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A methodology for modeling temporal (timesensitive) aspects of discrete-event systems is presented. A formalism of temporal logic which incorporates both point and interval descriptions of time is formulated, which is an extension of Allen's interval logic [1]. A formal axiomatic system of this point-interval logic is presented. A graph model is shown to implement the axiomatic system of point-interval logic. This graph-based approach transforms the system's specifications given by temporal statements into a graph structure. The graph-based temporal inference engine (TIE) identifies temporal ambiguities and errors (if present) in the system's specifications, infers new temporal relations among system's intervals, and identifies the user-defined intervals of interest.

This paper is an extension of an earlier work on a methodology for modeling temporal aspects of discrete-event systems. The methodology incorporates point and interval descriptions of time, and offers both qualitative and quantitative calculus for time. A graph-based temporal programmer (TEMPER) is shown to implement the axiomatic system of the temporal formalism. The approach transforms the system specifications given by temporal statements into a graph structure, identifies errors (if present) in the system, infers new temporal relations among system intervals, and calculates delays among time points and their actual time of occurrence.

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