Incorporating an implicit time dimension into the relational model and algebra

Abstract

Incorporating an implicit time dimension into the relational model and algebra Informatique théorique et applications, tome 30, n o 3 (1996), p. 231-260. <http://www.numdam.org/item?id=ITA_1996__30_3_231_0> © AFCET, 1996, tous droits réservés. L'accès aux archives de la revue « Informatique théorique et applications » implique l'accord avec les conditions générales d'utilisation (http://www.numdam. org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d'une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright. Article numérisé dans le cadre du programme Numérisation de documents anciens mathématiques http://www.numdam.org/ Informatique théorique et Applications/Theoretical Informaties and Applications (vol. 30, n° 3, 1996, pp. 231-260) INCORPORATING AN IMPLICIT TIME DIMENSION INTO THE RELATIONAL MODEL AND ALGEBRA (*) by Mehmet Ali ORGUN (*) Communicated by Christian CHOFFRUT Abstract.-The prevailing approach to modeling the time dimension in databases is, in oneform or another, the use of an explicit représentation oftime. In this paper we propose a temporal relational model and algebra, based on temporal semantics, to incorporate an implicit time dimension in databases. In temporal semantics, time-varying relations are an indexed collection of ordinary relations, one for each moment in time. A temporal database is modeled by a collection of timevarying relations. Temporal databases are queried using a temporal relational algebra (TRA) which extends the relational algebra point-wise upon the set of natural numbers, Although TRA lacks the ability to explicitly manipulate time, we show how temporal aggregation and when-type queries can be formulated using a technique called "tagging ". The formai properties of TRA, which can be usedfor query optimization, are also outlined. We also compare our work with other proposed temporal algebras.

Querying Historical Data Over Multiple Time-Lines

“…The closure property is one of the important criteria that temporal algebras should satisfy [36]. In the literature [39], an analogous result is given for a temporal algebra called Tra, which is just like except that all the relations are defined over the same global clock.…”

“…Time representation has played a central role in many applications in computer science research and applications where dynamic changes are essential, such as temporal database systems [12,39,63], reactive systems [33], medical applications [2], multi-agent systems [19,34], analysis of security protocols [9], temporal reasoning [52] and so on. In fact, especially when we are talking about the real world and the events that take place in it, there is often a need to deal with multiple timelines as well as multiple time granularities in a variety of knowledge-based systems, such as those used in ecological modeling [37], text processing [30], knowledge representation [47] and spatio-temporal reasoning [7] where we may need to consider how knowledge defined at different levels of time may be integrated.…”

“…These algebras do not deal with multiple granularity of time or different levels of time; their main motivation is to propose a temporal relational algebra which can be used as a basis for temporal relational completeness. When all relations are defined over the given time-line, degenerates into Orgun's algebra Tra [39]. It is shown in [40] that a recursive extension of Tra is as expressive as the algebras of Tuzhilin and Cifford's and Gabbay and McBrien's.…”

“…In , we adopt temporal operators of the algebra Tra proposed by Orgun and Wadge [39,43], however, Tra does not have the notion of clocks as all relations are defined over the same global time-line. Our algebra is more similar to that of Orgun [46], which is also based on multiple clocks but is enhanced with a temporal splicing operator to increase its expressive power.…”

Knowledge Representation, Reasoning and Integration Using Temporal Logic with Clocks

“…Time representation has played a central role in many applications in computer science research and applications where dynamic changes are essential, such as temporal database systems [10,35,46], concurrent and distributed systems [30,32], hybrid systems [33], medical applications [3], multi-agent systems [19,31], analysis of security protocols [8,23], temporal reasoning [1,42], and so on. In knowledge acquisition, representation and integration in knowledge-based systems, the representation of multiple time granularities [7,18,28,37] has also appeared 144 M. A. Orgun, C. Liu, and A. C. Nayak…”