{"status":"public","author":[{"id":"109969","first_name":"Anselm","full_name":"Haak, Anselm","last_name":"Haak"},{"last_name":"Kontinen","full_name":"Kontinen, Juha","first_name":"Juha"},{"first_name":"Fabian","last_name":"Müller","full_name":"Müller, Fabian"},{"full_name":"Vollmer, Heribert","last_name":"Vollmer","first_name":"Heribert"},{"first_name":"Fan","full_name":"Yang, Fan","last_name":"Yang"}],"department":[{"_id":"888"}],"publication_status":"published","doi":"10.1145/3771721","language":[{"iso":"eng"}],"abstract":[{"lang":"eng","text":"<jats:p>\r\n            We study descriptive complexity of counting complexity classes in the range from #P to\r\n            <jats:inline-formula content-type=\"math/tex\">\r\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\({\\text{#}\\!\\cdot\\!\\text{NP}}\\)</jats:tex-math>\r\n            </jats:inline-formula>\r\n            . 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\r\n            <jats:inline-formula content-type=\"math/tex\">\r\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\({\\text{#}\\!\\cdot\\!\\text{NP}}\\)</jats:tex-math>\r\n            </jats:inline-formula>\r\n            can be logically characterized by independence logic and existential second-order logic, whereas dependence logic and inclusion logic give rise to subclasses of\r\n            <jats:inline-formula content-type=\"math/tex\">\r\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\({\\text{#}\\!\\cdot\\!\\text{NP}}\\)</jats:tex-math>\r\n            </jats:inline-formula>\r\n            and #P , respectively. We further relate the class obtained from inclusion logic to the complexity class\r\n            <jats:inline-formula content-type=\"math/tex\">\r\n              <jats:tex-math notation=\"LaTeX\" version=\"MathJax\">\\({\\text{TotP}} \\subseteq{\\text{#P}}\\)</jats:tex-math>\r\n            </jats:inline-formula>\r\n            .\r\n          </jats:p>"}],"date_created":"2025-10-17T09:43:42Z","date_updated":"2025-10-17T09:44:06Z","publication_identifier":{"issn":["1529-3785","1557-945X"]},"type":"journal_article","citation":{"bibtex":"@article{Haak_Kontinen_Müller_Vollmer_Yang_2025, title={Counting of Teams in First-Order Team Logics}, DOI={<a href=\"https://doi.org/10.1145/3771721\">10.1145/3771721</a>}, number={3771721}, journal={ACM Transactions on Computational Logic}, publisher={Association for Computing Machinery (ACM)}, author={Haak, Anselm and Kontinen, Juha and Müller, Fabian and Vollmer, Heribert and Yang, Fan}, year={2025} }","mla":"Haak, Anselm, et al. “Counting of Teams in First-Order Team Logics.” <i>ACM Transactions on Computational Logic</i>, 3771721, Association for Computing Machinery (ACM), 2025, doi:<a href=\"https://doi.org/10.1145/3771721\">10.1145/3771721</a>.","ieee":"A. Haak, J. Kontinen, F. Müller, H. Vollmer, and F. Yang, “Counting of Teams in First-Order Team Logics,” <i>ACM Transactions on Computational Logic</i>, Art. no. 3771721, 2025, doi: <a href=\"https://doi.org/10.1145/3771721\">10.1145/3771721</a>.","ama":"Haak A, Kontinen J, Müller F, Vollmer H, Yang F. Counting of Teams in First-Order Team Logics. <i>ACM Transactions on Computational Logic</i>. Published online 2025. doi:<a href=\"https://doi.org/10.1145/3771721\">10.1145/3771721</a>","chicago":"Haak, Anselm, Juha Kontinen, Fabian Müller, Heribert Vollmer, and Fan Yang. “Counting of Teams in First-Order Team Logics.” <i>ACM Transactions on Computational Logic</i>, 2025. <a href=\"https://doi.org/10.1145/3771721\">https://doi.org/10.1145/3771721</a>.","apa":"Haak, A., Kontinen, J., Müller, F., Vollmer, H., &#38; Yang, F. (2025). Counting of Teams in First-Order Team Logics. <i>ACM Transactions on Computational Logic</i>, Article 3771721. <a href=\"https://doi.org/10.1145/3771721\">https://doi.org/10.1145/3771721</a>","short":"A. Haak, J. Kontinen, F. Müller, H. Vollmer, F. Yang, ACM Transactions on Computational Logic (2025)."},"title":"Counting of Teams in First-Order Team Logics","_id":"61874","year":"2025","article_number":"3771721","user_id":"109969","publication":"ACM Transactions on Computational Logic","publisher":"Association for Computing Machinery (ACM)"}