Subject: Value equivalence glossary entry

From: "Christian S. Jensen" <[email-masked]>
Date: Thu, 19 Nov 1992 18:22:22 +0100

The following is a proposal for an entry for the temporal database
glossary.

Best regards,
Christian S. Jensen

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\begin{document}

\subsection{Value Equivalence}

\entry{Definition}         

Informally, two tuples on the same (temporal) relation schema are {\em
value equivalent} if they have identical non-timestamp attribute
values.

To formally define the concept, let temporal relation schema $R$ have
$n$ time dimensions, $D_i$, $i = 1, \ldots, n$, and let $\tau^i$, $i =
1, \ldots, n$ be corresponding timeslice operators, e.g., the valid
timeslice and transaction timeslice operators. Then tuples $x$ and $y$
are value equivalent if

\begin{eqnarray*}
\exists t_1 \in D_1 \ldots \exists t_n \in D_n (\tau^n_{t_n}(
\ldots (\tau^1_{t_1}(x)) \ldots ) \neq \emptyset)
& \wedge &
\exists s_1 \in D_1, \ldots,  s_n \in D_n (\tau^n_{s_n}( \ldots
(\tau^1_{s_1}(y)) \ldots ) \neq \emptyset) \\
\Rightarrow \;\;\;
\bigcup_{\forall t_1 \in D_1,\ldots, t_n \in D_n}
    \hspace*{-.8cm}\tau^n_{t_n}(\ldots(\tau^1_{t_1}(x))\ldots)
\hspace{.6cm} & = &
  \bigcup_{\forall s_1 \in D_1,\ldots, s_n \in D_n}
    \hspace*{-.8cm}\tau^n_{s_n}(\ldots(\tau^1_{s_1}(y))\ldots)
\end{eqnarray*}

\noindent
Thus the set of tuples in snapshots of $x$ and the set of tuples in
snapshots of $y$ are required to be identical. This is required only
when each tuple has some non-empty snapshot.

\entry{Alternative Names}   

None.

\entry{Discussion}

The concept of value equivalent tuples has been shaped to be
convenient when addressing concepts such as coalescing, normal forms,
etc. The concept is distinct from related notions of the normal form
SG1NF and {\em mergeable} tuples.

Phrases such as ``having the same visible attribute values'' and
``having duplicate values'' have been used previously.

The orthogonality criterion (+E1) is satisfied. Further, the concept
is a straight-forward generalization of identity of tuples in the
snapshot-relational model. There are no competing names (+E3), the
name seems open-endend (+E4) and does not appear to have other
meanings (+E5). Further, the name is consistent with existing
terminology (+E7) and does not violate other criteria.

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