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Anna Rapberger

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31 papers
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31

AAAI Conference 2026 Conference Paper

Argumentative Debates for Transparent Bias Detection

  • Hamed Ayoobi
  • Nico Potyka
  • Anna Rapberger
  • Francesca Toni

As the use of AI in society grows, addressing emerging biases is essential to prevent systematic discrimination. Several bias detection methods have been proposed, but, with few exceptions, these tend to ignore transparency. Instead, interpretability and explainability are core requirements for algorithmic fairness, even more so than for other algorithmic solutions, given the human-oriented nature of fairness. We present ABIDE (Argumentative BIas detection by DEbate), a novel framework that structures bias detection transparently as debate, guided by an underlying argument graph as understood in (formal and computational) argumentation. The arguments are about the success chances of groups in local neighbourhoods and the significance of these neighbourhoods. We evaluate ABIDE experimentally and demonstrate its strengths in performance against an argumentative baseline.

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AAAI Conference 2026 Conference Paper

Heterogeneous Graph Neural Networks for Assumption-Based Argumentation

  • Preesha Gehlot
  • Anna Rapberger
  • Fabrizio Russo
  • Francesca Toni

Assumption‐Based Argumentation (ABA) is a powerful structured argumentation formalism, but exact computation of extensions under stable semantics is intractable for large frameworks. We present the first Graph Neural Network (GNN) approach to approximate credulous acceptance in ABA. To leverage GNNs, we model ABA frameworks via a dependency graph representation encoding assumptions, claims and rules as nodes, with heterogeneous edge labels distinguishing support, derive and attack relations. We propose two GNN architectures—ABAGCN and ABAGAT—that stack residual heterogeneous convolution or attention layers, respectively, to learn node embeddings. Our models are trained on the ICCMA 2023 benchmark, augmented with synthetic ABAFs, with hyperparameters optimised via Bayesian search. Empirically, both ABAGCN and ABAGAT outperform a state‐of‐the‐art GNN baseline that we adapt from the abstract argumentation iterature, achieving a node‐level F1 score of up to 0.71 on the ICCMA instances. Finally, we develop a sound polynomial time extension‐reconstruction algorithm driven by our predictor: it reconstructs stable extensions with F1 above 0.85 on small ABAFs and maintains an F1 of about 0.58 on large frameworks. Our work opens new avenues for scalable approximate reasoning in structured argumentation.

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KR Conference 2025 Conference Paper

On Gradual Semantics for Assumption-Based Argumentation

  • Anna Rapberger
  • Fabrizio Russo
  • Antonio Rago
  • Francesca Toni

In computational argumentation, gradual semantics are fine-grained alternatives to extension-based and labelling-based semantics. They ascribe a dialectical strength to (components of) arguments sanctioning their degree of acceptability. Several gradual semantics have been studied for abstract, bipolar and quantitative bipolar argumentation frameworks (QBAFs), as well as, to a lesser extent, for some forms of structured argumentation. However, this has not been the case for assumption-based argumentation (ABA), despite it being a popular form of structured argumentation with several applications where gradual semantics could be useful. In this paper, we fill this gap and propose a family of novel gradual semantics for equipping assumptions, which are the core components in ABA frameworks, with dialectical strengths. To do so, we use bipolar set-based argumentation frameworks as an abstraction of (potentially non-flat) ABA frameworks and generalise state-of-the-art modular gradual semantics for QBAFs. We show that our gradual ABA semantics satisfy suitable adaptations of desirable properties of gradual QBAF semantics, such as balance and monotonicity. We also explore an argument-based approach that leverages established QBAF modular semantics directly, and use it as baseline. Finally, we conduct experiments with synthetic ABA frameworks to compare our gradual ABA semantics with its argument-based counterpart and assess convergence.

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IJCAI Conference 2025 Conference Paper

On Independence and SCC-Recursiveness in Assumption-Based Argumentation

  • Lydia Blümel
  • Anna Rapberger
  • Matthias Thimm
  • Francesca Toni

We introduce a notion of conditional independence in (flat) assumption-based argumentation (ABA), where independence between (sets of) assumptions amounts to the presence of information about one set of assumptions not impacting the acceptability of another. We study general properties, computational complexity, and the relation to independence in abstract argumentation. In light of the high computational complexity of deciding independence, we introduce sound methods for checking independence in polynomial time via two different routes: the first utilizes the strongly connected components (SCCs) of the instantiated abstract argumentation framework; the second exploits the structure of the ABA framework directly. Along the way, we introduce the notion of SCC-recursiveness for ABA.

