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The temporal interval relationships formalized by Allen, and later extended to accommodate semi-intervals by Freksa, have been widely utilized in both data modeling and artificial intelligence research to facilitate reasoning between the relative temporal ordering of events. In practice, however, some modifications to the relationships are necessary when linear temporal sequences are provided, when event times are aggregated, or when data is supplied to a granularity which is larger than required. This paper discusses these modifications and outlines a solution to this problem which accommodates any available knowledge of interval midpoints.
Temporal reasoning, temporal uncertainty, Allen temporal relationships, Freksa semi-intervals.

C. H. Mooney and J. F. Roddick, "Linear Temporal Sequences and Their Interpretation Using Midpoint Relationships," in IEEE Transactions on Knowledge & Data Engineering, vol. 17, no. , pp. 133-135, 2005.
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