Calendrical calculations with time partitionings and fuzzy time intervals

This paper presents a piece in a big mosaic which consists of formalisms and software packages for representing and reasoning with everyday temporal notions. The kernel of the mosaic consists of several layers. At the bottom layer there are a number of basic datatypes for elementary temporal notions. These are time points, crisp and fuzzy time intervals and partitionings for representing periodical temporal notions like years, months, semesters etc. Partitionings can be arranged to form ‘durations ’ (e.g. ‘2 semester and 1 month’). Each formalism in the bottom layer comes with its own functions and relations. The second layer is presented in this paper. It contains a number of basic functions which use time points, intervals, partitionings and durations simultaneously. The functions are introduced and motivated with temporal expressions in natural language. The third layer, which is not presented in this paper, uses the functions and relations of the lower layers as building blocks in a specification language for specifying complex temporal notions. The whole mosaic contains a number of other formalisms, in particular a representation of calendar systems, and various databases with information about temporal notions