Temporal reasoning: A relativistic model

Abstract

In 1983, Allen presented an ingenious method for the representation and maintenance of temporal information in the presence of imprecise, uncertain, and relative knowledge about time of occurrence. He introduced 13 relations between his primitive “temporal intervals,” providing for the expression of “any relationship which can hold between two intervals.” the model, however, did not address the problem of temporally incomparable events, such as events occurring in a distributed system without a common clock. Lamport's interprocessor communication model furnishes an axiomatic system for describing such events and their possible relationships. This article demonstrates that Allen's temporal model can be subsumed in a more general model based on Lamport's axiomatics. It is further suggested that this extended model can provide the underpinnings of a temporal knowledge base containing time-dependent information measured by unsynchronized clocks or in relativistic space-time. In this model, the number of relations between intervals increases dramatically from Allen's 13 or Lamport's 2 or 3 to over 80. Within this context, a modification of Allen's algorithm for the maintenance of a temporal reasoning system is presented, thus permitting the advantages of such a system to extend to reasoning about a wider range of phenomena.