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

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)
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
Juliette Kennedy is interviewed by the Quanta Magazine
Jouko Väänänen receives the Magnus Ehrnrooth Foundation prize 2024.

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. Submitted.

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. Preprint. 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, Cambridge Elements series, to appear. 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.

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. Abstract to appear in the Bulletin of Symbolic Logic. Full paper submitted to a journal. Available in arXiv.

Modular SAT-based techniques for reasoning tasks in team semantics, with Arnaud Durand and Juha Kontinen, to appear. 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

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—Part 2, with Omer Ben-Neria and Menachem Magidor. 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.

Orchid

orcid.org/0000-0003-4356-7974

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//