The topology of surprise

Authors
Publication date 2022
Host editors
  • G. Kern-Isberner
  • G. Lakemeyer
  • T. Meyer
Book title Proceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning
Book subtitle Haifa, Israel. July 31–August 5, 2022
ISBN (electronic)
  • 9781956792010
Series KR
Event 19th International Conference on<br/>Principles of Knowledge Representation and Reasoning
Pages (from-to) 33-42
Publisher International Joint Conferences on Artificial Intelligence
Organisations
  • Interfacultary Research - Institute for Logic, Language and Computation (ILLC)
Abstract
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.
Document type Conference contribution
Language English
Published at https://doi.org/10.24963/kr.2022/4
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