On the representation of infinite temporal data and queries (extended abstract)

Symbolic user-defined periodicity in temporal relational databases

“…On the other hand, we define the operators P , P , Â P , À P , [ P , which extend standard snapshot operators (i.e., , , Â, À, [) to work on periodic tables, operating directly on our symbolic representation. 4 We denote by Sch(R) the schema of the data part of R and, by t(S), a tuple t restricted to the schema S. t(FT) denotes the frame time of a tuple t and t(PER) its periodicity (e.g., if t is the first tuple of COURSES, t(FT) = [1/10/98, 31/11/99] and tðPERÞ ¼ Mon : 12-13 [ C Wed :…”

“…In the following, given a tuple t and a relation R, EqData(t,R) denotes the set of all (and only) the tuples in R having the same data part as t. Let t be a tuple in a periodic table R 0 and let tðR 0 Þ indicate the data part of t. Let R a periodic table 4. Notice that the very same table can contain different periodicities expressed at different user-defined granularities and that the operators of the relational algebra operate on tables regardless of whether the granularities are different or not.…”

“…For example, periodicity and/or different time granularities are supported in [4], [5], [6], [7], [18], [22], [23], [29], [34], [45], [46], [49]. Many approaches only focused on the treatment of periodicity in the query (see, e.g., [46] and Oracle8; see www.oracle.com\databases\ timeseries.html).…”

“…The comparison between the extensional and the symbolic part of the answer to query Q2 in Section 7 is just one of the many examples of this fact. For these reasons, most TDB approaches chose to adopt an "intensional approach" (see, e.g., [4], [5], [6], [7], [22], [23], [34], [45], [49] and the survey [46]). However, from the "human-oriented" point of view, also constraint-based approaches using mathematical formulae to express periodicity (see, e.g., [22], [23], [45] and the survey in [46]) seem to us inadequate (see, e.g., the sharp criticism in [27], [34], and notice that Stevenne was one of the coauthors of the LRP paper [22]).…”

“…Moreover, many realworld applications, including planning, scheduling, process control, multimedia, active databases, banking, law, etc., need to deal with periodic events and the interest towards the treatment of periodic events is rapidly increasing. Thus, dealing with periodicity and user-defined calendars in the data and/or in the queries is a very important task, which has been faced by many approaches in the area of temporal databases (consider, e.g., [4], [5], [6], [7], [18], [22], [23], [29], [34], [45], [46], [49]). In particular, an implicit (i.e., not extensional) treatment is advantageous since it allows one to store data holding at periodic times in a compact way instead of explicitly listing all the instances of the given periodicity (e.g., all "days" in a possibly infinite frame of time).…”