Knowledge and control

Logics of propositional control, such as van der Hoek and Wooldridge’s CL-PC [14], were introduced in order to represent and reason about scenarios in which each agent within a system is able to exercise unique control over some set of system variables. Our aim in the present paper is to extend the study of logics of propositional control to settings in which these agents have incomplete information about the society they occupy. We consider two possible sources of incomplete information. First, we consider the possibility that an agent is only able to “read” a subset of the overall system variables, and so in any given system state, will have partial information about the state of the system. Second, we consider the possibility that an agent has incomplete information about which agent controls which variables. For both cases, we introduce a logic combining epistemic modalities with the operators of CL-PC, investigate its axiomatization, and discuss its properties.