Computational argumentation studies fundamental methods for reasoning within Artificial Intelligence (AI). Two prominent subfields in computational argumentation are abstract argumentation and structured argumentation. Abstract argumentation focuses on the interactions between arguments, ignoring their internal structure, while structured approaches utilize a given knowledge base to construct the arguments. Thus, the latter approach incorporates the internal structure of arguments into the reasoning process. In this work we introduce a form of abstraction on the well established structured approach of Assumption-Based Argumentation (ABA). Our goal is to provide methods to simplify complicated scenarios, by applying clustering over defeasible parts. Abstraction, particularly clustering, has been explored in recent research on abstract argumentation and in the adjacent field of logic programming. In fact, while clustering has also been applied to ABA, our approach takes a different, or rather dual, direction. In contrast to prior work on over-approximation on ABA, we propose the dual approach of under-approximation. We provide semantics for reasoning over clustered frameworks in a sound manner relative to original semantics, ensuring that any set deemed acceptable in the clustered scenario corresponds to an acceptable set. We show properties of the under-approximating semantics and illustrate our approach using a conceptual example based on medical recommendations.

Timed Argumentation Frameworks (TAFs) allow taking into account the availability of arguments and attacks in abstract argumentation. We propose a new reasoning approach for TAFs, where a standard Dung-style AF can be associated with each timepoint. We show that, although this framework is more expressive than Dung's framework, our approach does not lead to an increase in computational complexity for most reasoning problems and classical extension-based semantics.

In their daily use arguments are usually not completely enunciated. That is, we often rely on implicit parts, for example, unstated premises, sometimes referred to as enthymemes. Completions of partially stated arguments can favor knowledge engineering processes, where the workload of an engineer can be reduced by suggesting such completions. In this work, we focus on an integral aspect of completing arguments: valid argument structure of a completion. We phrase our results in the formal model of assumption-based argumentation (ABA). Based on an alternative characterization of tree-based arguments in ABA, we provide a declarative approach to compute completions of partial arguments in answer set programming (ASP), including the possibility of preferential reasoning in completions. We empirically evaluate a resulting prototype.

Reasoning under incomplete information is an important research direction in the study of computational argumentation. Most advances in this direction so far have focused on abstract argumentation frameworks. In particular, development of computational approaches to reasoning under incomplete information in structured formalisms remains to a large extent a challenge. We address this challenge by studying the problems of determining stability and relevance—with the aim of analyzing aspects of resilience of acceptance statuses in light of new information—in the central structured formalism of ASPIC+ . The specific ASPIC+ instantiation and grounded argumentation semantics we focus on are motivated by current applications in criminal investigation at the Netherlands Police. Our contributions consist of a theoretical analysis of the complexity of deciding stability and relevance as well as first exact algorithms for reasoning about stability and relevance in incomplete ASPIC+ theories. In terms of complexity results, we show that deciding stability is coNP-complete for incomplete ASPIC+ when assuming a preference ordering on defeasible rules via the last-link ordering, while deciding relevance is significantly more complex, namely NP^NP-complete. Complementing the complexity results, we develop practical algorithms for deciding stability and relevance based on the declarative paradigm of answer set programming (ASP). Furthermore, we provide an open-source implementation of the algorithms, and show empirically that the implementation exhibits promising scalability on both real-world and synthetic data. Our exact approach to stability is competitive with a previously proposed inexact approach, and the run times of our algorithms for both stability and relevance are sufficiently low on real-world data to be used in online settings.

Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. Here, we study an instantiation-based approach for reasoning in possibly non-flat ABA. For complete-based semantics, an approach of this kind was recently introduced, based on a semantics-preserving translation between ABA and bipolar argumentation frameworks (BAFs). Admissible semantics, however, require us to consider an extension of BAFs which also makes use of premises of arguments (pBAFs). We explore basic properties of pBAFs which we require as a theoretical underpinning for our proposed instantiation-based solver for non-flat ABA under admissible semantics. As our empirical evaluation shows, depending on the ABA instances, the instantiation-based solver is competitive against an ASP-based approach implemented in the style of state-of-the-art solvers for hard argumentation problems.

