Dialog proceeds over time, during which inferred beliefs come and go in the listener. Yet this temporal aspect of dialog and belief is typically ignored in theoretical treatments of dialog. Using a simple example of a dialog with an implicature that arises partway through and then is later retracted, we discuss how Gricean maxims and nonmonotonicity may relate to each other and to a computational treatment of implicature. In effect we seek to track reasoning along Gricean lines over time. We present our own computational approach to this, giving an implementation in the formalism of active logics. (Also cross-referenced as UMIACS-TR-96-42)