Announcement as effort on topological spaces

Hans van Ditmarsch; Sophia Knight; Aybüke Özgün

doi:10.1007/s11229-017-1592-8

Announcement as effort on topological spaces

Hans van Ditmarsch, Sophia Knight, Aybüke Özgün

Computer Science (Duluth)

Research output: Contribution to journal › Article › peer-review

9 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 language	English (US)
Pages (from-to)	2927-2969
Number of pages	43
Journal	Synthese
Volume	196
Issue number	7
DOIs	https://doi.org/10.1007/s11229-017-1592-8
State	Published - Jul 15 2019

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.

Keywords

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

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10.1007/s11229-017-1592-8

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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.",

keywords = "Arbitrary (public)announcements, Dynamic epistemic logic, Subset space logic, Topology",

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Announcement as effort on topological spaces

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