Applying Allen's constraint propagation algorithm for non-linear time

The famous Allen's interval relations constraint propagation algorithm was intended for linear time. Its 13 primitive relations define all the possible mutual locations of two intervals on the time-axis. In this paper an application of the algorithm for non-linear time is suggested. First, a new primitive relation is added. It is called excludes since an occurrence of one event in a certain course of events excludes an occurrence of the other event in this course. Next, new composition rules for relations between intervals are presented: some of the old rules are extended by the relation excludes, and entirely new ones are formulated for composing the relation excludes with the other relations. Four different composition tables are considered. The choice of a composition table depends on whether time is branching or not, and whether intervals can contain non-collinear subintervals or not.
Keywords constraint propagation  non-linear time  time representation algorithms
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DOI 10.1007/BF00173698
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Elżbieta Hajnicz (1995). Some Considerations on Non-Linear Time Intervals. Journal of Logic, Language and Information 4 (4):335-357.

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