An Algebraic Representation of Calendars

This paper uses an algebraic approach to define temporal granularities and calendars. All the granularities in a calendar are expressed as algebraic expressions based on a single “bottom” granularity. The operations used in the algebra directly reflect the ways with which people construct new granularities from existing ones, and hence yield more natural and compact granularities definitions. Calendar is formalized on the basis of the algebraic operations, and properties of calendars are studied. As a step towards practical applications, the paper also presents algorithms for granule conversions between granularities in a calendar.

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