Reasoning in Time and Space

Abstract

This paper describes a new approach to representing and reasoning with temporal and spatial information. A wide variety of temporal and spatial specifications can be converted into linear inequalities relating the midpoints of events or boundary surfaces of objects respectively, Linear programming is then used to represent these constraints and perform deductions. The temporal information is modularized into semantically related clusters of events each with its own tableau and related to each other by a reference frame transformation. A similar grouping can be done for objects making the system computationally efficient. For temporal reasoning, the system is formally adequate except for linguistic fuzziness. For geometric reasoning, polyhedra can be represented by allowing paramvtiization. The uniformity of the time and space representation makes this approach particularly attractive.