Subject: Glossary Terms (time sequence, temporal interpolation, temporal rule)

From: [email-masked] (Arie Segev)
Date: Sun, 2 May 93 23:11:00 PDT

Rick wrote:

>5. The discussion seems to equate "temporal value" with "value history"
>	("one can refer to a primitive temporal value like a
>	{\em SALARY history}"), as well as mentioning the "value of a
>	value history at time t" ("the (non-temporal) {\em value of
>	a SALARY history at time t}"). This is somewhat confusing. Even
>	more confusing is the term "{\em SALARY history}". Is this
>	in fact a value history? If so, then it would help if that were
>	stated explicitly.
>
>I think that if these aspects were addressed, a more clear and useful
>definition of this important concept would result.
>
>Paolo, Fabio, and Maria, is there a connection with "temporal value"
>and/or "value history" and your concept of a history variable?

I also think that the current definition of Jim is too ambiguous
and possibly misleading (the full intent of the definition is not clear
to me).

>
>Arie, is there a connection with "value history" and your concept of
>a tuple sequence?

Yes, there is a connection. I disagree with Fabio et al's statement
that
>``History'' is a general and orthogonal (+E1) concept.
>Alternative names apply when it specializes into attribute history
>(temporal value) or entity/relationship history (time sequence).

In our '87 SIGMOD Paper a Time Sequence (TS) was defined with respect
to attribute histories as well as entity/relationship histories.
A TS is identified by a surrogate and includes meta-data properties.
In our ER '91 conf paper (on temporal OO model) a types "sequence"
and "temporal sequence" were defined. The term TS is useful in
many cases and I suggest a definition below. I am not using it
to define a database but rather a type of object.  I find the term
history-oriented to characterize a database somewhat problematic,
pausing the same issues that we had originally w.r.t to historical
databases, i.e.,  the common use of history is in reference to the past,
but a temporal database can have a time sequence that spans (partly
or completely) future times. Frankly, the proposed definitions
try to characterise the database as OO (but without important OO
features), so the use of OO will be misleading here. 
Below I propose the terms of time sequence, temporal interpolation,
and temporal rule.

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\begin{document}

\subsection{Time Sequence}

\entry{Definition}         

A {\em Time Sequence} (TS) is a sequence (ordered by time) of pairs <v,t> where
v is an arbitrary data object and t are time points of a given
granularity designating past and/or future times. A TS is identified
by a surrogate (possibly a time-invarient key). If each v is a single
value the TS is said to be {\em simple}, and if v is a complex object (e.g.,
a set, a sequence, etc) then TS is  {\em complex}.
A TS can have properties and/or constraints be attached to it.

\entry{Alternative Names}   
History, Time-Series

\entry{Discussion}
The above definition is model-independent and can have different
representations in different models. For example in the relational
model where a relation is attribute time stamped (points), each point
in the sequence will be a tuple. For tuple stamping, v will be a set
of attribute values. Note that temporal elements are derivable from
a time sequence.

\subsection{Temporal Interpolation}

\entry{Definition}         
Deriving a temporal value at a TS time point which is not stored explictly
in the database, as a function of preceding and succeeding values, is
referred to as {\em Temporal Interpolation}.  {\em Temporal Extrapolation} 
is defined similaryl.

\entry{Alternative Names}   
Temporal Derivation

\entry{Discussion}
This feature is important for large sequences (in partcular, for
continuous scientific data) where data is collected only for a
subset of the time points in the time sequence, or all time points
contain data but interpolation is used as a form of compression.
The alternative name of {\em temporal Derivation} will apply if the
definition is extended to encompass cases where the derivation is
not based on interpolation but on other compuations or rules.

\subsection{Temporal Rule}

\entry{Definition}         

A database rule is a {\em Temporal Rule} if either the condition part
or the action part involve time points or temporal elements.

\entry{Alternative Names}   

\entry{Discussion}

This definition is intended to distinguish between temporal and 
non-temporal rules in temporal active databases. A non-temporal
rule can still cause changes over time in the case of retroactive
or proactive (may change to predictive if term adopted) changes to
temporal data. 

\end{document}