In Value-based Argumentation Frameworks (VAFs), values are ascribed to abstract arguments and ordered one to another to reflect an audience’s preferences. An attack of one argument on another is successful only if the audience does not prefer the value of the attacked argument to the value of the attacking argument. Audiences can disagree about admissible arguments relative to their value preferences. Complementary to VAFs, this paper presents a novel integration of Value-Based Reasoning Frameworks (VBFs) with instantiated argumentation, specifically we focus on the structured argumentation approach of ASPIC+. Agents associate literals with social values and weight of values; together, these are used to filter the literals compatible with their values. Such a set of literals is used to construct agent-relative ASPIC+ knowledge bases, agent-relative instantiated arguments, and argumentation frameworks (AFs). Agents can attack one another’s arguments. VAF and VBF present complementary perspectives on values on arguments. VBF contributes a new, formal, articulated view of agreement and disagreement amongst agents, which is grounded in their values. In addition, VBF helps us understand how different agents choose what to argue from out of a pool of common resources.

Abstract dialectical frameworks (ADFs) have been introduced as a formalism for modeling and evaluating argumentation, allowing for general logical acceptance conditions of arguments. Different criteria used to settle the acceptance of arguments are called semantics. Two-valued semantics of ADFs reflect the ‘black-and-white’ character of classical logic in non-monotonic frameworks. Stable semantics of ADFs were introduced to exclude cycles of self-justification of arguments among two-valued models. The stable semantics faces the challenge of potential non-existence of stable models. However, one might still want to draw conclusions even in case that an ADF has no two-valued models or stable models. Recently, the notions of semi-two-valued semantics and semi-stable semantics were introduced for ADFs. In the current work, we study the computational complexity of these two novel semantics. We show that the complexity of the semi-stable semantics is in general one level up in the polynomial hierarchy, compared to the stable semantics. We study the prominent reasoning tasks of credulous and skeptical reasoning, as well as the verification problem.

Reasoning with defeasible and conflicting knowledge in an argumentative form is a key research field in computational argumentation. Reasoning under various forms of uncertainty is both a key feature and a challenging barrier for automated argumentative reasoning. It was shown that argumentative reasoning using probabilities faces in general high computational complexity, in particular for the so-called constellation approach. In this paper, we develop an algorithmic approach to overcome this obstacle. We refine existing complexity results and show that two main reasoning tasks, that of computing the probability of a given set being an extension and an argument being acceptable, diverge in their complexity: the former is #P-complete and the latter is #-dot-NP-complete when considering their underlying counting problems. We present an algorithm for the complex task of computing the probability of a set of arguments being a complete extension by using dynamic programming operating on tree-decompositions. An experimental evaluation shows promise of our approach.

Approaches to computational argumentation provide foundational ways to reason argumentatively within Artificial Intelligence (AI). The underlying formal approaches can oftentimes be classified into structured argumentation and abstract argumentation. The former prescribe rigorous workflows, starting from knowledge bases to finding arguments in favour and against claims under scrutiny, and drawing conclusions. Abstract argumentation provides formal semantics operating on arguments whose internal structure is hidden and only relations are kept for reasoning, resulting in so-called argumentation frameworks (AFs). In this work, we apply a form of existential abstraction on the prominent structured approach of assumption-based argumentation (ABA), leading to an interactive way of simplifying argumentation scenarios by abstracting irrelevant details, towards supporting explainability. Existential abstraction was shown to be promising in many areas of AI, including a recent work on AFs. We lift this approach to the structured level---which is, as we show, both not direct from AFs and can benefit from utilization of the internal structure of arguments. Among our contributions, we introduce existential abstraction on ABA via clustering assumptions, develop semantics on clustered ABA frameworks for reasoning on such clusterings, show differences to the level of AFs, and provide a prototype interactive tool that obtains faithful clusterings that do not lead to any spurious reasoning.

We provide complexity results and algorithms for reasoning in the central structured argumentation formalism of ASPIC+. Considering ASPIC+ accommodated with preferences under the last-link principle, the results are made possible by rephrasing several argumentation semantics---admissible, complete, stable, preferred and grounded---in terms of defeasible elements of an ASPIC+ theory for both democratic and elitist last-link lifting. Via the rephrasing, we establish that acceptance is polynomial-time computable under grounded semantics, and complete for either NP, coNP, or Pi_P^2, depending on the reasoning mode and semantics. We also detail answer set programming encodings for deciding acceptance for the NP/coNP-complete reasoning tasks, and empirically show that it scales significantly better than first translating ASPIC+ reasoning tasks to abstract argumentation. Finally, we show that, in contrast to the last-link principle, it is NP-hard to compute the grounded extension under the weakest-link principle.

