Planning temporal events using point–interval logic

The paper presents a temporal logic and its application to planning time-critical missions. An extended version of the Point–Interval Logic (PIL) is presented that incorporates both point and interval descriptions of time. The points and intervals in this formalism represent time stamps and time delays, respectively, associated with events/activities in a mission as constraints on or as resultants of a planning process. The lexicon of the logic offers the flexibility of qualitative and/or quantitative descriptions of temporal relationships between points and intervals of a system. The provision for qualitative temporal relationships makes the approach suitable for situations where all the required quantitative information may not be available to planners. A graph-based approach, called the Point Graph (PG) methodology, is shown to implement the axiomatic system of PIL by transforming the temporal specifications into Point Graphs. A temporal inference engine uses the Point Graph representation to infer and verify the feasibility of temporal relations among system intervals/points. The paper demonstrates the application of PIL and its inference engine to a mission-planning problem.