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Kenneth Skiba

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12 papers
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12

AAAI Conference 2025 Conference Paper

An Extension-Based Argument-Ranking Semantics: Social Rankings in Abstract Argumentation

  • Lars Bengel
  • Giovanni Buraglio
  • Jan Maly
  • Kenneth Skiba

In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property.

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FLAP Journal 2025 Journal Article

The Semantical Structure of Conditionals, and its Relation to Formal Argumentation

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

Conditionals, i. e. expressions of the logical form “if A, then B”, have been a central topic of study ever since logic was on the academic menu. In contem- porary logic, there is a consensus that the semantics of conditionals are best obtained by stipulating a subset of possible worlds in which the antecedent is true, and verifying whether the consequent is true in those worlds. Such a subset of possible worlds can represent, for example, the most typical worlds in which the antecedent is true. This idea has proven a fruitful basis, allowing for many systematic characterisation results as well as for making connections to other topics, such as belief revision and modal logic. In formal argumentation, the potential of these semantical ideas has not gone unnoticed in the last years, and

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NMR Workshop 2024 Conference Paper

An Extension-Based Argument-Ranking Semantics: Social Rankings in Abstract Argumentation

  • Lars Bengel
  • Giovanni Buraglio
  • Jan Maly 0001
  • Kenneth Skiba

In this paper, we introduce a new family of argument-ranking semantics which can be seen as a refinement of the classification of arguments into skeptically accepted, credulously accepted and rejected. To this end we use so-called social ranking functions which have been developed recently to rank individuals based on their performance in groups. We provide necessary and sufficient conditions for a social ranking function to give rise to an argument-ranking semantics satisfying the desired refinement property. Moreover, we analyse the properties of the argument-ranking semantics induced by the most prominent social ranking function that satisfies all of these conditions by investigating the satisfaction of principles known from the argument-ranking literature.

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KR Conference 2024 Conference Paper

Optimisation and Approximation in Abstract Argumentation: The Case of Admissibility

  • Kenneth Skiba
  • Matthias Thimm

We propose two soft notions of the notion of admissibility in abstract argumentation. The first one weakens the defence notion by allowing, to a certain degree, undefended attacks, and the second one allows, to a certain degree, conflicts within sets of arguments. We analyse these new semantical notions based on the computational complexity of optimisation and approximation. Finally, we discuss and analyse soft notions for preferred semantics.

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AIJ Journal 2023 Journal Article

Revision, defeasible conditionals and non-monotonic inference for abstract dialectical frameworks

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals, and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that relationships between belief revision, defeasible conditionals, and nonmonotonic inference similar to those in propositional logic hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

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AAAI Conference 2022 Conference Paper

Conditional Abstract Dialectical Frameworks

  • Jesse Heyninck
  • Matthias Thimm
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba

Abstract dialectical frameworks (in short, ADFs) are a unifying model of formal argumentation, where argumentative relations between arguments are represented by assigning acceptance conditions to atomic arguments. This idea is generalized by letting acceptance conditions being assigned to complex formulas, resulting in conditional abstract dialectical frameworks (in short, cADFs). We define the semantics of cADFs in terms of a non-truth-functional four-valued logic, and study the semantics in-depth, by showing existence results and proving that all semantics are generalizations of the corresponding semantics for ADFs.

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IJCAI Conference 2022 Conference Paper

Possibilistic Logic Underlies Abstract Dialectical Frameworks

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

Abstract dialectical frameworks (in short, ADFs) are one of the most general and unifying approaches to formal argumentation. As the semantics of ADFs are based on three-valued interpretations, we ask which monotonic three-valued logic allows to capture the main semantic concepts underlying ADFs. We show that possibilistic logic is the unique logic that can faithfully encode all other semantical concepts for ADFs. Based on this result, we also characterise strong equivalence and introduce possibilistic ADFs.

