Direct Granularity Conversions among Temporal Constraints

This paper considers temporal constraints that can impose a minimum and maximum time distance between the occurrences of two events by specifying the minimum and maximum values in terms of a time granularity. When several constraints using different time granularities are part of the specification of a single problem, a reasonable question is how to convert the constraints in terms of a single granularity in order to apply standard temporal constraint algorithms. This paper investigates the problem of converting a distance constraint expressed in terms of a granularity into another one in terms of a different time granularity. An expressive formal model for time granularities is assumed including common granularities like hours and days as well as user-defined granularities like business days and academic semesters.