Mapping Calendar Expressions into Periodical Granularities

An effort has been devoted in the recent years to study and formalize the concept of time granularity and to design applications and services using the formalization. Among other proposals, a calendar algebra has been defined to facilitate the specification of new granularities and to perform conversions among them. This paper shows how granularities defined as algebraic calendar expressions can be represented as periodical sets of instants. More precisely, the paper shows how each algebraic operator changes the periodical structure of the granularities given as operands. These results have an immediate application enabling users to easily specify new granularities and using them in the only constraint solver supporting time granularities that is currently available.