Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing a qualitative comparison of assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics-grounded and complete semantics-is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture the attack relation between assumptions in ABA+. Second, we exploit this correspondence between ABA+ and HYPAFs to obtain relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. Finally, we discuss fundamental properties and provide a thorough complexity analysis for both the abstract HYPAFs as well as ABA+.

Answer Set Programming (Asp) is used in many real-world applications as an easy-to-use and efficient modeling paradigm. In Asp, rules (containing variables) are instantiated against facts to derive conclusions (i.e., grounding the program). However, a large number of variables and facts (more precisely: domain values) leads to the well-known “grounding bottleneck”: the variables in a rule are instantiated by every combination of domain values, leading to potentially infeasibly large ground programs. This is especially problematic for rules with large rule bodies containing many variables, as standard grounding approaches cause an exponential blowup in the total number of variables in a rule. This paper presents a novel method to overcome this obstacle. In contrast to the standard approach, our technique “decouples” the body atoms, i.e., the instantiation handles each body atom separately. In particular, our procedure translates a non-ground tight program to a ground disjunctive program that is exponential only in the maximum predicate arity, and is thus polynomial if this arity is fixed to a constant. We extend this to non-ground, normal programs, and ultimately use similar ideas to translate non-ground, disjunctive programs to ground epistemic logic programs—all while decoupling the body atoms. We demonstrate the feasibility of this new method experimentally by comparing it to standard Asp technology in terms of grounding size, grounding time and total runtime.

In the current paper we re-examine the concepts of attack semantics and collective attacks in abstract argumentation, and examine how these concepts interact with each other. For this, we systematically map the space of possibilities. Starting with standard argumentation frameworks (which consist of a directed graph with nodes and arrows) we briefly state both node semantics and arrow semantics (the latter a.k.a. attack semantics) in both their extensions-based form and labellings-based form. We then proceed with SETAFs (which consist of a directed hypergraph of nodes and arrows, to take into account the notion of collective attacks) and state both node semantics and arrow semantics, in both their extensions-based and labellings-based form. We then show equivalence between the extensions-based and labellings-based form, for node semantics and arrow semantics of AFs, as well as for node semantics and arrow semantics of SETAFs. Moreover, we show equivalence between node semantics and arrow semantics for AFs, and equivalence between node semantics and arrow semantics for SETAFs (with the notable exception of semi-stable). We also provide a novel way of converting a SETAF to an AF such that semantics are preserved, without the use of any “meta arguments”. Although the main part of our work is on the level of abstract argumentation, we do provide an application of our theory on the instantiated level. More specifically, we show that the classical characterisation of Assumption-Based Argumentation (ABA) can be seen as an instantiation based on a SETAF, whereas the contemporary characterisation of ABA can be seen as an instantiation based on a standard AF. Our theory of how to convert a SETAF to an AF can then be used to account for both the similarities and the differences between the classical and contemporary characterisations of ABA. Most prominently, our theory is able to explain the semantic mismatch for semi-stable semantics that arises in the ABA instantiation process.

argumentation has proven to be a versatile tool to model and analyze various problems in an argumentative setting. The addition of collective attacks syntactically extends Dung’s original argumentation frameworks (AFs), while retaining the most desirable properties—the resulting class of frameworks is called SETAFs. While most reasoning tasks in the realm of abstract argumentation have been shown to be intractable, real-world instances oftentimes are not entirely random but admit a certain structure that allows for efficient computational shortcuts. In certain cases, we can characterize this structure via an integer parameter, and exploit these insights with advanced algorithmic techniques. A thorough analysis of the computational aspects of SETAFs w.r.t. parameterized algorithms has not yet been conducted. We start the investigation of these approaches by applying the backdoor and treewidth approaches to SETAFs. A backdoor is a part of a problem instance, such that removing the backdoor leads to a simple structure. If we can find such a backdoor and guess the solution on this part (respectively, extensions), the rest of the solution follows almost effortlessly. Similarly, the treewidth of a problem instance is a parameter that characterizes the properties of the instance’s graph structure. Intuitively, the lower the treewidth of a graph, the more “tree-like” it is. Since most argumentation problems become easy on trees, one can exploit low treewidth for efficient algorithms. In this paper, we establish that for SETAFs with constant backdoor sizes general argumentation tasks become efficiently solvable—they are fixed-parameter tractable. We generalize the respective techniques that are known for the special case of Dung-style AFs and show that they also apply to the more general case of SETAFs. In addition, we can show an improvement in the asymptotic runtime compared to earlier approaches for AFs via two-valued guesses instead of the state-of-the-art three-valued approach. Along the way, we point out similarities and interesting situations arising from the more general setting. While treewidth is well-studied in the context of AFs with their graph structure, it cannot be directly applied to the (directed) hypergraphs representing SETAFs. We thus introduce two generalizations of treewidth based on different graphs that can be associated with SETAFs, that is, the primal graph and the incidence graph. We show that while some of these notions allow for parameterized tractability results, reasoning remains intractable for other notions, even if we fix the parameter to a small constant. We present parameterized algorithms for efficient reasoning on SETAFs via tree decompositions by characterizing extensions not only by labeling the arguments, but also by assigning (temporary) labels to the attacks.

