Spatio-Temporal Stream Reasoning with Incomplete Spatial Information

Reasoning about time and space is essential for many applications, especially for robots and other autonomous systems that act in the real world and need to reason about it. In this paper we present a pragmatic approach to spatio-temporal stream reasoning integrated in the Robot Operating System through the DyKnow framework. The temporal reasoning is done in the Metric Temporal Logic and the spatial reasoning in the Region Connection Calculus RCC8. Progression is used to evaluate spatio-temporal formulas over incrementally available streams of states. To handle incomplete information the underlying first-order logic is extended to a three-valued logic. When incomplete spatial information is received, the algebraic closure of the known information is computed. Since the algebraic closure might have to be re-computed every time step, we separate the spatial variables into static and dynamic variables and reuse the algebraic closure of the static variables, which reduces the time to compute the full algebraic closure. The end result is an efficient and useful approach to spatio-temporal reasoning over streaming information with incomplete information.