Most common sense reasoning formalisms do not account for the passage of time a s the reasoning occurs, and hence are inadequate from the point of view of modeling an agent's {\em ongoing} process of reasoning. We present a modal active-logic that treats time as a valuable resource that is consumed in each step of the agent's reasoning. We provide a sound and complete characterization for this logic and examine how it addresses the problem of logical omniscience. (Also cross-referenced as UMIACS-TR-94-39)