Symbolic representation of user-defined time granularities

In the recent literature on time representation, an effort has been made to characterize the notion of time granularity and the relationships between granularities. The main goals are having a common framework for their specification, and allowing the interoperability of systems adopting different time granularities. This paper considers the mathematical characterization of finite and periodic time granularities, and investigates the requirements for a user-friendly symbolic formalism that could be used for their specification. Instead of proposing yet another formalism, the paper analyzes the expressiveness of known symbolic formalisms for the representation of granularities, using the mathematical characterization as a reference model. Based on this analysis, a significant extension to the collection formalism defined in [15] is proposed, in order to capture a practically interesting class of periodic granularities