Representing and Reasoning about Motion in a Two-Dimensional World

We present a point-based spatiotemporal first-order logic for representing the qualitative and quantitative spatial temporal knowledge needed to reason about motion in a two-dimensional space. A feature of the logic is the uniform treatment of space and time. The knowledge of a simplified world, a two-dimensional street network with active traffic lights, is represented, and the reasoning problem of how a robot moves from one place to another in the world is formalized with the proposed logic.