Team Semantics and Dependence logic (TEAMDEP)

European Research Council Advanced Grant

This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. [101020762- TEAMDEP])

Beneficiary: University of Helsinki

PI: Jouko Väänänen, prof.

Members:

Miika Hannula, Juliette Kennedy, Siiri Kivimäki, Menachem Magidor, Miguel Moreno, Joni Puljuärvi, Otto Rajala, Tapio Saarinen, Boban Velickovic, Ur Ya'ar,

Helsinki Logic Group

Abstract

In the traditional so-called Tarski's Truth Definition the semantics of first order logic is defined with respect to an assignment of values to the free variables. A richer family of semantic concepts can be modelled if semantics is defined with respect to a set (a "team") of such assignments. This is what is called team semantics, a term coined by the PI in his 2007 monograph, and used ever since to describe this highly non-trivial modification of Tarskian semantics. Team semantics was introduced around the same time in inquisitive logic under the name state semantics. Examples of semantic concepts available in team semantics but not in traditional Tarski semantics are the concepts of dependence and independence. The PI introduced what he called dependence logic around these concepts. It appears that teams appear naturally in several areas of sciences and humanities which has made it possible to apply dependence logic and its variants to these areas. Now is the right moment to move from dependence logic to a broader explication of team semantics. This is what the TEAMDEP project proposes to do. In the TEAMDEP project we take team semantics to a new level by focusing on its hard axiomatizability questions and to its applications to the foundations of quantum mechanics and to the multiverse of set theory.

Events

XVI International Luminy Workshop in Set Theory (2021)
Juliette Kennedy is interviewed by the Quanta Magazine (2021)
Women in Logic and Philosophy of Mathematics and Language (2022)
Arctic Set Theory Workshop 5 (2022)
INTERNAL CATEGORICITY CONFERENCE (2022)
Arctic Set Theory Workshop 6 (2023)
THE MATHEMATICAL DRAWING/DIAGRAM: AN INTERDISCIPLINARY SYMPOSIUM (2023)
XVII International Luminy Workshop in Set Theory (2023)
Juliette Kennedy receives the Guggenheim Fellowship (2022)
Jouko Väänänen receives the Magnus Ehrnrooth Foundation prize 2024.
Arctic Set Theory Workshop 7 (2025)
The 8th Workshop on Generalized Descriptive Set Theory (2025)

Publications

  • Tractability Frontier of Data Complexity in Team Semantics, with Arnaud Durand, Nicolas de Rugy-Altherre, and Juha Kontinen, ACM Transactions on Computational Logic 23 (1), 1-21, 2022. Full version of #125. Available in ArXiv.

  • Inner Models from Extended Logics: Part 2, with J. Kennedy and M. Magidor. Journal of Mathematical Logic, Paper No. 2550009. 47 pp, (2025), Available in arXiv.

  • Logicality and model classes, with Juliette Kennedy. Bulletin of Symbolic Logic 27(4), 385-414, 2021, Link. Available in arXiv.

  • Team Semantics and Independence Notions in Quantum Physics, with Samson Abramsky and Joni Puljujärvi. Bulletin of Symbolic Logic, 2025:1-58. Available in arXiv.

  • An atom's worth of anonymity. Logic Journal of the IGPL, November 2022. Available in arXiv.

  • Positive logics, with S. Shelah. Archive for Mathematical Logic 62, 207-223, (2023). Available in arXiv.

  • Diversity, Dependence and Independence (Journal version), with P. Galliani, Annals of Mathematics and Artificial Intelligence, November, vol. 90 (2-3), pages 211-233 (2022). Arxiv

  • When cardinals determine the power set: inner models and Härtig quantifier logic, with P. Welch, Mathematical Logic Quarterly, Online available 2023. Available also in Arxiv.

  • Philosophical Uses of Categoricity Arguments, with Penelope Maddy, Elements in the Philosophy of Mathematics. Cambridge: Cambridge University Press. 55 p. (2023).

  • On the categoricity of complete second order theories, with Tapio Saarinen and Hugh Woodin. Journal of Symbolic Logic, online first 27 August 2025. Available in arXiv.

  • Model theory of second order logic. In Beyond First Order Model Theory, Volume 2, CRC Press, edited by Jose Iovino, 2023, Chapter 7, 289-304.

  • Chain logic and Shelah's infinitary logic, with M. Džamonja, Israel Journal of Mathematics vol. 245, pages 93-134, 2021. Available online, also in arXiv.

  • Logics of Dependence and Independence. A special issue of the Annals of Pure and Applied Logic, edited with Philip Scott and Fan Yang. Annals of Pure and Applied Logic 173(10), 2022.

  • Dimension in team semantics, with Lauri Hella and Kerkko Luosto. Mathematical Structures in Computer Science, vol. 34 (2024), 410-454. Available in arXiv.

  • Sandback catalog 2024

  • Modular SAT-based techniques for reasoning tasks in team semantics, with Arnaud Durand and Juha Kontinen, Journal of Computer and System Sciences vol. 146 (2024). Available in arXiv.

  • The strategic balance of games in logic. In: Samson Abramsky on Logic and Structure in Computer Science and Beyond (edited by Alessandra Palmigiano and Mehrnoosh Sadrzadeh), Volume 25 in the series "Outstanding Contributions to Logic", Springer, 2023. arXiv

  • Bounded Symbiosis and Upwards Reflection, with Lorenzo Galeotti and Yurii Khomskii, Arch. Math. Logic (2024). https://doi.org/10.1007/s00153-024-00955-0. Available in arXiv.

