Some logics of belief assume that an agent believes all the consequences of each of its beliefs; others do not. Both options seem to have their drawbacks. The author's idea is to go between the two by ``dynamizing'' the system of logic, so that we may take into account the mental operations carried out to come to believe an item. Formally, the author adds to the connectives of ordinary epistemic logic a unary operator \(\langle F_i\rangle\) with \(\langle F_i\rangle K_iA\) read as saying ``if agent \(i\) makes sufficiently many calculations of the right kind, it will come to know \(A\)''. An axiom system is presented for this augmented epistemic language in which, for example, the standard epistemic postulate K: \(K_i(A\to B)\to (K_iA\to K_iB)\) is elaborated into DE1: \(K_i(A\to B)\to(K_i A\to\langle F_i\rangle K_iB)\). Some theses and non-theses of the axiom system are noted.