Nordic Online Logic Seminar: next talk on 19 December by Alexandru Baltag

[Graham Leigh]

The Nordic Online Logic Seminar (NOL 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.

See the announcement for the next talk below. 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 .

Val Goranko and Graham Leigh
NOL seminar organisers

Nordic Online Logic Seminar
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<https://eprints.illc.uva.nl/id/document/11528>.
• 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<https://eprints.illc.uva.nl/id/document/11192>.
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