  • Interpolation in model theory. To appear in Balder ten Cate, Jean Christoph Jung, Patrick Koopmann, Christoph Wernhard and Frank Wolter, editors, Theory and Applications of Craig Interpolation. Ubiquity Press. To appear.

  • The Liar Paradox and the three logics framework. With J. Kennedy. For the volume The Liar Paradox, Classic Philosophical Arguments series of Cambridge University Press, Lorenzo Rossi, editor. To appear.

  • Aronszajn trees and maximality, with Omer Ben-Neria, Siiri Kivimäki and Menachem Magidor. To appear. Available in arXiv.

  • The flattening operator in team-based logics, with Arnaud Durand, Juha Kontinen, and Werner Merian. Journal of Logic and Computation, 35(6), 2025. Available in arXiv.

  • Inner models from extended logics and the Delta-operation, with Ur Ya'ar, Israel Journal of Mathematics, to appear. Available in arXiv.

  • Matematiikka - epätäydellisyyden valtakunta (engl. Mathematics - A Realm of Incompleteness), Finnish Society of Sciences and Letters, 2025, to appear, 190 pages.

  • On some infinitary logics, with Boban Velickovic. To appear. Available in arXiv.

  • On Borel subsets of generalized Baire spaces, with Tapani Hyttinen and Miguel Moreno. Submitted. Available in arXiv.

  • Cartagena logic, with Siiri Kivimäki and Andres Villaveces, to appear. Available in arXiv.

  • New inner models from second order logics, with Menachem Magidor, to appear. Available in arXiv.

  • Expressibility and inexpressibility in propositional team logics, with Matilda Häggblom and Minna Hirvonen, to appear. Available in arXiv.

  • How first order is first order logic?, with Juliette Kennedy. For The Oxford Handbook of Philosophy of Logic, editors: Elke Brendel, Massimiliano Carrara, Filippo Ferrari, Ole Hjortland, Gil Sagi, Gila Sher, Florian Steinberger, Oxford University Press. To appear.

  • Conditional independence on semiring relations Hannula, Miika, arXiv

  • Information inequality problem over set functions Hannula, Miika, arXiv

  • Unified Foundations of Team Semantics via Semirings, Timon Barlag; Miika Hannula; Juha Kontinen; Nina Pardal; Jonni Virtema, Proceedings of the 20th International Conference on Principles of Knowledge Representation and Reasoning

  • Logics with probabilistic team semantics and the Boolean negation, Hannula, Miika; Hirvonen, Minna; Kontinen, Juha; Mahmood, Yasir; Meier, Arne; Virtema, Jonni, arXiv

  • SHELAH'S MAIN GAP AND THE GENERALIZED BOREL REDUCIBILITY, Miguel Moreno, arXiv.

  • Axiomatizing modal inclusion logic and its variants, Aleksi Anttila, Matilda Häggblom, Fan Yang, arXiv.

  • Timon Barlag, Nicolas Fröhlich, Teemu Hankala, Miika Hannula, Minna Hirvonen, Vivian Holzapfel, Juha Kontinen, Arne Meier, and Laura Strieker. Logic and computation through the lens of semirings. CoRR, abs/2502.12939, 2025.

  • Timon Barlag, Nicolas Fröhlich, Teemu Hankala, Miika Hannula, Minna Hirvonen, Vivian Holzapfel, Juha Kontinen, Arne Meier, and Laura Strieker. Logical approaches to non-deterministic polynomial time over semirings. CoRR, abs/2509.26214, 2025.

  • Timon Barlag, Miika Hannula, Juha Kontinen, Nina Pardal, and Jonni Virtema. Local consistency and axioms of functional dependence. CoRR, abs/2505.11057, 2025.

  • Teemu Hankala, Miika Hannula, Yasir Mahmood, and Arne Meier. Parameterised complexity of consistent query answering via graph represen- tations. CoRR, abs/2412.08324, 2024.

  • Miika Hannula, Minna Hirvonen, Juha Kontinen, and Sebastian Link. Independence under incomplete information. To appear in FoIKS 2026.

  • Miika Hannula, Minna Hirvonen, Juha Kontinen, Yasir Mahmood, Arne Meier, and Jonni Virtema. Logics with probabilistic team semantics and the boolean negation. J. Log. Comput., 35(3), 2025.

  • Otto Rajala. An Inner Model from Stationary Logic and the Next Admissible Set. Dissertationes Universitatis Helsingiensis, 2025, 326. University of Helsinki, Helsinki, 2025.

  • Miguel Moreno. Shelah's Main Gap and the generalized Borel-reducibility, submitted. DOI: 10.48550/arXiv.2308.07510.

  • On Borel sets in ideal topologies. With Beatrice Pitton, submitted. DOI: 10.48550/arXiv.2512.21140.

    Orchid

    ORCID iD iconorcid.org/0000-0003-4356-7974

    Google Scholar

    Google Scholar

    Address

    e-mail:
    Department of Mathematics and Statistics
    Pietari Kalmin katu 5
    PL 68
    FIN-00014 University of Helsinki, Finland
    www.mv.helsinki.fi/home/jvaanane//