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KR Conference 2025 Conference Paper

On Strong and Weak Admissibility in Non-Flat Assumption-Based Argumentation

  • Matti Berthold
  • Lydia Blümel
  • Anna Rapberger

In this work, we broaden the investigation of admissibility notions in the context of assumption-based argumentation (ABA). More specifically, we study two prominent alternatives to the standard notion of admissibility from abstract argumentation, namely strong and weak admissibility, and introduce the respective preferred, complete and grounded semantics for general (sometimes called non-flat) ABA. To do so, we use abstract bipolar set-based argumentation frameworks (BSAFs) as formal playground since they concisely capture the relations between assumptions and are expressive enough to represent general non-flat ABA frameworks, as recently shown. While weak admissibility has been recently investigated for a restricted fragment of ABA in which assumptions cannot be derived (flat ABA), strong admissibility has not been investigated for ABA so far. We introduce strong admissibility for ABA and investigate desirable properties. We furthermore extend the recent investigations of weak admissibility in the flat ABA fragment to the non-flat case. We show that the central modularization property is maintained under classical, strong, and weak admissibility. We also show that strong and weakly admissible semantics in non-flat ABA share some of the shortcomings of standard admissible semantics and discuss ways to address these.

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KR Conference 2024 Conference Paper

Argumentative Causal Discovery

  • Fabrizio Russo
  • Anna Rapberger
  • Francesca Toni

Causal discovery amounts to unearthing causal relationships amongst features in data. It is a crucial companion to causal inference, necessary to build scientific knowledge without resorting to expensive or impossible randomised control trials. In this paper, we explore how reasoning with symbolic representations can support causal discovery. Specifically, we deploy assumption-based argumentation (ABA), a well-established and powerful knowledge representation formalism, in combination with causality theories, to learn graphs which reflect causal dependencies in the data. We prove that our method exhibits desirable properties, notably that, under natural conditions, it can retrieve ground-truth causal graphs. We also conduct experiments with an implementation of our method in answer set programming (ASP) on four datasets from standard benchmarks in causal discovery, showing that our method compares well against established baselines.

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KR Conference 2024 Conference Paper

Capturing Non-flat Assumption-based Argumentation with Bipolar SETAFs

  • Matti Berthold
  • Anna Rapberger
  • Markus Ulbricht

While the flat fragment of assumption-based argumentation (ABA) is widely studied in the literature, the general, non-flat case has mostly been neglected so far. Until recently, there was no possible way to instantiate non-flat ABA in terms of an abstract argumentation framework. While this gap has been closed for complete-based ABA semantics, capturing admissible-based semantics cannot yet be achieved by looking at the relation between the instantiated arguments only; it requires augmenting arguments with their premises, hence being a semi-abstract instantiaiton. In this paper, we provide a compact and fully abstract instantiation by making use of both collective attack and support relations. Then, inspired by fundamental properties of abstract formalisms, we identify flaws of native ABA semantics in the non-flat case and provide refinements thereof, utilizing our novel instatiation.

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KR Conference 2024 Conference Paper

Contestable AI Needs Computational Argumentation

  • Francesco Leofante
  • Hamed Ayoobi
  • Adam Dejl
  • Gabriel Freedman
  • Deniz Gorur
  • Junqi Jiang
  • Guilherme Paulino-Passos
  • Antonio Rago

AI has become pervasive in recent years, but state-of-the-art approaches predominantly neglect the need for AI systems to be contestable. Instead, contestability is advocated by AI guidelines (e. g. by the OECD) and regulation of automated decision-making (e. g. GDPR). In this position paper we explore how contestability can be achieved computationally in and for AI. We argue that contestable AI requires dynamic (human-machine and/or machine-machine) explainability and decision-making processes, whereby machines can 1. interact with humans and/or other machines to progressively explain their outputs and/or their reasoning as well as assess grounds for contestation provided by these humans and/or other machines, and 2. revise their decision-making processes to redress any issues successfully raised during contestation. Given that much of the current AI landscape is tailored to static AIs, the need to accommodate contestability will require a radical rethinking, that, we argue, computational argumentation is ideally suited to support.

