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

On the Equivalence between Abstract Dialectical Frameworks and Logic Programs

Abstract Dialectical Frameworks (ADFs) are argumentation frameworks where each node is associated with an acceptance condition. This allows us to model different types of dependencies as supports and attacks. Previous studies provided a translation from Normal Logic Programs (NLPs) to ADFs and proved the stable models semantics for a normal logic program has an equivalent semantics to that of the corresponding ADF. However, these studies failed in identifying a semantics for ADFs equivalent to a three-valued semantics (as partial stable models and well-founded models) for NLPs. In this work, we focus on a fragment of ADFs, called Attacking Dialectical Frameworks (ADF+s), and provide a translation from NLPs to ADF+s robust enough to guarantee the equivalence between partial stable models, well-founded models, regular models, stable models semantics for NLPs and respectively complete models, grounded models, preferred models, stable models for ADFs. In addition, we define a new semantics for ADF+s, called L-stable, and show it is equivalent to the L-stable semantics for NLPs