Subject: Updated glossary entries.

From: "Christian S. Jensen" <[email-masked]>
Date: Wed, 10 Mar 1993 01:02:14 +0100

Dear colleague,

Earlier this year, it was requested that two concepts from the initial
glossary that appeared in SIGMOD Record be generalized slightly.
Below, I include proposals for such generalized, revised entries.

As always, comments and new proposals are welcome.

Best regards,
Christian

Comment: The definition has been revised to include n-d chronons, and
some discussion has been moved from the definition to the discussion
section (to obtain a short, dictionary-like definition).

\subsection{Chronon}

\entry{Definition}

In one dimension, a {\em chronon} is the shortest duration of time
supported by a temporal DBMS, i.e., a nondecomposable unit of time. A
particular one-dimensional chronon is a subinterval of fixed duration
on a time-line. An $n$-dimensional chronon is a non-decomposable
region in $n$-dimensional time. Important special types of chronons
include valid-time, transaction-time, and bitemporal chronons.

\entry{Alternative Names}

Instant, moment, time quantum, time unit.

\entry{Discussion}

Various models of time have been proposed in the philosophical and
logical literature of time (e.g., van Benthem). These view time, among
other things, as discrete, dense, or continuous. Intuitively, discrete
models of time are isomorphic to the natural numbers, i.e., there is
the notion that every moment of time has a unique successor. Dense
models of time are isomorphic to (either) the real or rational
numbers: between any two moments of time there is always another.
Continuous models of time are isomorphic to the real numbers, i.e.,
both dense and also, unlike the rational numbers, with no ``gaps.''

``Instant'' and ``moment'' invite confusion between a {\em point} in
the continuous model and a nondecomposable {\em unit} in the discrete
model ($-$E8). Clocking instruments invariably report the occurrence
of events in terms of time intervals, not time ``points.'' Hence,
events, even so-called ``instantaneous'' events, can best be measured
as having occurred during an interval ($-$E9). ``Time quantum'' is
precise, but is longer and more technical than ``chronon'' ($-$E2).
``Time unit'' is perhaps less precise~($-$E9).

Comment: To be consistent with other entries, multidimensional
intervals are used rather than rectangles and boxes. To obtain a
shorter definition, material has been moved to the discussion section.
Finally, chronons are mentioned in the discussion.

\subsection{Temporal Element}

\entry{Definition}

A {\em temporal element} is a finite union of $n$-dimensional
intervals. Special cases of temporal elements include {\em valid-time
elements}, {\em transaction time elements}, and {\em bitemporal
elements}. They are finite unions of valid-time intervals,
transaction-time intervals, and bitemporal intervals, respectively.

\entry{Alternative Names}

Temporal element.

\entry{Discussion}

Observe that temporal elements are closed under the set theoretic
operations of union, intersection and complementation. Temporal
elements are often used as timestamps. A temporal element may be
represented by a set of chronons.

A valid time element was previously termed a temporal element.
However, for the naming to be consistent with the remainder of the
glossary, ``temporal'' is reserved as a generic modifier, and more
specific modifiers are adopted.