses is essential. Compared to Dung argumentation frameworks, where several subclasses such as acyclic and symmetric frameworks are well understood, there has been no in-depth analysis for ADFs in such direction yet (with the notable exception of bipolar ADFs). In this work, we introduce certain subclasses of ADFs and investigate their properties. In particular, we show that for acyclic ADFs, the different semantics coincide. On the other hand, we show that the concept of symmetry is less powerful for ADFs and further restrictions are required to achieve results that are similar to the known ones for Dung's frameworks. A particular such subclass (support-free symmetric ADFs) turns out to be closely related to argumentation frameworks with collective attacks (SETAFs); we investigate this relation in detail and obtain as a by-product that even for SETAFs symmetry is less powerful than for AFs. We also discuss the role of odd-length cycles in the subclasses we have introduced. Finally, we analyse the expressiveness of the ADF subclasses we introduce in terms of signatures

Synthesizing Argumentation Frameworks from Examples

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Advanced Algorithms for Abstract Dialectical Frameworks based on Complexity Analysis of Subclasses and SAT Solving

dialectical frameworks (ADFs) constitute one of the most powerful formalisms in abstract argumentation. Their high computational complexity poses, however, certain challenges when designing efficient systems. In this paper, we tackle this issue by (i) analyzing the complexity of ADFs under structural restrictions, (ii) presenting novel algorithms which make use of these insights, and (iii) implementing these algorithms via (multiple) calls to SAT solvers. An empirical evaluation of the resulting implementation on ADF benchmarks generated from ICCMA competitions shows that our solver is able to outperform state-of-the-art ADF systems. (c) 2022 The Author(s). Published by Elsevier B.V.Peer reviewe