The Scandinavian Logic Society

NOL Seminar with Alexandru Baltag

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
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.