Recently forms of abstraction have been proposed for both logic programs (LPs) under the answer set semantics (ASP) and for the related formalism of assumption-based argumentation (ABA), e.g., via clustering of atoms or assumptions, in order to simplify a given LP or ABA framework. In both approaches after clustering the original answer sets and assumption sets are over-approximated, with the aim of avoiding spuriousness. In contrast, in ASP a given LP is syntactically modified to achieve over-approximation, while on ABA the framework is minimally modified and the semantics is abstracted. In this work we follow the latter approach and provide a novel semantical abstraction for LPs and for ABA frameworks corresponding to LPs.

Abstract We address complex reasoning tasks in assumption-based argumentation (ABA) by developing dynamic programming algorithms based on tree-decompositions. As one of the prominent approaches in computational argumentation, our focus is on NP-hard reasoning in ABA. We utilize tree-width, a structural measure describing closeness to trees, for an approach to handle computationally complex tasks in ABA. We contribute to the state of the art by first showing that many reasoning tasks in ABA are fixed-parameter tractable w.r.t. tree-width using Courcelle’s theorem, informally signaling wide applicability of dynamic programming algorithms for ABA. Secondly, we develop such algorithms operating on tree-decompositions of given ABA frameworks. We instantiate the algorithms in the recent D-FLAT framework allowing for declarative and extensible specification of dynamic programming algorithms. In an experimental evaluation on a resulting prototype, we show promise of the approach in particular for complex counting tasks.

A key ingredient of computational argumentation in AI is the generation of arguments in favor of or against claims under scrutiny. In this paper we look at the complexity of argument construction and reasoning in the prominent structured formalism of assumption-based argumentation (ABA). We point out that reasoning in ABA by means of constructing an abstract argumentation framework (AF) gives rise to two main sources of complexity: (i) constructing the AF and (ii) reasoning within the constructed graph. Since both steps are intractable in general, it is no surprise that the best performing state-of-the-art ABA reasoners skip the instantiation procedure entirely and perform tasks directly on the input knowledge base. Driven by this observation, we identify and study atomic and symmetric ABA, two ABA fragments that preserve the expressive power of general ABA, and that can be utilized to have milder complexity in the first or second step. We show that using atomic ABA allows for an instantiation procedure for general ABA leading to polynomially-bounded AFs and that symmetric ABA can be used to create AFs that have mild complexity to reason on. By an experimental evaluation, we show that using the former approach with modern AF solvers can be competitive with state-of-the-art ABA solvers, improving on previous AF instantiation approaches that are hindered by intractable argument construction.

Reasoning under incomplete information is an important research direction in AI argumentation. Most computational advances in this direction have so-far focused on abstract argumentation frameworks. Development of computational approaches to reasoning under incomplete information in structured formalisms remains to-date to a large extent a challenge. We address this challenge by studying the so-called stability and relevance problems---with the aim of analyzing aspects of resilience of acceptance statuses in light of new information---in the central structured formalism of ASPIC+. Focusing on the case of the grounded semantics and an ASPIC+ fragment motivated through application scenarios, we develop exact ASP-based algorithms for stability and relevance in incomplete ASPIC+ theories, and pinpoint the complexity of reasoning about stability (coNP-complete) and relevance (Sigma_2^P-complete), further justifying our ASP-based approaches. Empirically, the algorithms exhibit promising scalability, outperforming even a recent inexact approach to stability, with our ASP-based iterative approach being the first algorithm proposed for reasoning about relevance in ASPIC+.

We study a model of preference revision in which a prior preference over a set of alternatives is adjusted in order to accommodate input from an authoritative source, while maintaining certain structural constraints (e.g., transitivity, completeness), and without giving up more information than strictly necessary. We analyze this model under two aspects: the first allows us to capture natural distance-based operators, at the cost of a mismatch between the input and output formats of the revision operator. Requiring the input and output to be aligned yields a second type of operator, which we characterize using preferences on the comparisons in the prior preference Prefence revision is set in a logic-based framework and using the formal machinery of belief change, along the lines of the well-known AGM approach: we propose rationality postulates for each of the two versions of our model and derive representation results, thus situating preference revision within the larger family of belief change operators.

