## NOL Seminar with Alexandru Baltag

published: 2022-12-09

event date:
2022-12-19

The Nordic Online Logic Seminar is organised monthly over Zoom, with expository talks on topics of interest for the broader logic community. The seminar is open for professional or aspiring logicians and logic aficionados worldwide. If you wish to receive the Zoom ID and password for it, as well as further announcements, please subscribe here: https://listserv.gu.se/sympa/subscribe/nordiclogic.

**Date** Monday, 19 December 2022 at 16:00 (CET), over Zoom

**Speaker** Alexandru Baltag (Associate Professor, ILLC, Amsterdam)

**Title** From Surprise Exams to Topological Mu-Calculus

**Abstract**

I present a topological epistemic logic, motivated by a famous epistemic puzzle:
the Surprise Exam Paradox. It is a fixed-point modal logic, with modalities for
knowledge (modelled as the universal modality), knowability of a proposition
(represented by the topological interior operator), and (un)knowability of the
actual world. The last notion has a non-self-referential reading (modelled by
Cantor derivative: the set of limit points of a given set) and a
self-referential one (modelled by the so-called perfect core of a given set: its
largest subset which is a fixed point of relativized derivative). I completely
axiomatize this logic, showing that it is decidable and PSPACE-complete, as well
as briefly explain how the same model-theoretic method can be elaborated to
prove the completeness and decidability of the full topological mu-calculus.
Finally, I apply it to the analysis of the Surprise Exam Paradox and other
puzzles.

References:

- A. Baltag, N. Bezhanishvili, D. Fernández-Duque. The Topology of Surprise. Proceedings of the International Conference on Principles of Knowledge Representation and Reasoning. Vol. 19 (1), 33–42, 2022. Available online in ILLC Prepublication (PP) series PP-2022-06.
- A. Baltag, N. Bezhanishvili, D. Fernández-Duque. The Topological Mu-Calculus: Completeness and Decidability. LICS ‘21: Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, vol 89: 1–13, 2021, (doi:10.1109/lics52264.2021.9470560). Available online in ILLC Prepublication (PP) series PP-2021-07.