Reasoning about recurrence

Abstract

This dissertation examines the issue of representing knowledge about recurring states and events, and develops mechanisms for reasoning about recurrence. A first-order axiomatization is developed based on the interval calculus that allows entities (events, properties, processes, etc.) to be associated, incidentally or repeatedly, with temporal intervals. We describe the implementation of a self-organizing interval database manager and inference engine, as well as a system which intergrates the interval reasoner with a general purpose theorem prover and provides a restricted version of the recurrence logic. The recurrence formalism is applied to the domain of planning in a world with traffic control lights. An extensive example is developed, showing how the use of recurrence can enable a planner to determine that a plan to travel from a source to a destination is feasible, even if an intervening traffic light is red at the time it is encountered. In order to develop this example, a novel application of the interval logic to the spatial domain is presented, which allows us to reason about trajectories and their traversal over time. The combination of paths and temporal intervals, together with the recurrence axioms and actions such as traverse, allow us to prove several theorems about the use of traffic lights, and to show how an agent can validate plans to get past them.