Contributed Talk

# Team semantics for modal mu-calculus

## Raúl Ruiz Mora

Friday, 14:25, J336

**Authors:** Bahareh Afshari and Raúl Ruiz Mora

Team semantics can be seen as a generalisation of Tarskian model theoretic semantics originally developed by Hodges in [1]. In recent work, see e.g. [3], team semantics have been developed for LTL, CTL and CTL*. Also, team semantics have been defined and studied for modal logic [2] and first order logic giving rise to dependence logic, independence logic and inclusion logic [5].

We define a team semantics for modal mu-calculus, show it enjoys the flatness property and aligns well with existing team temporal logics. The approach taken utilises team semantics for modal logic and involves an algebraic study of powerset structures in order to assign a reasonable team semantics to fixed-points [4].

## Bibliography

- Hodges, W.,
*Compositional semantics for a language of imperfect information*. Logic Journal of the IGPL,**5(4)**(1997) pp. 539–563. - Kontinen, J., Müller, J. S., Schnoor, H., & Vollmer, H.,
*A van Benthem theorem for modal team semantics*. Leibniz International Proceedings in Informatics (LIPIcs), 2014. - Krebs, A., Meier, A., & Virtema, J.,
*A team based variant of CTL*. 22nd International Symposium on Temporal Representation and Reasoning (TIME) (2015) pp. 140–149. IEEE. - Ruiz, R.,
*Team semantics for modal mu-calculus*. Master’s thesis, University of Amsterdam, 2023. - Väänänen, J,
*Dependence logic: a new approach to independence friendly logic*. London Mathematical Society student texts,**70**, Cambridge university Press (2007).