Katheeln Hornsby,
Max Egenhofer, and Patrick Hayes Advances in Conceptual Modeling, Paris, France,
P. Chen, D. Embley, J. Kouloumdjian, S. Liddle, and J. Roddick (eds.), Lecture Notes in Computer Science, Vol. 1227, Springer-Verlag, pp. 98-109, November 1999.
Abstract
Database support of time-varying phenomena typically assumes that
entities change in a linear fashion. Many phenomena, however,
change cyclically over time. Examples include monsoons, tides, and
travel to the workplace. In such cases, entities may appear and
disappear on a regular basis or their attributes or location may
change with periodic regularity. This paper introduces an approach
for modeling cycles based on cyclic intervals. Intervals are an
important abstraction of time, and the consideration of cyclic
intervals reveals characteristics about these intervals that are
unique from the linear case. This work examines binary cyclic
relations, distinguishing sixteen cyclic interval relations. We
identify their conceptual neighborhood graph, showing which
relations are most similar and demonstrating that this set of
sixteen relations is complete. The results of this investigation
provide the basis for extended data models and query languages that
address cyclically varying phenomena.
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Katheeln Hornsby,
Max Egenhofer, and 
Patrick Hayes