Abstract 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.

Abstract Powerful formalisms for abstract argumentation have been proposed, among them abstract dialectical frameworks (ADFs) that allow for a succinct and flexible specification of the relationship between arguments and the GRAPPA framework which allows argumentation scenarios to be represented as arbitrary edge-labeled graphs. The complexity of ADFs and GRAPPA is located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from ADFs and GRAPPA to ASP. More specifically, we provide reductions for the five main ADF semantics of admissible, complete, preferred, grounded, and stable interpretations, and exemplify how these reductions need to be adapted for GRAPPA for the admissible, complete, and preferred semantics.

Abstract 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 indepth 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. We also provide experiments to analyse the performance of solvers when applied to particular subclasses of ADFs.

Abstract 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) empirically evaluating a resulting implementation which relies on calls to SAT solvers.

Powerful formalisms for abstract argumentation have been proposed. Their complexity is often located beyond NP and ranges up to the third level of the polynomial hierarchy. The combined complexity of Answer-Set Programming (ASP) exactly matches this complexity when programs are restricted to predicates of bounded arity. In this paper, we exploit this coincidence and present novel efficient translations from abstract dialectical frameworks (ADFs) and GRAPPA to ASP.We also empirically compare our approach to other systems for ADF reasoning and report promising results.

We introduce a parametrized equivalence notion for abstract argumentation that subsumes standard and strong equivalence as corner cases. Under this notion, two argumentation frameworks are equivalent if they deliver the same extensions under any addition of arguments and attacks that do not affect a given set of core arguments. As we will see, this notion of equivalence nicely captures the concept of local simplifications. We provide exact characterizations and complexity results for deciding our new notion of equivalence.

Dung's abstract argumentation theory is a widely used formalism to model conflicting information and to draw conclusions in such situations. Hereby, the knowledge is represented by argumentation frameworks (AFs) and the reasoning is done via semantics extracting acceptable sets. All reasonable semantics are based on the notion of conflict-freeness which means that arguments are only jointly acceptable when they are not linked within the AF. In this paper, we study the question which information on top of conflict-free sets is needed to compute extensions of a semantics at hand. We introduce a hierarchy of verification classes specifying the required amount of information and show that well-known semantics are exactly verifiable through a certain such class. This also gives a means to study semantics lying between known semantics, thus contributing to a more abstract understanding of the different features argumentation semantics offer.

We introduce a general framework for analyzing realizability in abstract dialectical frameworks (ADFs) and various of its subclasses. In particular, the framework applies to Dung argumentation frameworks, SETAFs by Nielsen and Parsons, and bipolar ADFs. We present a uniform characterization method for the admissible, complete, preferred and model/stable semantics. We employ this method to devise an algorithm that decides realizability for the mentioned formalisms and semantics; moreover the algorithm allows for constructing a desired knowledge base whenever one exists. The algorithm is built in a modular way and thus easily extensible to new formalisms and semantics. We have implemented our approach in answer set programming, and used the implementation to obtain several novel results on the relative expressiveness of the abovemen-tioned formalisms.

The resolution-based grounded semantics constitutes one of the most interesting approaches for the evaluation of abstract argumentation frameworks. This particular semantics satisfies a large number of desired properties, among them all properties proposed by Baroni and Giacomin. In recent years, the analysis of argumentation semantics has been extended by further topics, among them characterizations for equivalence notions, intertranslatability issues, and expressibility in terms of signatures (all possible sets of extensions a semantics is capable to express). In this line of research, resolution-based grounded semantics has been neglected so far. We close this gap here, compare the expressibility of resolution-based grounded semantics with other prominent semantics, provide a characterization for strong equivalence and complement existing complexity results.

Among the abundance of generalizations of abstract argumentation frameworks, the formalism of abstract dialectical frameworks (ADFs) proved to be powerful in modelling various argumentation problems. Implementations of reasoning tasks that come within ADFs struggle with their high computational complexity. Thus methods simplifying the evaluation process are required. One such method is splitting, which was shown to be an effective optimization technique in other nonmonotonic formalisms. We apply this approach to ADFs by providing suitable techniques for directional splitting (allowing links only from the first to the second part of the splitting) under all the standard semantics of ADFs as well as preliminary results on general splitting.

Abstract argumentation frameworks (AFs) are one of the most studied formalisms in AI. In this work, we introduce a certain subclass of AFs which we call compact. Given an extension-based semantics, the corresponding compact AFs are characterized by the feature that each argument of the AF occurs in at least one extension. This not only guarantees a certain notion of fairness; compact AFs are thus also minimal in the sense that no argument can be removed without changing the outcome. We address the following questions in the paper: (1) How are the classes of compact AFs related for different semantics? (2) Under which circumstances can AFs be transformed into equivalent compact ones? (3) Finally, we show that compact AFs are indeed a non-trivial subclass, since the verification problem remains coNP-hard for certain semantics.