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IJCAI Conference 2024 Conference Paper

Instantiations and Computational Aspects of Non-Flat Assumption-based Argumentation

  • Tuomo Lehtonen
  • Anna Rapberger
  • Francesca Toni
  • Markus Ulbricht
  • Johannes P. Wallner

Most existing computational tools for assumption-based argumentation (ABA) focus on so-called flat frameworks, disregarding the more general case. In this paper, we study an instantiation-based approach for reasoning in possibly non-flat ABA. We make use of a semantics-preserving translation between ABA and bipolar argumentation frameworks (BAFs). By utilizing compilability theory, we establish that the constructed BAFs will in general be of exponential size. To keep the number of arguments and computational cost low, we present three ways of identifying redundant arguments. Moreover, we identify fragments of ABA which admit a poly-sized instantiation. We propose two algorithmic approaches for reasoning in non-flat ABA; the first utilizes the BAF instantiation while the second works directly without constructing arguments. An empirical evaluation shows that the former outperforms the latter on many instances, reflecting the lower complexity of BAF reasoning. This result is in contrast to flat ABA, where direct approaches dominate instantiation-based solvers.

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AAAI Conference 2024 Conference Paper

Non-flat ABA Is an Instance of Bipolar Argumentation

  • Markus Ulbricht
  • Nico Potyka
  • Anna Rapberger
  • Francesca Toni

Assumption-based Argumentation (ABA) is a well-known structured argumentation formalism, whereby arguments and attacks between them are drawn from rules, defeasible assumptions and their contraries. A common restriction imposed on ABA frameworks (ABAFs) is that they are flat, i.e. each of the defeasible assumptions can only be assumed, but not derived. While it is known that flat ABAFs can be translated into abstract argumentation frameworks (AFs) as proposed by Dung, no translation exists from general, possibly non-flat ABAFs into any kind of abstract argumentation formalism. In this paper, we close this gap and show that bipolar AFs (BAFs) can instantiate general ABAFs. To this end we develop suitable, novel BAF semantics which borrow from the notion of deductive support. We investigate basic properties of our BAFs, including computational complexity, and prove the desired relation to ABAFs under several semantics.

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NMR Workshop 2024 Conference Paper

On the Correspondence of Non-flat Assumption-based Argumentation and Logic Programming with Negation as Failure in the Head

  • Anna Rapberger
  • Markus Ulbricht 0001
  • Francesca Toni

The relation between (a fragment of) assumption-based argumentation (ABA) and logic programs (LPs) under stable model semantics is well-studied. However, for obtaining this relation, the ABA framework needs to be restricted to being flat, i. e. , a fragment where the (defeasible) assumptions can never be entailed, only assumed to be true or false. Here, we remove this restriction and show a correspondence between non-flat ABA and LPs with negation as failure in their head. We then extend this result to so-called setstable ABA semantics, originally defined for the fragment of non-flat ABA called bipolar ABA. We showcase how to define set-stable semantics for LPs with negation as failure in their head and show the correspondence to set-stable ABA semantics.

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AAAI Conference 2024 Conference Paper

Redefining ABA+ Semantics via Abstract Set-to-Set Attacks

  • Yannis Dimopoulos
  • Wolfgang Dvorak
  • Matthias König
  • Anna Rapberger
  • Markus Ulbricht
  • Stefan Woltran

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.

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KR Conference 2024 Conference Paper

Repairing Assumption-Based Argumentation Frameworks

  • Anna Rapberger
  • Markus Ulbricht

The field of formal argumentation is driven by situations where conflicting information need to be balanced out argumentatively. However, if the given knowledge base does not induce any reasonable viewpoint, these methods are stretched to their limits. In this paper, we address this issue in the context of assumption-based argumentation (ABA). More specifically, we study repairing notions for knowledge bases where no assumption can be accepted. We develop genuine repairing techniques for ABA, based on the modification of the building blocks of ABA frameworks, i. e. , rules and assumptions. Thereby, we start from basic operators towards more and more fine-grained approaches. We compare their behavior to each other and demonstrate their compliance with suitable repairing desiderata.