Computational argumentation is primed to strengthen the current hot research field of Explainable Artificial Intelligence (XAI), e.g., by dialectical approaches. In this paper, we extend and discuss a recently proposed approach of so-called strong acceptance on abstract argumentation that aims to support explaining argumentative acceptance. Our goal is to push these results into the realm of structured argumentation. In this setting, a knowledge base induces an abstract argumentation framework (AF) via instantiation. We investigate how and under which conditions it is possible to transfer results regarding strong acceptance between the given knowledge base and the induced AF. To this end we consider generic functions formalizing the interaction of the AF and the knowledge base. This approach helps us to infer rather general results making basic assumptions rather than dealing with the technical details of several structured argumentation formalisms. Along the way, we apply our techniques to the concrete approach of assumption-based argumentation (ABA) which constitutes one of the primal structured argumentation formalisms.

Dialectical Frameworks [1] (ADF) are a generalisation of Dung's Argumentation frameworks [2].Multiple approaches for reasoning under various semantics have been proposed over the last decade [3,4,5,6].We present "Abstract Dialectical Frameworks solved by Binary Decision Diagrams, developed in Dresden" (ADF-BDD) 2 , a novel approach that relies on the translation of the acceptance conditions of a given ADF into reduced ordered binary decision diagrams (roBDD) [7].Our system is based on the consideration that many otherwise hard to decide problems in ADF semantics (e. g., answering SAT-questions) can be solved in polynomial time on roBDDs (see [8] for an in-depth analysis).Our novel approach differs to the currently used systems, like the SAT-based approach K++ADF [5] or the wide spectrum of answer set programming (ASP) focused approaches like the DIAMOND family (e.g., DIAMOND [3] or GODIA-MOND [4]) and YADF [6].ADF-BDD is written in RUST [9] to provide good performance while enforcing a high amount of memory-and type-safety.In addition the rust-compiler produces highly optimised machine code, while keeping the whole tech stack simple.ADF-BDD accepts the established input format, introduced first in [10].There statements are unary predicates s, defining the labels and the acceptance conditions are binary predicates ac, relating the label to a formula.It allows to enumerate the grounded and complete interpretations, and stable models of the given input instance.The set of statements is the shared signature of all acceptance conditions, hence our implementation uses a single structure to store the nodes of all the roBDDs, which represent each acceptance condition.This allows for efficient caching of nodes and to eliminate duplicate node candidates.Another side-effect is that shared sub-BDDs are computed only once.ADF-BDD provides the explained implementation of roBDDs as the representation of the acceptance conditions.As the instantiation of roBDDs is a computational hard task, it is possible to utilise another state-of-the art competitive library called Biodivine/LibBDD 3 .It is part of the Biodivine software in the AEON project [11].While LibBDD is faster in 1 This work is partly supported by the BMBF, Grant 01IS20056 NAVAS, by the Center for Scalable Data Analytics and Artificial Intelligence (ScaDS.AI), and by the DFG through the Collaborative Research Center, Grant TRR 248 project ID 389792660.2

Assumption-based argumentation (ABA) is one of the most-studied formalisms for structured argumentation. While ABA is a general formalism that can be instantiated with various different logics, most attention from the computational perspective has been focused on the logic programming (LP) instantiation of ABA. Going beyond the LP-instantiation, we develop an algorithmic approach to reasoning in the propositional default logic (DL) instantiation of ABA. Our approach is based on iterative applications of Boolean satisfiability (SAT) solvers as a natural choice for implementing derivations as entailment checks in DL. We instantiate the approach for deciding acceptance and for assumption-set enumeration in the DL-instantiation of ABA under several central argumentation semantics, and empirically evaluate an implementation of the approach.

