Time, tense, and relativity revisited

Abstract

Interest in the problem of expressing temporal relations between events in a coherent fashion has undergone a revival due to the creation of data bases and knowledge bases containing time-dependent information and also through the scrutiny of concurrent algorithms and real-time systems. Presented herein is a simple temporal model, designated an F-complex, which develops from a single future operator and a single order axiom yet encompasses several of the current proposals for models to systematize reasoning about one or more of the aforementioned areas. The rudimentary F-complex commits to no special ontology of time, giving the advantage of clarifying the properties which are common to most methods of temporal modeling. Concepts of past, future, and temporal precedence are formulated within the posited structure, allowing comparison to the published temporal models of Lamport [11], Allen [1], Milner [14], Rodriguez [17], and others [21]. Specifically, Allen's thirteen linear-time and Rodriguez's eighty-two relativistic atomic relations are characterized, as well as the axiomatic scheme of Lamport. The models are treated more thoroughly than in [6]. Furthermore, the main theorem is strengthened.