Atomic temporal interval relations in branching time: calculation and application

A practical method of reasoning about intervals in a branching-time model which is dense, unbounded, future-branching, without rejoining branches is presented. The discussion is based on heuristic constraint- propagation techniques using the relation algebra of binary temporal relations among the intervals over the branching-time model. This technique has been applied with success to models of intervals over linear time by Allen and others, and is of cubic-time complexity. To extend it to branding-time models, it is necessary to calculate compositions of the relations; thus, the table of compositions for the 'atomic' relations is computed, enabling the rapid determination of the composition of arbitrary relations, expressed as disjunctions or unions of the atomic relations.

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