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 argumentation constitutes both a major research strand and a key approach that provides the core reasoning engine for a multitude of formalisms in computational argumentation in AI. Reasoning in abstract argumentation is carried out by viewing arguments and their relationships as abstract entities, with argumentation frameworks (AFs) being the most commonly used abstract formalism. Argumentation semantics then drive the reasoning by specifying formal criteria on which sets of arguments, called extensions, can be deemed as jointly acceptable. Such extensions provide a basic way of explaining argumentative acceptance. Inspired by recent research, we present a more general class of explanations: in this paper we propose and study so-called strong explanations for explaining argumentative acceptance in AFs. A strong explanation is a set of arguments such that a target set of arguments is acceptable in each subframework containing the explaining set. We formally show that strong explanations form a larger class than extensions, in particular giving the possibility of having smaller explanations. Moreover, assuming basic properties, we show that any explanation strategy, broadly construed, is a strong explanation. We show that the increase in variety of strong explanations comes with a computational trade-off: we provide an in-depth analysis of the associated complexity, showing a jump in the polynomial hierarchy compared to extensions.

Argumentation in Artificial Intelligence (AI) builds on formal approaches to reasoning argumentatively. Common to many such approaches is to use argumentation frameworks (AFs) as reasoning engines, with AFs being composed of arguments and attacks between arguments, which are instantiated from knowledge bases in a principle-based manner. While representing what can be argued for in an AF provides a conceptually clean way, this process can face challenges arising from generating a large number of arguments, which can act as a barrier to explainability. Inspired by successful approaches to model checking where the state explosion is mitigated by applying existential abstraction, we study an adaption of existential abstraction in form of clustering arguments in an AF to address an associated "argument explosion". In this paper, we provide a foundational investigation of this form of existential abstraction by defining semantics of the resulting clustered AFs, which balance two inherent aspects of existential abstractions: abstracting from concrete AFs and not permitting too much spuriousness (i.e., conclusions that hold on the abstraction but not on the original AF). Moreover, we show properties of clustered AFs, including complexity results, discuss use of clusterings for explaining results of reasoning tasks, and employ the recently introduced methodology of abstraction in answer set programming (ASP) for obtaining and reasoning over clustered AFs.

The study of computational models for argumentation is a vibrant area of artificial intelligence and, in particular, knowledge representation and reasoning research. Arguments most often have an intrinsic structure made explicit through derivations from more basic structures. Computational models for structured argumentation enable making the internal structure of arguments explicit. Assumption-based argumentation (ABA) is a central structured formalism for argumentation in AI. In this article, we make both algorithmic and complexity-theoretic advances in the study of ABA. In terms of algorithms, we propose a new approach to reasoning in a commonly studied fragment of ABA (namely the logic programming fragment) with and without preferences. While previous approaches to reasoning over ABA frameworks apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct declarative approach to ABA reasoning by encoding ABA reasoning tasks in answer set programming. We show via an extensive empirical evaluation that our approach significantly improves on the empirical performance of current ABA reasoning systems. In terms of computational complexity, while the complexity of reasoning over ABA frameworks is well-understood, the complexity of reasoning in the ABA+ formalism integrating preferences into ABA is currently not fully established. Towards bridging this gap, our results suggest that the integration of preferential information into ABA via so-called reverse attacks results in increased problem complexity for several central argumentation semantics.

Abstract Assumption-based argumentation (ABA) is a central structured argumentation formalism. As shown recently, answer set programming (ASP) enables efficiently solving NP-hard reasoning tasks of ABA in practice, in particular in the commonly studied logic programming fragment of ABA. In this work, we harness recent advances in incremental ASP solving for developing effective algorithms for reasoning tasks in the logic programming fragment of ABA that are presumably hard for the second level of the polynomial hierarchy, including skeptical reasoning under preferred semantics as well as preferential reasoning. In particular, we develop non-trivial counterexample-guided abstraction refinement procedures based on incremental ASP solving for these tasks. We also show empirically that the procedures are significantly more effective than previously proposed algorithms for the tasks.

In this paper we introduce proportionality to belief merging. Belief merging is a framework for aggregating information presented in the form of propositional formulas, and it generalizes many aggregation models in social choice. In our analysis, two incompatible notions of proportionality emerge: one similar to standard notions of proportionality in social choice, the other more in tune with the logic-based merging setting. Since established merging operators meet neither of these proportionality requirements, we design new proportional belief merging operators. We analyze the proposed operators against established rationality postulates, finding that current approaches to proportionality from the field of social choice are, at their core, incompatible with standard rationality postulates in belief merging. We provide characterization results that explain the underlying conflict, and provide a complexity analysis of our novel operators.

