 We could say that \(G\) is the precondition for the resetting action \(R\). Now the idea of \(\textsf{DPL}\) is to take the meaning of \(\exists x P(x)\) to be not the precondition \(G\) (as in classical static first order logic) but the resetting action \(R\). In this way we do not lose information since \(G\) can always be obtained from \(R\). Moreover, the range of the relation \(R\) consists of assignments \(\beta\) that differ from assignments in the precondition \(G\) at most with respect to the value of \(x\) and that are also in \(F\) (i.e., \(\beta(x)\) is in the interpretation of \(P)\). The \(x\) values stored in the range of the binary relation \(R\) are precisely the \(x\) values that satisfy \(P\), i.e., the values we were looking for.