Reasoning in Time and Space

Abstract

This paper describes a new approach to representing and reasoning with temporal and spaUal information. A wide variety of temporal and spatial specifications can be converted into linear inequalities relatii1g the endpoints of events or bourul:1ry surfaces of objects respecUvely. Linear programming is /,lwn nsed to represent these constraints and perform dcducUons. The temporal information is modularized into sema ntically relal.ed clusters of events each with its own tahleau 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 ade quate except for linguistic fuzziness. For geometric reasoning, polyhedra can be represented by allowing parametrization. The uniformity of the time and space representaUon makes this approach particularly attractive.