 Logics for propositional control have modalities of the type \([[i]]\varphi\), meaning that player \(i\) has a “control” strategy to see to it that, no matter how the other agents choose their control strategies, then \(\varphi\) holds in the end. But they also have modalities of the type \([[C]]\varphi\), meaning that players in \(C\) have a joint control strategy ensuring \(\varphi\) in the end. A strategy profile is thus equivalent to a valuation function, which assigns a truth value of every proposition available. In turn, a strategy of a player \(i\) can thus be seen as a partial valuation function, that assigns a truth value only to the propositions controlled by \(i\).