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JAIR Journal 2024 Journal Article

The Effect of Preferences in Abstract Argumentation under a Claim-Centric View

  • Michael Bernreiter
  • Wolfgang Dvořák
  • Anna Rapberger
  • Stefan Woltran

In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, these reductions give rise to four new classes of claim-augmented argumentation frameworks. These classes behave differently from each other with respect to semantic properties and computational complexity, but also in connection with structured argumentation formalisms such as assumption-based argumentation. This strengthens the view that the actual choice for handling preferences has to be taken with care.

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KR Conference 2023 Conference Paper

Argumentation Frameworks Induced by Assumption-based Argumentation: Relating Size and Complexity

  • Tuomo Lehtonen
  • Anna Rapberger
  • Markus Ulbricht
  • Johannes P. Wallner

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.

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JAIR Journal 2023 Journal Article

Equivalence in Argumentation Frameworks with a Claim-centric View: Classical Results with Novel Ingredients

  • Ringo Baumann
  • Anna Rapberger
  • Markus Ulbricht

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration is claimaugmented argumentation frameworks (CAFs) which provide a formal basis to analyze conclusion-oriented problems in argumentation by adapting a claim-focused perspective. CAFs extend Dung AFs by associating a claim to each argument representing its conclusion. In this paper, we investigate both ordinary and strong equivalence in CAFs. Thereby, we take the fact into account that one might either be interested in the actual arguments or their claims only. The former point of view naturally yields an extension of strong equivalence for AFs to the claim-based setting while the latter gives rise to a novel equivalence notion which is genuine for CAFs. We tailor, examine and compare these notions and obtain a comprehensive study of this matter for CAFs. We conclude by investigating the computational complexity of naturally arising decision problems.

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KR Conference 2023 Conference Paper

Forgetting Aspects in Assumption-Based Argumentation

  • Matti Berthold
  • Anna Rapberger
  • Markus Ulbricht

We address the issue of forgetting in assumption-based argumentation (ABA). Forgetting is driven by the goal to remove certain elements from a knowledge base, while preserving the structure of its models as well as possible. We introduce several forgetting operators tailored to accomplish the removal of different pieces of the ABA knowledge base—assumptions, contraries, and atoms—formalizing a diverse selection of perspectives on this issue. We examine the quality of our operators by studying their compliance with suitable desiderata we propose. Thereby, we investigate the impact of the operators on the syntax of the given ABA knowledge base, its semantics, but also the instantiated argumentation framework; thus bridging recent forgetting studies on non-monotonic formalisms including argumentation theory.

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JAIR Journal 2023 Journal Article

On Dynamics in Structured Argumentation Formalisms

  • Anna Rapberger
  • Markus Ulbricht

This paper is a contribution to the research on dynamics in assumption-based argumentation (ABA). We investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Notably, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semanticspreserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the abstract framework. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture dynamics in ABA. This yields the desired tractable fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

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JELIA Conference 2023 Conference Paper

On the Expressive Power of Assumption-Based Argumentation

  • Matti Berthold
  • Anna Rapberger
  • Markus Ulbricht 0001

Abstract The expressiveness of any given formalism lays the theoretical foundation for more specialized topics such as investigating dynamic reasoning environments. The modeling capabilities of the formalism under investigation yield immediate (im)possibility results in such contexts. In this paper we investigate the expressiveness of assumption-based argumentation (ABA), one of the major structured argumentation formalisms. In particular, we examine so-called signatures, i. e. , sets of extensions that can be realized under a given semantics. We characterize the signatures of common ABA semantics for flat, finite frameworks with and without preferences. We also give several results regarding conclusion-based semantics for ABA.

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NMR Workshop 2023 Conference Paper

Sets Attacking Sets in Abstract Argumentation

  • Yannis Dimopoulos
  • Wolfgang Dvorák
  • Matthias König 0002
  • Anna Rapberger
  • Markus Ulbricht 0001
  • Stefan Woltran

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.

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AAAI Conference 2023 Conference Paper

The Effect of Preferences in Abstract Argumentation under a Claim-Centric View

  • Michael Bernreiter
  • Wolfgang Dvorak
  • Anna Rapberger
  • Stefan Woltran

In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, these reductions give rise to different classes of claim-augmented argumentation frameworks, and behave differently in terms of semantic properties and computational complexity. This strengthens the view that the actual choice for handling preferences has to be taken with care.

