Thinking takes Time: A Modal Active-Logic for Reasoning in Time

Most commonsense reasoning formalisms do not account for the passage of time as the reasoning occurs, and hence are inadequate from the point of view of modeling an agent’s 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 exarnine how it addresses the problem of logical omniscience.