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Logics of propositional control

The 'Cooperation Logic of Propositional Control', CL-PC, of van der Hoek and Wooldridge is a logic for reasoning about the ability of agents and groups of agents to obtain a certain state of affairs in a situation in which each of the agents controls a number of propositional variables.We present a number of generalizations of this model, to represent situations in which agents only partially control the value of a variable, or cases in which agents share the control of a variable. We discuss and axiomatize some of these logics of 'partial control.' In addition, we show how this family of logics are closely connected to a body of work in mathematical logic: Cylindric Modal Logic.