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NMR Workshop 2022 Conference Paper

Argumentation Frameworks Induced by Assumption-Based Argumentation: Relating Size and Complexity

  • Anna Rapberger
  • Markus Ulbricht 0001
  • Johannes P. Wallner

A key ingredient of computational argumentation in AI is the generation of arguments in favor or against claims under scrutiny. In this paper we look at the complexity of the argument generation procedure in the prominent structured formalism of assumption-based argumentation (ABA). We show several results connecting expressivity of ABA fragments and number of constructed arguments. First, for several NP-hard fragments of ABA, the number of generated arguments is not bounded polynomially. Even under equivalent rewritings of the given ABA framework there are situations where one cannot avoid an exponential blow-up. We establish a weaker notion of equivalence under which this blow-up can be avoided. As a general tool for analyzing ABA frameworks and resulting arguments and their conflicts, we extend results regarding dependency graphs of ABA frameworks, from which one can infer structural properties on the induced attacks among arguments.

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AAAI Conference 2022 Conference Paper

Equivalence in Argumentation Frameworks with a Claim-Centric View – Classical Results with Novel Ingredients

  • Ringo Baumann
  • Anna Rapberger
  • Markus Ulbricht

A common feature of non-monotonic logics is that the classical notion of equivalence does not preserve the intended meaning in light of additional information. Consequently, the term strong equivalence was coined in the literature and thoroughly investigated. In the present paper, the knowledge representation formalism under consideration is claimaugmented argumentation frameworks (CAFs) which provide a formal basis to analyze conclusion-oriented problems in argumentation by adapting a claim-focused perspective. CAFs extend Dung AFs by associating a claim to each argument representing its conclusion. In this paper, we investigate both ordinary and strong equivalence in CAFs. Thereby, we take the fact into account that one might either be interested in the actual arguments or their claims only. The former point of view naturally yields an extension of strong equivalence for AFs to the claim-based setting while the latter gives rise to a novel equivalence notion which is genuine for CAFs. We tailor, examine and compare these notions and obtain a comprehensive study of this matter for CAFs. We conclude by investigating the computational complexity of naturally arising decision problems.

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KR Conference 2022 Conference Paper

On Dynamics in Structured Argumentation Formalisms

  • Anna Rapberger
  • Markus Ulbricht

In this paper we contribute to the investigation of dynamics in assumption-based argumentation (ABA) and investigate situations where a given knowledge base undergoes certain changes. We show that two frequently investigated problems, namely enforcement of a given target atom and deciding strong equivalence of two given ABA frameworks, are intractable in general. Interestingly, these problems are both tractable for abstract argumentation frameworks (AFs) which admit a close correspondence to ABA by constructing semantics-preserving instances. Inspired by this observation, we search for tractable fragments for ABA frameworks by means of the instantiated AFs. We argue that the usual instantiation procedure is not suitable for the investigation of dynamic scenarios since too much information is lost when constructing the AF. We thus consider an extension of AFs, called cvAFs, equipping arguments with conclusions and vulnerabilities in order to better anticipate their role after the underlying knowledge base is extended. We investigate enforcement and strong equivalence for cvAFs and present syntactic conditions to decide them. We show that the correspondence between cvAFs and ABA frameworks is close enough to capture ABA also in dynamic scenarios. This yields the desired tractable ABA fragment. We furthermore discuss consequences for the corresponding problems for logic programs.

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NMR Workshop 2022 Conference Paper

The Effect of Preferences in Abstract Argumentation Under a Claim-Centric View

  • Michael Bernreiter
  • Wolfgang Dvorák
  • Anna Rapberger
  • Stefan Woltran

In this paper, we study the effect of preferences in abstract argumentation under a claim-centric perspective. Recent work has revealed that semantical and computational properties can change when reasoning is performed on claim-level rather than on the argument-level, while under certain natural restrictions (arguments with the same claims have the same outgoing attacks) these properties are conserved. We now investigate these effects when, in addition, preferences have to be taken into account and consider four prominent reductions to handle preferences between arguments. As we shall see, these reductions give rise to different classes of claim-augmented argumentation frameworks, and behave differently in terms of semantic properties and computational complexity. This strengthens the view that the actual choice for handling preferences has to be taken with care.

