Subject: additional glossary definitions

From: "Michael Soo" <soo>
Date: Wed, 10 Mar 1993 15:32:24 MST

Proposed definitions of "calendar," "calendric system," and 
"temporal natural join" are enclosed.  

Best regards,
Mike Soo
[email-masked]

\subsection{Calendar}

\entry{Definition}

A {\it calendar} provides a human interpretation of time.  
As such, calendars ascribe meaning to temporal values where 
the particular meaning or interpretation is relevant to the user.  
In particular, calendars determine the mapping between human-meaningful
time values and an underlying time-line.

\entry{Alternative Names}

None.

\entry{Discussion}

Calendars are generally cyclic, allowing human-meaningful
time values to be expressed succinctly.  For example,
dates in the common Gregorian calendar may be expressed in the 
form $<${\em month\/} {\em day}, {\em year\/}$>$ where each of the 
fields month, day, and year cycle as time passes.

The concept of calendar defined here subsumes commonly used calendars
such as the Gregorian calendar, the Hebrew calendar, 
and the Lunar calendar, though the given definition is much more general.
This usage is consistent with the conventional
English meaning of the word (+E3).  It is also intuitive for
the same reason (+E8).

\subsection{Calendric System}

\entry{Definition}

A calendric system is a collection of calendars.  Each calendar in a
calendric system is defined over contiguous and non-overlapping 
intervals of an underlying time-line.  Calendric systems 
define the human interpretation of time for a particular locale 
as different calendars may be employed during different intervals. 

\entry{Alternative Names}   

None.

\entry{Discussion}

A calendric system is the abstraction of time available at the 
conceptual (query language) level.
The term ``calendric system'' has been used to describe the calculation 
of events within a single calendar---it therefore has a conflicting meaning
(-E7).  Our definition generalizes this usage to multiple calendars 
in a very natural way, however.  Furthermore, our meaning is intuitive
in that the calendric system interprets time values at the conceptual 
level (+E8).

\subsection{Temporal Natural Join}

\entry{Definition}

A temporal natural join is a binary operator that generalizes
the snapshot natural join to incorporate one or more time dimensions.
Tuples in a temporal natural join are merged if their explicit
join attribute values match, and they are temporally conincident
in the given time dimensions.  As in the snapshot natural join,
the relation schema resulting from a temporal natural join is 
the union of the explicit attribute values present in both operand schemas,
along with one or more timestamps.  The value of a result timestamp is
the temporal intersection of the input timestamps, that is, the 
chronons contained in both.

\entry{Alternative Names}

Natural time-join, time-equijoin.

\entry{Discussion}

The snapshot natural join can be generalized to incorporate valid-time 
(the {\em valid-time natural join}), transaction-time
(the {\em transaction-time natural join}), or both
(the {\em bitemporal natural join}).  
In each case, the schema
resulting from the join is identical to that of the snapshot
natural join appended with the timestamp(s) of the input relations.

``Temporal natural join'' directly generalizes the snapshot
term ``natural join'' in that ``temporal'' is
used as a modifier consistent with its previously proposed 
glossary definition (+E7).  ``Natural time-join'' is less precise 
since it is unclear what is natural, i.e., is the join over 
``natural time'' or is the time-join ``natural'' (-E7, -E9).  
``Time-equijoin'' is also less precise since, in the snapshot model, the 
natural join includes a projection while the equijoin does not (-E7, -E9).

\end{document}