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<p><b>Abstract</b>—Calendars and periodicity play a fundamental role in many applications. Recently, some commercial databases started to support <it>user-defined</it> periodicity in the <it>queries</it> in order to provide “<it>a human-friendly way of handling time</it>” (see, e.g., TimeSeries in Oracle 8). On the other hand, only few <it>relational data models</it> support user-defined periodicity in the <it>data</it>, mostly using “<it>mathematical</it>” expressions to represent periodicity. In this paper, we propose a high-level “<it>symbolic</it>” language for representing user-defined periodicity which seems to us more <it>human-oriented</it> than mathematical ones, and we use the domain of Gadia's temporal elements in order to define its properties and its extensional semantics. We then propose a temporal relational model which supports user-defined “<it>symbolic</it>”<it>periodicity</it> (e.g., to express “on the second Monday of each month”) in the validity time of tuples and also copes with <it>frame times</it> (e.g., “from 1/1/98 to 28/2/98”). We define the temporal counterpart of the standard operators of the relational algebra, and we introduce new temporal operators and functions. We also prove that our temporal algebra is a consistent extension of the classical (atemporal) one. Moreover, we define both a fully symbolic evaluation method for the operators on the periodicities in the validity times of tuples, which is correct but not complete, and semisymbolic one, which is correct and complete, and study their computational complexity.</p>
Temporal relational model and algebra, user-defined symbolic periodicity in the validity time, high-level “symbolic” language, symbolic (intensional) evaluation method, semisymbolic evaluation method, user-friendly treatment of periodicity, integration and extension of artificial intelligence and temporal databases techniques.

P. Terenziani, "Symbolic User-Defined Periodicity in Temporal Relational Databases," in IEEE Transactions on Knowledge & Data Engineering, vol. 15, no. , pp. 489-509, 2003.
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