Modelling Periodic Temporal Notions by Labelled Partitionings of the Real Numbers – The PartLib Library

The key notion for modelling calendar systems and many other periodic temporal notion is the mathematical concept of a partitioning of the real numbers. A partitioning of R splits the time axis into a sequence of intervals. Basic time units like seconds, minutes, hours, days, weeks, months, years etc. can all be represented by partitionings of R with finite partitions. Besides the basic time units in calendar systems, there are a lot of other temporal notions which can be modelled as partitions: 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 labelled partitionings of R is presented. The formalism is implemented as the C++ library PartLib (Partitioning Library). The interface to PartLib is presented in the appendix. keywords: calendrical calculations, representation of time, ontology of temporal notions, time granularities, knowledge representation,.