PP-2022-06: The Topology of Surprise

PP-2022-06: Baltag, Alexandru and Bezhanishvili, Nick and Fernandez Duque, David (2022) The Topology of Surprise. [Pre-print]

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In this paper we present a topological epistemic logic, with modalities for knowledge (modeled as the universal modality), knowability (represented by the topological interior operator), and unknowability of the actual world. The last notion has a non-self-referential reading (modeled by Cantor derivative: the set of limit points of a given set) and a self-referential one (modeled by Cantor’s perfect core of a given set: its largest subset without isolated points). We completely axiomatize this logic, showing that it is decidable and PSPACE-complete, and we apply it to the analysis of a famous epistemic puzzle: the Surprise Exam Paradox.

Item Type: Pre-print
Report Nr: PP-2022-06
Series Name: Prepublication (PP) Series
Year: 2022
Subjects: Computation
Depositing User: Nick Bezhanishvili
Date Deposited: 27 Apr 2022 13:08
Last Modified: 27 Apr 2022 13:14
URI: https://eprints.illc.uva.nl/id/eprint/1885

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