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IS Journal 2021 Journal Article

Complexity of Nonempty Existence Problems in Incomplete Argumentation Frameworks

  • Kenneth Skiba
  • Daniel Neugebauer
  • Jorg Rothe

Abstract argumentation frameworks (AFs) are a prevailing model for the formal representation of argumentations in AI research. The generalized model of incomplete AFs extends the basic model by allowing for the representation of unquantified uncertainty about the existence of elements in an argumentation. For this extended model of AFs, we formally define a natural generalization of the nonempty existence problem, which asks whether there exists a nonempty set of arguments satisfying the conditions specified by a given semantics. Focusing on the fundamental semantics for incomplete AFs and considering a possible and a necessary variant of the nonempty existence problem, this yields a family of related problems, and we provide a full analysis of their computational complexity.

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KR Conference 2021 Short Paper

Distinguishability in Abstract Argumentation

  • Isabelle Kuhlmann
  • Tjitze Rienstra
  • Lars Bengel
  • Kenneth Skiba
  • Matthias Thimm

In abstract argumentation, the admissible semantics can be said to distinguish the preferred semantics in the sense that argumentation frameworks with the same admissible extensions also have the same preferred extensions. In this paper we present an exhaustive study of such distinguishability relationships, including those between sets of semantics. We further examine restricted classes of argumentation frameworks, such as self-attack-free and acyclic frameworks. We discuss the relevance of our results in the context of the argumentation framework elicitation problem.

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IJCAI Conference 2021 Conference Paper

Ranking Extensions in Abstract Argumentation

  • Kenneth Skiba
  • Tjitze Rienstra
  • Matthias Thimm
  • Jesse Heyninck
  • Gabriele Kern-Isberner

Extension-based semantics in abstract argumentation provide a criterion to determine whether a set of arguments is acceptable or not. In this paper, we present the notion of extension-ranking semantics, which determines a preordering over sets of arguments, where one set is deemed more plausible than another if it is somehow more acceptable. We obtain extension-based semantics as a special case of this new approach, but it also allows us to make more fine-grained distinctions, such as one set being "more complete'' or "more admissible'' than another. We define a number of general principles to classify extension-ranking semantics and develop concrete approaches. We also study the relation between extension-ranking semantics and argument-ranking based semantics, which rank individual arguments instead of sets of arguments.

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KR Conference 2021 Conference Paper

Revision and Conditional Inference for Abstract Dialectical Frameworks

  • Jesse Heyninck
  • Gabriele Kern-Isberner
  • Tjitze Rienstra
  • Kenneth Skiba
  • Matthias Thimm

For propositional beliefs, there are well-established connections between belief revision, defeasible conditionals and nonmonotonic inference. In argumentative contexts, such connections have not yet been investigated. On the one hand, the exact relationship between formal argumentation and nonmonotonic inference relations is a research topic that keeps on eluding researchers despite recently intensified efforts, whereas argumentative revision has been studied in numerous works during recent years. In this paper, we show that similar relationships between belief revision, defeasible conditionals and nonmonotonic inference hold in argumentative contexts as well. We first define revision operators for abstract dialectical frameworks, and use such revision operators to define dynamic conditionals by means of the Ramsey test. We show that such conditionals can be equivalently defined using a total preorder over three-valued interpretations, and study the inferential behaviour of the resulting conditional inference relations.

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ECAI Conference 2020 Conference Paper

Complexity of Possible and Necessary Existence Problems in Abstract Argumentation

  • Kenneth Skiba
  • Daniel Neugebauer
  • Jörg Rothe

This work focuses on generalizing the existence problems for extensions in abstract argumentation to incomplete argumentation frameworks. In this extended model, incomplete or conflicting knowledge about the state of the arguments and attacks are allowed. We propose possible and necessary variations of the existence and nonemptiness problems, originally defined for (complete) argumentation frameworks, to extend these problems to incomplete argumentation frameworks. While the computational complexity of existence problems is already known for the standard model, we provide a full analysis of the complexity for incomplete argumentation frameworks using the most prominent semantics, namely, the conflict-free, admissible, complete, grounded, preferred, and stable semantics. We show that the complexity rises from NP-completeness to ∏ p 2 -completeness for most “necessary” problem variants when uncertainty is allowed.

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v2026.09.13