Already in Dung’s seminal paper introducing Abstract Argumentation Frameworks (AFs), several connections to seemingly unrelated reasoning formalisms have been illustrated. In this work, we continue this trend and establish a connection between abstract argumentation frameworks and boolean networks (BNs). BNs, in a nutshell, mimic simple binary-valued systems, where for each point in time, the value of each bit (component) depends only on the other components’ values of the previous point in time of the network. This formalism is widely used to formally analyze biological processes, where from simple rules complex behavior emerges. We show that stable extensions of an arbitrary AF correspond to single state attractors of its canonically corresponding BN, the complete extensions correspond to a distinctive 2-state attractor, and the admissible sets correspond to the seeds of the BN. We thereby lay the groundwork for a fruitful exchange of ideas between the two research areas.

Assumption-based argumentation (ABA) is a powerful defeasible reasoning formalism which is based on the interplay of assumptions, their contraries, and inference rules. ABA with preferences (ABA+) generalizes the basic model by allowing qualitative comparison between assumptions. The integration of preferences however comes with a cost. In ABA+, the evaluation under two central and well-established semantics---grounded and complete semantics---is not guaranteed to yield an outcome. Moreover, while ABA frameworks without preferences allow for a graph-based representation in Dung-style frameworks, an according instantiation for general ABA+ frameworks has not been established so far. In this work, we tackle both issues: First, we develop a novel abstract argumentation formalism based on set-to-set attacks. We show that our so-called Hyper Argumentation Frameworks (HYPAFs) capture ABA+. Second, we propose relaxed variants of complete and grounded semantics for HYPAFs that yield an extension for all frameworks by design, while still faithfully generalizing the established semantics of Dung-style Argumentation Frameworks. We exploit the newly established correspondence between ABA+ and HYPAFs to obtain variants for grounded and complete ABA+ semantics that are guaranteed to yield an outcome. Finally, we discuss basic properties and provide a complexity analysis. Along the way, we settle the computational complexity of several ABA+ semantics.

In formal argumentation one aims for intuitive and concise justifications for the acceptance of arguments. Discussion games and dispute trees are established methods to obtain such a justification. However, so far these techniques are based on instantiating the knowledge base into graph-based Dung style abstract argumentation frameworks (AFs). These instantiations are known to produce frameworks with a large number of arguments and thus also yield long discussion games and large dispute trees. To obtain more concise justifications for argument acceptance, we propose to instantiate the knowledge base as an argumentation framework with collective attacks (SETAF). Remarkably, this approach yields smaller frameworks compared to traditional AF instantiation, while exhibiting increased expressive power. We then introduce discussion games and dispute trees tailored to SETAFs, show that they correspond to credulous acceptance w.r.t. the well-known preferred semantics, analyze and tune them w.r.t. the size, and compare the two notions. Finally, we illustrate how our findings apply to assumption-based argumentation.

