Time: Oct. 20th (Tuesday) 15:10 - 18:00

Location: Teaching Building No.2 (二教) 411

Talk 1

Title: A Categorical Perspective on Kripke Models and Dynamic Epistemic Logic

Speaker: Haitian Wang (University of Amsterdam)

Abstract:

Kripke models are a standard relational semantics for modal logic and intuitionistic logic, and they also provide a natural representation of state-based systems with uncertainty. In this talk we present ongoing work on viewing Kripke models through a categorical lens, and work in the category of Kripke models. We investigate how the categorical properties vary along several dimensions, including unpointed vs. pointed vs. multi-pointed models, restrictions to particular classes of frames/models, and different choices of morphisms (e.g. monotone maps vs. bounded morphisms). A main motivation comes from Dynamic Epistemic Logic (DEL), where actions (such as public/private announcements and factual changes) are represented using action models and applied to Kripke models via product update, transforming a Kripke model into a new one after the update. Related work by Kishida (2017) gives a categorical perspective on DEL at the level of frames. We extend the framework to the level of models and analyze the functoriality of product update: with monotone maps as morphisms, action models with arbitrary modal preconditions do not in general induce endofunctors, and this motivates alternative treatments such as restricting preconditions or moving to partial-map/Kleisli-style categories. Finally, we outline how these categorical constructions may provide a new understanding of constructions in DEL such as action emulation, where we seek a categorical notion of equivalence between action models.

Talk 2

Title: Finite-variable Goldblatt-Thomason Theorems

Speaker: Qianli Zeng (University of St Andrews)

Abstract:

We characterize the frame definability of modal theories where each formula contains at most n propositional variables. The approach introduces algebraic localizations, showing that a frame is definable if and only if it is closed under generated subframes, disjoint unions, and surjective bounded images, along with the reflection of n-localizations. This gives a uniform algebraic framework to re-establish some examples from the earlier literature, including optimal variable bounds for bounded out-degree, common-successor confluence, density, width, and weak connectedness, etc., as well as some new applications. We also address the global modality and relative definability relative to finite transitive frame classes. 

Reference: 

[1] Balbiani, P., Fernández-Duque, D., Herzig, A., & Iliev, P. (2022). Frame-validity games and lower bounds on the complexity of modal axioms. Logic Journal of the IGPL, 30(1), 155–185. 

[2] Goldblatt, R. I., & Thomason, S. K. (1975). Axiomatic classes in propositional modal logic. In J. N. Crossley (Ed.), Algebra and Logic (Vol. 450, pp. 163–173). Springer. 

[3]  Iliev, P. (2025). On the number of different variables required to define the n-density or the bounded n-width of Kripke frames with some consequences for Sahlqvist formulae. Logic Journal of the IGPL, 33(1), 95–124. 

[4] Vakarelov, D. (2003). Modal definability in languages with a finite number of propositional variables and a new extension of the Sahlqvist's class. In P. Balbiani, N.-Y. Suzuki, F. Wolter, & M. Zakharyaschev (Eds.), Advances in Modal Logic (Vol. 4, pp. 499–518). King's College Publications.