@inbook{57238,
  abstract     = {{<jats:p>Abstract argumentation is a popular toolkit for modeling, evaluating, and comparing arguments. Relationships between arguments are specified in argumentation frameworks (AFs), and conditions are placed on sets (extensions) of arguments that allow AFs to be evaluated. For more expressiveness, AFs are augmented with acceptance conditions on directly interacting arguments or a constraint on the admissible sets of arguments, resulting in dialectic frameworks or constrained argumentation frameworks. In this paper, we consider flexible conditions for rejecting an argument from an extension, which we call rejection conditions (RCs). On the technical level, we associate each argument with a specific logic program. We analyze the resulting complexity, including the structural parameter treewidth. Rejection AFs are highly expressive, giving rise to natural problems on higher levels of the polynomial hierarchy.</jats:p>}},
  author       = {{Fichte, Johannes K. and Hecher, Markus and Mahmood, Yasir and Meier, Arne}},
  booktitle    = {{Frontiers in Artificial Intelligence and Applications}},
  isbn         = {{9781643685489}},
  issn         = {{0922-6389}},
  location     = {{Santiago de Compostela, Spain}},
  publisher    = {{IOS Press}},
  title        = {{{Rejection in Abstract Argumentation: Harder Than Acceptance?}}},
  doi          = {{10.3233/faia240867}},
  year         = {{2024}},
}

@inbook{62702,
  abstract     = {{<jats:p>Clifford algebras are a natural extension of division algebras, including real numbers, complex numbers, quaternions, and octonions. Previous research in knowledge graph embeddings has focused exclusively on Clifford algebras of a specific type, which do not include nilpotent base vectors—elements that square to zero. In this work, we introduce a novel approach by incorporating nilpotent base vectors with a nilpotency index of two, leading to a more general form of Clifford algebras named degenerate Clifford algebras. This generalization to degenerate Clifford algebras does allow for covering dual numbers and as such include translations and rotations models under the same generalization paradigm for the first time. We develop two models to determine the parameters that define the algebra: one using a greedy search and another predicting the parameters based on neural network embeddings of the input knowledge graph. Our evaluation on seven benchmark datasets demonstrates that this incorporation of nilpotent vectors enhances the quality of embeddings. Additionally, our method outperforms state-of-the-art approaches in terms of generalization, particularly regarding the mean reciprocal rank achieved on validation data. Finally, we show that even a simple greedy search can effectively discover optimal or near-optimal parameters for the algebra.</jats:p>}},
  author       = {{Kamdem Teyou, Louis Mozart and Demir, Caglar and Ngonga Ngomo, Axel-Cyrille}},
  booktitle    = {{Frontiers in Artificial Intelligence and Applications}},
  isbn         = {{9781643685489}},
  issn         = {{0922-6389}},
  location     = {{Santiago de Compostela}},
  publisher    = {{IOS Press}},
  title        = {{{Embedding Knowledge Graphs in Degenerate Clifford Algebras}}},
  doi          = {{10.3233/faia240627}},
  year         = {{2024}},
}