Author name cluster

Markus Ulbricht 0001

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

6 papers

1 author row

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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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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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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JELIA Conference 2019 Conference Paper

Repairing Non-monotonic Knowledge Bases

Markus Ulbricht 0001

Abstract Minimal inconsistent subsets of knowledge bases in monotonic logics play an important role when investigating the reasons for conflicts and trying to handle them. In the context of non-monotonic reasoning this notion is not as meaningful due to the possibility of resolving conflicts by adding information. In this paper we investigate inconsistency in non-monotonic logics while taking this issue into account. In particular, we show that the well-known classical duality between hitting sets of minimal inconsistent subsets and maximal consistent subsets generalizes to arbitrary logics even if we allow adding novel information to a given knowledge base. We illustrate the versatility of the main theorems by covering more sophisticated situations and demonstrate how to utilize our results to analyze inconsistency in abstract argumentation.

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JELIA Conference 2016 Conference Paper

Measuring Inconsistency in Answer Set Programs

Markus Ulbricht 0001
Matthias Thimm
Gerhard Brewka

Abstract We address the issue of quantitatively assessing the severity of inconsistencies in logic programs under the answer set semantics. While measuring inconsistency in classical logics has been investigated for some time now, taking the non-monotonicity of answer set semantics into account brings new challenges that have to be addressed by reasonable accounts of inconsistency measures. We investigate the behavior of inconsistency in logic programs by revisiting existing rationality postulates for inconsistency measurement and developing novel ones taking non-monotonicity into account. Further, we develop new measures for this setting and investigate their properties.

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