The role of labelled partitionings for modelling periodic temporal notions

The key notion for modelling calendar systems as well as many periodic events, for example the seasons, is the notion of a partitioning of the real numbers. A partitioning of R splits the time axis into a finite or infinite sequence of intervals. Basic time units like seconds, minutes, hours, days, weeks, months, years etc. can all be represented by finite partitionings of R. There are a lot of other temporal notions which can be modelled as partitions either: the seasons, the ecclesiastical calendars, financial years, semesters at universities, the sequence of sunrises and sunsets, the sequence of the tides, the sequence of school holidays etc. In this paper, a formalization of periodic temporal notions by means of partitionings R is presented.