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Si us plau utilitzeu sempre aquest identificador per citar o enllaçar aquest document: https://hdl.handle.net/2445/231339
The topology of surprise
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In this paper we present a topological epistemic logic, with modalities for knowledge (modelled 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 (modelled by Cantor derivative: the set of limit points of a given set) and a self-referential one (modelled by Cantor’s perfect core of a given set: its largest subset without isolated points, where is isolated iff { } is open). 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.
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BALTAG, Alexandru, BEZHANISHVILI, Guram and FERNÁNDEZ DUQUE, David. The topology of surprise. Artificial Intelligence. 2025. Vol. 349. ISSN 0004-3702. [consulted: 12 of September of 2026]. Available at: https://hdl.handle.net/2445/231339