@unpublished{61065,
  abstract     = {{Abduction is the task of computing a sufficient extension of a knowledge base (KB) that entails a conclusion not entailed by the original KB. It serves to compute explanations, or hypotheses, for such missing entailments. While this task has been intensively investigated for perfect data and under classical semantics, less is known about abduction when erroneous data results in inconsistent KBs. In this paper we define a suitable notion of abduction under repair semantics and propose a set of minimality criteria that guides abduction towards `useful' hypotheses. We provide initial complexity results on deciding existence of and verifying abductive solutions with these criteria, under different repair semantics and for the description logics DL-Lite and EL_bot.}},
  author       = {{Haak, Anselm and Koopmann, Patrick and Mahmood, Yasir and Turhan, Anni-Yasmin}},
  booktitle    = {{arXiv:2507.21955}},
  title        = {{{Why not? Developing ABox Abduction beyond Repairs}}},
  year         = {{2025}},
}

@inproceedings{63888,
  author       = {{Haak, Anselm and Koopmann, Patrick and Mahmood, Yasir and Turhan, Anni-Yasmin}},
  booktitle    = {{Proceedings of the 38th International Workshop on Description Logics - DL 2025}},
  editor       = {{Tendera, Lidia and Ibanez Garcia, Yazmin and Koopmann, Patrick}},
  location     = {{Opole, Poland}},
  title        = {{{Why not? Developing ABox Abduction beyond Repairs}}},
  year         = {{2025}},
}

@article{61874,
  abstract     = {{<jats:p>
            We study descriptive complexity of counting complexity classes in the range from #P to
            <jats:inline-formula content-type="math/tex">
              <jats:tex-math notation="LaTeX" version="MathJax">\({\text{#}\!\cdot\!\text{NP}}\)</jats:tex-math>
            </jats:inline-formula>
            . The proof of Fagin’s characterization of NP by existential second-order logic generalizes to the counting setting in the following sense: The class #P can be logically described as the class of functions counting satisfying assignments to free relation variables in first-order formulae. This was first observed by Saluja et al. (1995). In this paper we extend this study to classes beyond #P and extensions of first-order logic with team semantics. These team-based logics are closely related to existential second-order logic and its fragments, hence our results also shed light on the complexity of counting for extensions of first-order logic in Tarski’s semantics. Our results show that the class
            <jats:inline-formula content-type="math/tex">
              <jats:tex-math notation="LaTeX" version="MathJax">\({\text{#}\!\cdot\!\text{NP}}\)</jats:tex-math>
            </jats:inline-formula>
            can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of
            <jats:inline-formula content-type="math/tex">
              <jats:tex-math notation="LaTeX" version="MathJax">\({\text{#}\!\cdot\!\text{NP}}\)</jats:tex-math>
            </jats:inline-formula>
            and #P , respectively. We further relate the class obtained from inclusion logic to the complexity class
            <jats:inline-formula content-type="math/tex">
              <jats:tex-math notation="LaTeX" version="MathJax">\({\text{TotP}} \subseteq{\text{#P}}\)</jats:tex-math>
            </jats:inline-formula>
            .
          </jats:p>}},
  author       = {{Haak, Anselm and Kontinen, Juha and Müller, Fabian and Vollmer, Heribert and Yang, Fan}},
  issn         = {{1529-3785}},
  journal      = {{ACM Transactions on Computational Logic}},
  publisher    = {{Association for Computing Machinery (ACM)}},
  title        = {{{Counting of Teams in First-Order Team Logics}}},
  doi          = {{10.1145/3771721}},
  year         = {{2025}},
}

@inproceedings{60168,
  author       = {{Dell, Holger and Haak, Anselm and Kallmayer, Melvin and Wennmann, Leo}},
  booktitle    = {{Proceedings of the 2025 Annual ACM-SIAM Symposium on Discrete Algorithms (SODA)}},
  isbn         = {{9781611978322}},
  location     = {{New Orleans, Louisiana, U.S.}},
  publisher    = {{Society for Industrial and Applied Mathematics}},
  title        = {{{Solving Polynomial Equations Over Finite Fields}}},
  doi          = {{10.1137/1.9781611978322.90}},
  year         = {{2025}},
}