Arbitrary announcements in propositional belief revision

Hunter, Aaron (Aaron Hunter (Aaron_Hunter)) (author)
Schwarzentruber, Francois (author)
(editor)
(translator)

Copyright © 2015 for the individual papers by the papers' authors. Copying permitted only for private and academic purposes.

Proceedings of the International Workshop on Defeasible and Ampliative Reasoning (DARe-15) in Buenos Aires, Argentina, July 27, 2015. Public announcements cause each agent in a group to modify their beliefs to incorporate some new piece of information, while simultaneously being aware that all other agents are doing the same. Given some fixed goal formula, it is natural to ask if there exists an announcement that will make the formula true in a multi-agent context. This problem is known to be undecidable in a general modal setting, where the presence of nested beliefs can lead to complex dynamics. In this paper, we consider not necessarily truthful public announcements in the setting of propositional belief revision. We are given a goal formula for each agent, and we are interested in finding a single announcement that will make each agent believe the corresponding goal following AGM-style belief revision. If the goals are inconsistent, then this can be seen as a form of ampliative reasoning. We prove that determining if there is an arbitrary public announcement in this setting is not only decidable, but that it is simpler than the corresponding problem in the most simplified modal logics. Moreover, we argue that propositional announcements and beliefs are sufficient for modelling many practical problems, including simple robot controllers.

http://ceur-ws.org/Vol-1423/DARe-15_4.pdf