Temporal Database Systems - Advanced Database Technology and Design - page 144

Now, much of the foregoing discussion was deliberately meant to raise
certain questions in your mind. Regardless of whether we succeeded in that
aim, we now raise those questions explicitly and try to answer them.

1. Does not the expression all times t such that s e raise the

specter of infinite sets and the conceptual and computational diffi-
culties such sets suffer from?
Answer: Well, yes, it does appear to, but we dismiss the specter
and circumvent the difficulties by adopting the assumption that the
timeline consists of a finite sequence of discrete, indivisible time
quanta. The interval with start time s and end time e thus involves a
finite number of such quanta, a fortiori.
Note: Much of the literature refers to a time quantum as a chronon.
However, it then typically goes on to define a chronon as an inter-
val (see, for example, the glossary in [4]), implying that it has a start
point and an end point, and perhaps further points in between, and
so is not indivisible after all. (What exactly are those points? What
else can they be but chronons?) We find some confusion here and
prefer to avoid the term.

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2. Statements 1, 2, and 3 seem to assume that time quanta are days,

but surely the system supports time precisions down to tiny frac-
tions of a second. If S1 was a supplier on July 1, 1999, but not on
June 30, 1999, what is to be done about the presumed period of
time from the start of July 1 up to the very instant of appointment,
during which S1 was still not officially under contract?
Answer: We need to distinguish carefully between time quanta as
such, which are the smallest time units the system can possibly
represent, and the time units that are useful for some particular
purpose, which might be years or months or days or weeks, and so
forth. We call such units timepoints (points for short) in order to
stress the fact that for the purpose at hand they too are considered
to be indivisible. Now, we might say, informally, that a timepoint is
a section of the timeline—that is, the set of time quanta—that
stretches from one boundary quantum to the next (for example,
from midnight on one day to midnight on the next). We might
therefore say, again informally, that timepoints have a dura-
tion—one day, in our example. Formally, however, timepoints are
(to repeat) indivisible, and the concept of duration strictly does not
apply.