A logic of revelation and concealment

TLDR: A new logic for reasoning about the interaction between knowledge and action is introduced, in which each agent in a system is assumed to perceive some subset of the overall set of Boolean variables in the system; these variables give rise to epistemic indistinguishability relations.

Abstract: The last decade has been witness to a rapid growth of interest in logics intended to support reasoning about the interactions between knowledge and action Typically, logics combining dynamic and epistemic components contain ontic actions (which change the state of the world, eg, switching a light on) or epistemic actions (which affect the information possessed by agents, eg, making an announcement) We introduce a new logic for reasoning about the interaction between knowledge and action, in which each agent in a system is assumed to perceive some subset of the overall set of Boolean variables in the system; these variables give rise to epistemic indistinguishability relations, in that two states are considered indistinguishable to an agent if all the variables visible to that agent have the same value in both states In the dynamic component of the logic, we introduce actions r(p, i) and c(p, i): the effect of r(p, i) is to reveal variable p to agent i; the effect of c(p, i) is to conceal p from i By using these dynamic operators, we can represent and reason about how the knowledge of agents changes when parts of their environment are concealed from them, or by revealing parts of their environment to them Our main technical result is a sound and complete axiomatisation for our logic