In this work we revisit computational aspects of strongly admissible semantics in Dung's abstract argumentation frameworks. First, we complement the existing complexity analysis by focusing on the problem of computing strongly admissible sets of minimum size that contain a given argument and providing NP-hardness as well as hardness of approximation results. Based on these results, we then investigate two approaches to compute (minimum-sized) strongly admissible sets based on Answer Set Programming (ASP) and Integer Linear Programming (ILP), and provide an experimental comparison of their performance.

A major research direction in AI argumentation is the study and development of practical computational techniques for reasoning in different argumentation formalisms. Compared to abstract argumentation, developing algorithmic techniques for different structured argumentation formalisms, such as assumption-based argumentation and the general ASPIC+ framework, is more challenging. At present, there is a lack of efficient approaches to reasoning in ASPIC+. We develop a direct declarative approach based on answer set programming (ASP) to reasoning in an instantiation of the ASPIC+ framework. We establish formal foundations for direct declarative encodings for reasoning in ASPIC+ without preferences for several central argumentation semantics, and detail ASP encodings of semantics for which reasoning about acceptance is NP-hard in ASPIC+. Empirically, the ASP approach scales up to frameworks of significant size, thereby answering the current lack of practical computational approaches to reasoning in ASPIC+ and providing a promising base for capturing further generalizations within ASPIC+.

Focusing on assumption-based argumentation (ABA) as a central structured formalism to AI argumentation, we propose a new approach to reasoning in ABA with and without preferences. While previous approaches apply either specialized algorithms or translate ABA reasoning to reasoning over abstract argumentation frameworks, we develop a direct approach by encoding ABA reasoning tasks in answer set programming. This significantly improves on the empirical performance of current ABA reasoning systems. We also give new complexity results for reasoning in ABA+, suggesting that the integration of preferential information into ABA results in increased problem complexity for several central argumentation semantics.

Argumentation is today a topical area of artificial intelligence (AI) research. Abstract argumentation, with argumentation frameworks (AFs) as the underlying knowledge representation formalism, is a central viewpoint to argumentation in AI. Indeed, from the perspective of AI and computer science, understanding computational and representational aspects of AFs is key in the study of argumentation. Realizability of AFs has been recently proposed as a central notion for analyzing the expressive power of AFs under different semantics. In this work, we propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. In particular, realizability gives means of establishing exact conditions on when a given collection of subsets of arguments has an AF with exactly the given collection as its set of extensions under a specific argumentation semantics. However, in various settings within the study of dynamics of argumentation---including revision and aggregation of AFs---non-realizability can naturally occur. To accommodate such settings, our notion of AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we study both theoretical and practical aspects of the problem. In particular, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to NP-hard AF synthesis using the constraint optimization paradigms of maximum satisfiability and answer set programming, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalizations of AF synthesis.

Abstract Dialectical Frameworks (ADFs) generalize Dung's argumentation frameworks allowing various relationships among arguments to be expressed in a systematic way. We further generalize ADFs so as to accommodate arbitrary acceptance degrees for the arguments. This makes ADFs applicable in domains where both the initial status of arguments and their relationship are only insufficiently specified by Boolean functions. We define all standard ADF semantics for the weighted case, including grounded, preferred and stable semantics. We illustrate our approach using acceptance degrees from the unit interval and show how other valuation structures can be integrated. In each case it is sufficient to specify how the generalized acceptance conditions are represented by formulas, and to specify the information ordering underlying the characteristic ADF operator. We also present complexity results for problems related to weighted ADFs.

Many recent studies of dynamics of formal argumentation in AI focus on the well-known formalism of argumentation frameworks (AFs). Despite their use-fulness in many areas of argumentation, their abstract notion of arguments creates a barrier for operators that modify a given AF, namely in the case that dependencies between arguments have been abstracted away that might be subsequently missed. In this paper we aim to support development of dynamic operators on formal models in abstract argumentation by providing constraints imposed on the modification of the structure that can be used to incorporate information that has been abstracted away. Towards a broad reach, we base our results on the general formalism of abstract dialectical frameworks (ADFs) in abstract argumentation, and study the complexity of the proposed structural constraints. To show applicability, we adapt an extension enforcement operator on AFs to ADFs that is allowed to only add support relations between arguments. We show feasibility of our approach by an experimental evaluation of an implementation of this operator.

