Subject: more definitions

From: "Rick Snodgrass" <rts>
Date: Fri, 12 Mar 1993 13:14:00 MST

Lots of work is now going on in a subdiscipline of temporal databases,
that of spatiotemporal databases. The March, 1993 issue of SIGMOD
Record lists all the papers through December, 1992 in this area.

In the following, I extend five of the previous terms in the glossary
to also apply to spatiotemporal databases.

Comments and critique would be welcome.

Sincerely,
	Rick

\subsection{Spatiotemporal as Modifier}

\entry{Definition}

The modifier {\em spatiotemporal} is used to indicate that the
modified concept concerns simultaneous support of some aspect of time
and some aspect of space, in one or more dimensions.

\entry{Alternative Names}

Spatio-temporal, temporal-spatial, space-time-oriented.

\entry{Discussion}

This term is already in use, interchangeably with ``spatio-temporal,''
in the geographic information systems community (+E3) (hence, the
preference over ``temporal-spatial''), and is consistent with the
``temporal'' modifier (+E7). Avoiding the hyphen makes it easier to
type (+E2), another reason to prefer it over ``temporal-spatial''. It
may be applied generically as a modifier for ``database,''
``algebra,'' ``query language,'' ``data model,'' and ``DBMS.'

\subsection{Spatial Quantum}

\entry{Definition}

A {\em spatial quantum} (or simply {\em quantum}, when the sense is
clear) is the shortest distance (or area or volume) of space supported
by a spatial DBMS---it is a nondecomposable region of space. It can be
associated with one or more dimensions. A particular
unidimensional quantum is an interval of fixed length along a single
spatial dimension. A particular three-dimensional quantum is a fixed-sized,
located cubic volume of space.

\entry{Alternative Name}   

Spatial unit.

\entry{Discussion}

We prefer ``spatial quantum'' to ``spatial unit'' because spatial distances
and volumes are usually given as measurements of some unit (such as meters), 
but the ``unit of measurement'' is not the same as 
the ``spatial quantum.''  The former term (``spatial quantum'')
is more precise (+E9), in part,
because it avoids this possible confusion.

\subsection{Spatiotemporal Quantum}

\entry{Definition}

A {\em spatiotemporal quantum} (or simply {\em quantum}, when the
sense is clear) is a non-decomposable region in two, three, or
four-space, where one or more of the dimensions are spatial and the
rest, at least one, are temporal.

\entry{Alternative Name}

Spatiotemporal unit, spatiotemporal chronon.

\entry{Discussion}

This term is a generalization of chronon and spatial quantum.
``Unit'' is perhaps less precise (-E9). `Chronon' specifically relates
to time, and thus is inconsistent with the adjective `spatiotemporal'.

\subsection{Spatiotemporal Interval}

A {\em spatiotemporal interval} is a region in $n$-space, where at
least one of the axes is a spatial dimension and the remaining axes
are temporal dimensions, with the region having sides that are
parallel to all axes. It identifies when and where a fact was true.

\entry{Alternative Names}

None.

\entry{Discussion}

A spatiotemporal interval can be represented by a non-empty set of
spatiotemporal quanta.

\subsection{Spatiotemporal Element}

\entry{Definition}

A {\em spatiotemporal element} is a finite set of
spatiotemporal intervals. Spatiotemporal elements are closed under the
set theoretic operations of union, intersection and complementation.

\entry{Discussion}

This is the natural generalization of ``temporal element.''
It can be represented with a set of spatiotemporal quanta.