Announcement as effort on topological spaces

Hans van Ditmarsch, Sophia Knight, Aybüke Özgün

Research output: Contribution to journalArticlepeer-review

4 Scopus citations

Abstract

We propose a multi-agent logic of knowledge, public announcements and arbitrary announcements, interpreted on topological spaces in the style of subset space semantics. The arbitrary announcement modality functions similarly to the effort modality in subset space logics, however, it comes with intuitive and semantic differences. We provide axiomatizations for three logics based on this setting, with S5 knowledge modality, and demonstrate their completeness. We moreover consider the weaker axiomatizations of three logics with S4 type of knowledge and prove soundness and completeness results for these systems.

Original languageEnglish (US)
Pages (from-to)2927-2969
Number of pages43
JournalSynthese
Volume196
Issue number7
DOIs
StatePublished - Jul 15 2019
Externally publishedYes

Bibliographical note

Funding Information:
Acknowledgements We thank Philippe Balbiani, Alexandru Baltag, and Adam Bjorndahl for various detailed suggestions over the past year on how to improve our single-agent and multi-agent results in subset space logic and topological logics. We have found them very supportive of our efforts. We also thank the TARK 2015 reviewers for their valuable comments. Hans van Ditmarsch is also affiliated to IMSc (Institute of Mathematical Sciences), Chennai, as research associate. We acknowledge support from European Research Council Grant EPS 313360.

Funding Information:
We thank Philippe Balbiani, Alexandru Baltag, and Adam Bjorndahl for various detailed suggestions over the past year on how to improve our single-agent and multi-agent results in subset space logic and topological logics. We have found them very supportive of our efforts. We also thank the TARK 2015 reviewers for their valuable comments. Hans van Ditmarsch is also affiliated to IMSc (Institute of Mathematical Sciences), Chennai, as research associate. We acknowledge support from European Research Council Grant EPS 313360.

Publisher Copyright:
© 2017, Springer Nature B.V.

Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

Keywords

  • Arbitrary (public)announcements
  • Dynamic epistemic logic
  • Subset space logic
  • Topology

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