We study a type of change on knowledge bases inspired by the dynamics of formal argumentation systems, where the goal is to enforce acceptance of certain arguments. We put forward that enforcing acceptance of arguments can be viewed as a member of the wider family of belief change operations, and that an axiomatic treatment of it is therefore desirable. In our case, laying down axioms enables a precise account of the close connection between enforcing arguments and belief revision. Our analysis of enforcing arguments proceeds by (i) axiomatizing it as an operation in propositional logic and providing a representation result in terms of rankings on sets of interpretations, (ii) showing that it stands in close relationship to belief revision, and (iii) using it as a gateway towards a principled treatment of enforcement in abstract argumentation.

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.

Argumentation is an active area of modern artificial intelligence (AI) research, with connections to a range of fields, from computational complexity theory and knowledge representation and reasoning to philosophy and social sciences, as well as application-oriented work in domains such as legal reasoning, multi-agent systems, and decision support. Argumentation frameworks (AFs) of abstract argumentation have become the graph-based formal model of choice for many approaches to argumentation in AI, with semantics defining sets of jointly acceptable arguments, i.e., extensions. Understanding the dynamics of AFs has been recently recognized as an important topic in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation as a recently proposed form of argumentation dynamics. We provide a nearly complete computational complexity map of argument-fixed extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constraint optimization under the maximum satisfiability (MaxSAT) paradigm. Going beyond NP, we propose novel MaxSAT-based counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.

Understanding the dynamics of argumentation frameworks (AFs) is important in the study of argumentation in AI. In this work, we focus on the so-called extension enforcement problem in abstract argumentation. We provide a nearly complete computational complexity map of fixed-argument extension enforcement under various major AF semantics, with results ranging from polynomial-time algorithms to completeness for the second-level of the polynomial hierarchy. Complementing the complexity results, we propose algorithms for NP-hard extension enforcement based on constrained optimization. Going beyond NP, we propose novel counterexample-guided abstraction refinement procedures for the second-level complete problems and present empirical results on a prototype system constituting the first approach to extension enforcement in its generality.

Argumentation is nowadays a core topic in AI research. Understanding computational and representational aspects of abstract argumentation frameworks (AFs) is a central topic in the study of argumentation. The study of realizability of AFs aims at understanding the expressive power of AFs under different semantics. We propose and study the AF synthesis problem as a natural extension of realizability, addressing some of the shortcomings arising from the relatively stringent definition of realizability. Specifically, AF synthesis seeks to construct, or synthesize, AFs that are semantically closest to the knowledge at hand even when no AFs exactly representing the knowledge exist. Going beyond defining the AF synthesis problem, we (i) prove NP-completeness of AF synthesis under several semantics, (ii) study basic properties of the problem in relation to realizability, (iii) develop algorithmic solutions to AF synthesis using constrained optimization, (iv) empirically evaluate our algorithms on different forms of AF synthesis instances, as well as (v) discuss variants and generalization of AF synthesis.

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.

Abstract The design of efficient solutions for abstract argumentation problems is a crucial step towards advanced argumentation systems. One of the most prominent approaches in the literature is to use Answer-Set Programming (ASP) for this endeavor. In this paper, we present new encodings for three prominent argumentation semantics using the concept of conditional literals in disjunctions as provided by the ASP-system clingo. Our new encodings are not only more succinct than previous versions, but also outperform them on standard benchmarks.

Abstract dialectical frameworks (ADFs) constitute a recent and powerful generalization of Dung's argumentation frameworks (AFs), where the relationship between the arguments is specified via Boolean formulas. Recent results have shown that this enhancement comes with the price of higher complexity compared to AFs. In fact, acceptance problems in the world of ADFs can be hard even for the third level of the polynomial hierarchy. In order to implement reasoning problems on ADFs, systems for quantified Boolean formulas (QBFs) thus are suitable engines to be employed. In this paper we present QBF encodings on ADF problems generalizing recent work on QBFs for AF labellings. Our encodings not only provide a uniform and modular way of translating reasoning in ADFs to QBFs, but also build the basis for a novel system. We present a prototype implementation for the admissible and preferred semantics and evaluate its performance in comparison with another state-of-the-art tool for ADFs.