In this work, we present a multi-agent logic of knowledge and change of knowledge interpreted on topological structures. Our dynamics are of the so-called semi-private character where a group G of agents is informed of some piece of information φ, while all the other agents observe that group G is informed, but are uncertain whether the information provided is φ or ¬ φ. This article follows up on our prior work (van Ditmarsch et al. in Proceedings of the 15th TARK. pp 95-102, 2015) where the dynamics were public events. We provide a complete axiomatization of our logic, and give two detailed examples of situations with agents learning information through semi-private announcements.
Bibliographical noteFunding Information:
Acknowledgements. We thank the anonymous reviewers for their valuable comments. Hans van Ditmarsch is also affiliated to IMSc (Institute of Mathematical Sciences), Chennai, as research associate. The authors acknowledge financial support from European Research Council grant EPS 313360.
© 2017, The Author(s).
- Dynamic epistemic logic
- Private announcements
- Subset space logic
- Topological semantics