KR2022Proceedings of the 19th International Conference on Principles of Knowledge Representation and ReasoningProceedings of the 19th International Conference on Principles of Knowledge Representation and Reasoning

Haifa, Israel. July 31–August 5, 2022.

Edited by
  1. Gabriele Kern-Isberner
  2. Gerhard Lakemeyer
  3. Thomas Meyer

ISSN: 2334-1033
ISBN: 978-1-956792-01-0

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Published by

Copyright © 2022 International Joint Conferences on Artificial Intelligence Organization

The Topology of Surprise

  1. Alexandru Baltag(ILLC, University of Amsterdam)
  2. Nick Bezhanishvili(ILLC, University of Amsterdam)
  3. David Fernández-Duque(ICS of the Czech Academy of Sciences, Department of Mathematics WE16, Ghent University)
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BibTeX
https://doi.org/10.24963/kr.2022/4

Keywords

  1. Reasoning about knowledge, beliefs, and other mental attitudes
  2. Belief revision and update, belief merging, information fusion
  3. KR and cognitive modelling
  4. Knowledge representation languages

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.