Is an argument acceptable if all potential counter-arguments are unacceptable themselves? In standard models of argumentation, the answer to this question is counter-intuitively not necessarily yes. However, based on the notion of weak admissibility, a family of semantics has been established where these unreasonable attacks do not successfully counter otherwise strong arguments. While in the abstract setting weak admissibility is well-understood, a similar issue arises in the context of structured argumentation formalisms like assumption based argumentation (ABA). It is well known that under standard argumentation semantics, ABA frameworks can be reduced to abstract argumentation frameworks (AFs), however, it turns out that in the case of weak admissibility this approach surprisingly fails. We instead propose to utilize a recently published instantiation technique utilizing collective attacks (SETAFs). We first define weak admissibility for SETAFs and study basic properties; afterwards, we push our proposal to the structured setting. We show that via our approach the characteristic properties of weak admissibility carry over to ABA, and thus establish a basis for further studies of these common scenarios also in ABA and related structured argumentation formalisms.

Argumentation frameworks (AFs) are a key formalism in AI research. Their semantics have been investigated in terms of principles, which define characteristic properties in order to deliver guidance for analyzing established and developing new semantics. Because of the simple structure of AFs, many desired properties hold almost trivially, at the same time hiding interesting concepts behind syntactic notions. We extend the principle-based approach to argumentation frameworks with collective attacks (SETAFs) and provide a comprehensive overview of common principles for their semantics. Our analysis shows that investigating principles based on decomposing the given SETAF (e.g. directionality or SCC-recursiveness) poses additional challenges in comparison to usual AFs. We introduce the notion of the reduct as well as the modularization principle for SETAFs which will prove beneficial for this kind of investigation. We then demonstrate how our findings can be utilized for incremental computation of extensions and show how we can use graph properties of the frameworks to speed up these algorithms.

•Right atrial bubbles were detected without active infusion during stress echocardiography.•Bubbles can be caused by the VP.•The VP occurs as a result of degeneration of intervertebral disks.

In abstract argumentation, arguments jointly attacking single arguments is a well-understood concept, captured by the established notion of SETAFs—argumentation frameworks with collective attacks. In contrast, the idea of sets attacking other sets of arguments has not received much attention so far. In this work, we contribute to the development of set-to-set defeat in formal argumentation. To this end, we introduce so called hyper argumentation frameworks (HYPAFs), a new formalism that extends SETAFs by allowing for set-to-set attacks. We investigate this notion by interpreting these novel attacks in terms of universal, indeterministic, and collective defeat. We will see that universal defeat can be naturally captured by the already existing SETAFs. While this is not the case for indeterministic defeat, we show a close connection to attack-incomplete argumentation frameworks. To formalize our interpretation of collective defeat, we develop novel semantics yielding a natural generalization of attacks between arguments to set-to-set attacks. We investigate fundamental properties and identify several surprising obstacles; for instance, the well-known fundamental lemma is violated, and the grounded extension might not exist. Finally, we investigate the computational complexity of the thereby arising problems.

Qualitative Choice Logic (QCL) extends classical propositional formulas by a connective called ordered disjunction that is used to express preferences. We translate QCL theories to Argumentation Frameworks with Collective Attacks (SETAFs), and show that the preferred models of the original theory directly correspond to the semi-stable extensions of the target framework. This further allows us to decide the problem of preferred model entailment for QCL via SETAFs.

Argumentation frameworks (AFs) are a core formalism in the field of formal argumentation. As most standard computational tasks regarding AFs are hard for the first or second level of the Polynomial Hierarchy, a variety of algorithmic approaches to achieve manageable runtimes have been considered in the past. Among them, the backdoor-approach and the treewidth-approach turned out to yield fixed-parameter tractable fragments. However, many applications yield high parameter values for these methods, often rendering them infeasible in practice. We introduce the backdoor-treewidth approach for abstract argumentation, combining the best of both worlds with a guaranteed parameter value that does not exceed the minimum of the backdoor- and treewidth-parameter. In particular, we formally define backdoor-treewidth and establish fixed-parameter tractability for standard reasoning tasks of abstract argumentation. Moreover, we provide systems to find and exploit backdoors of small width, and conduct systematic experiments evaluating the new parameter.