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AAAI Conference 2021 Conference Paper

The Complexity Landscape of Claim-Augmented Argumentation Frameworks

  • Wolfgang Dvořák
  • Alexander Greßler
  • Anna Rapberger
  • Stefan Woltran

Claim-augmented argumentation frameworks (CAFs) provide a formal basis to analyze conclusion-oriented problems in argumentation by adapting a claim-focused perspective; they extend Dung AFs by associating a claim to each argument representing its conclusion. This additional layer offers various possibilities to generalize abstract argumentation semantics, i. e. the re-interpretation of arguments in terms of their claims can be performed at different stages in the evaluation of the framework: One approach is to perform the evaluation entirely at argument-level before interpreting arguments by their claims (inherited semantics); alternatively, one can perform certain steps in the process (e. g. , maximization) already in terms of the arguments’ claims (claim-level semantics). The inherent difference of these approaches not only potentially results in different outcomes but, as we will show in this paper, is also mirrored in terms of computational complexity. To this end, we provide a comprehensive complexity analysis of the four main reasoning problems with respect to claim-level variants of preferred, naive, stable, semi-stable and stage semantics and complete the complexity results of inherited semantics by providing corresponding results for semi-stable and stage semantics. Moreover, we show that deciding, whether for a given framework the two approaches of a semantics coincide (concurrence), can be surprisingly hard, ranging up to the third level of the polynomial hierarchy.

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KR Conference 2020 Conference Paper

Argumentation Semantics under a Claim-centric View: Properties, Expressiveness and Relation to SETAFs

  • Wolfgang Dvořák
  • Anna Rapberger
  • Stefan Woltran

Claim-augmented argumentation frameworks (CAFs) constitute a generic formalism for conflict resolution of conclusion-oriented problems in argumentation. CAFs extend Dung argumentation frameworks (AFs) by assigning a claim to each argument. So far, semantics for CAFs are defined with respect to the underlying AF by interpreting the extensions of the respective AF semantics in terms of the claims of the accepted arguments; we refer to them as inherited semantics of CAFs. A central concept of many argumentation semantics is maximization, which can be done with respect to arguments as in preferred semantics, or with respect to the range as in semi-stable semantics. However, common instantiations of argumentation frameworks require maximality on the claim-level and inherited semantics often fail to provide maximal claim-sets even if the underlying AF semantics yields maximal argument sets. To address this issue, we investigate a different approach and introduce claim-level semantics (cl-semantics) for CAFs where maximization is performed on the claim-level. We compare these two approaches for five prominent semantics (preferred, naive, stable, semi-stable, and stage) and relate in total eleven CAF semantics to each other. Moreover, we show that for a certain subclass of CAFs, namely well-formed CAFs, the different versions of preferred and stable semantics coincide, which is not the case for the remaining semantics. We furthermore investigate a recently established translation between well-formed CAFs and SETAFs and show that, in contrast to the inherited naive, semi-stable and stage semantics, the cl-semantics correspond to the respective SETAF semantics. Finally, we investigate the expressiveness of the considered semantics in terms of their signatures.

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ECAI Conference 2020 Conference Paper

On the Relation Between Claim-Augmented Argumentation Frameworks and Collective Attacks

  • Wolfgang Dvorák
  • Anna Rapberger
  • Stefan Woltran

Dung’s abstract argumentation frameworks (AFs) are a popular conceptual tool to define semantics for advanced argumentation formalisms. Hereby, arguments representing a possible inference of a claim are constructed and an attack relation between arguments indicates certain conflicts between the claim of one argument and the inference of another. Based on this abstract model, sets of jointly acceptable arguments are then gathered and finally interpreted in terms of their claims. Argumentation formalisms following this type of instantiating Dung AFs naturally produce several arguments with the same claim. This causes several issues and challenges for argumentation systems: on the one hand, the relation between claims remains implicit and, on the other hand, determining the acceptance of claims requires additional computations on top of argument acceptance. An instantiation that avoids this situation could provide additional insights and advantages, thus complementing the standard instantiation process via Dung AFs. Consequently, the research question we tackle is as follows: Can one combine different arguments sharing the same claim to a single abstract argument without affecting the overall results (and which abstract formalisms can serve such a purpose)? As a main result we show that a certain class of frameworks, where arguments with the same claim have the same outgoing attacks, can be equivalently (for all standard semantics) represented as argumentation frameworks with collective attacks where each claim occurs in exactly one argument. We further identify a class of frameworks where one even obtains an equivalent Dung AF with just one argument per claim.

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