Argumentation Frameworks (AFs) are a key formalism in AI research. Their semantics have been investigated in terms of principles, which define characteristic properties in order to deliver guidance for analysing established and developing new semantics. Because of the simple structure of AFs, many desired properties hold almost trivially, at the same time hiding interesting concepts behind syntactic notions. We extend the principle-based approach to Argumentation Frameworks with Collective Attacks (SETAFs) and provide a comprehensive overview of common principles for their semantics. Our analysis shows that investigating principles based on decomposing the given SETAF (e.g. directionality or SCC-recursiveness) poses additional challenges in comparison to usual AFs. We introduce the notion of the reduct as well as the modularization principle for SETAFs which will prove beneficial for this kind of investigation. We then demonstrate how our findings can be utilized for incremental computation of extensions and give a novel parameterized tractability result for verifying preferred extensions.

Many structured argumentation approaches proceed by constructing a Dung-style argumentation framework (AF) corresponding to a given knowledge base. While a main strength of AFs is their simplicity, instantiating a knowledge base oftentimes requires exponentially many arguments or additional functions in order to establish the connection. In this paper we make use of more expressive argumentation formalisms. We provide several novel translations by utilizing claim-augmented AFs (CAFs) and AFs with collective attacks (SETAFs). We use these frameworks to translate assumption-based argumentation (ABA) frameworks as well as logic programs (LPs) into the realm of graph-based argumentation.

Many structured argumentation approaches proceed by constructing a Dung-style argumentation framework (AF) corresponding to a given knowledge base. While a main strength of AFs is their simplicity, instantiating a knowledge base oftentimes requires exponentially many arguments or additional functions in order to establish the connection. In this paper we make use of more expressive argumentation formalisms. We provide several novel translations by utilizing claim-augmented AFs (CAFs) and AFs with collective attacks (SETAFs). We use these frameworks to translate assumption-based argumentation (ABA) frameworks as well as logic programs (LPs) into the realm of graph-based argumentation.

Analyzing computational aspects of argumentation has the ultimate goal to find efficient tools to reason in an argumentative setting. In particular, exploiting islands of tractability leads to enhancements of our ability to create such tools. In this work, we identify as such an island of tractability deletion-backdoors for argumentation frameworks with collective attacks (SETAFs). A backdoor is the part of a problem instance, the removal of which leads to a simple structure. If we can find such a backdoor and guess the solution on this part (in the context of argumentation: extensions), the rest of the solution follows almost effortlessly. In terms of complexity analysis, this means for constant backdoor sizes, general argumentation tasks become efficiently solvable—they are fixed-parameter tractable. In this work, we generalize the respective techniques that are known for the special case of Dung-style argumentation frameworks (AFs) and show that they also apply to the more general case of SETAFs. In addition, we can show an improvement in the asymptotic runtime compared to earlier approaches for AFs. Along the way, we point out similarities and interesting situations arising from the more general setting.

In this solver description we present ASPARTIX-V, in its 2021 edition, which participates in the International Competition on Computational Models of Argumentation (ICCMA) 2021. ASPARTIX-V is capable of solving all classical (static) reasoning tasks part of ICCMA'21 and extends the ASPARTIX system suite by incorporation of recent ASP language constructs (e.g. conditional literals), domain heuristics within ASP, and multi-shot methods. In this light ASPARTIX-V deviates from the traditional focus of ASPARTIX on monolithic approaches (i.e., one-shot solving via a single ASP encoding) to further enhance performance.

Argumentation frameworks with collective attacks (SETAFs) have gained increasing attention in recent years as they provide a natural extension of the well-known abstract argumentation frameworks (AFs) due to Dung. Concerning complexity, it is known that for the standard reasoning tasks in abstract argumentation, SETAFs show the same behavior as AFs, i.e. they are mainly located on the first or second level of the polynomial hierarchy. However, while for AFs there is a rich literature on easier fragments, complexity analyses in this direction are still missing for SETAFs. In particular, the well-known graph-classes of acyclic AFs, even-cycle-free AFs, symmetric AFs, and bipartite AFs have been shown tractable. In this paper, we aim to extend these results to the more general notion of SETAFs. In particular, we provide various syntactic notions on SETAFs that naturally generalize the graph properties for directed hypergraphs, and perform a complexity analysis of the prominent credulous and skeptical acceptance problems for several different widely used semantics.