Subject: SUMMARY OF TDB TERMS

From: "Christian S. Jensen" <[email-masked]>
Date: Mon, 21 Dec 1992 19:43:59 +0100

SUMMARY OF PROPOSED TEMPORAL DATABASE TERMS

A summary of the temporal database terms proposed during Fall 1992 is
now available via anonymous ftp from cs.arizona.edu.  The summary
document is titled statusDec92 and may be found in the tsql directory,
in ".dvi," ".ps," and ".tex" formats.  In addition, the ".tex" version
is appended below.

The summary is provided as a service to current and prospective
contributors of glossary entries.  Comments, improvements and
criticisms, and proposals for new terms are highly encouraged. They
should be sent to the mailing list, [email-masked].

The goal of this initiative is to create a consensus glossary of
temporal database terms.  For additional details, please see the
introductory section of the summary and the other documents in the
tsql directory.

Christian S. Jensen
Aalborg University
[email-masked]

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\begin{document}

\title{\Large\bf Proposed Glossary Entries---December 1992}
\author{Christian~S.~Jensen, editor\thanks{These definitions were
proposed by Jim Clifford, Curtis Dyreson, Shashi Gadia, Sushil
Jajodia, Christian S.~Jensen, Nick Kline, Daniel Nonen, John
F.~Roddick, Arie Segev, Richard T.~Snodgrass, Mike D.~Soo, and
Abdullah Tansel. Correspondence may be directed to the TSQL electronic
mail distribution, {\tt [email-masked]}, or to the editor at
Aalborg University, Datalogi, Fr.~Bajers Vej 7E, DK--9220 Aalborg
{\O}, Denmark, {\tt [email-masked]}.}}
\date{}
\maketitle
\small
\subsection*{\centering Abstract}

This document describes the current status, as of December 15, 1992,
of an initiative aimed at creating a consensus glossary of temporal
database concepts and names. It contains the set of currently
proposed, complete glossary entries. Existing terms and criteria for
evaluation of glossary entries are contained in appendices.

The document is intended to help future contributors of glossary
entries. Proposed glossary entries should be sent to {\tt
[email-masked]}. Other information related to the initiative may
be found at {\tt cs.arizona.edu} in the {\tt tsql} directory,
accessible via anynomous ftp.

\small\normalsize

\section{Introduction}
\label{sec:int}

This document is a structured presentation of the current status of an
initiative aimed at creating a consensus glossary of temporal database
terms. It contains the list of complete proposals for temporal database
concepts and names which have so far been submitted to the mailing
list {\tt [email-masked]}. The purpose of the document is to give
potential contributors an overview of the terms proposed so far.

In order to obtain a consensus glossary, the proposed concepts and
names are intended to be discussed during the first workshop on
temporal databases (``International Workshop on an Infrastructure for
Temporal Databases''), scheduled to be held in Arlington, TX, June
14-16, 1993. The objective of this workshop is to define and establish
a common infrastructure of temporal databases and to develop a
consensus base document that will provide a foundation for
implementation and standardization as well as for further research.

During the preparation of a forthcoming book on temporal databases
({\em Temporal Databases: Theory, Design, and Implementation,} edited
by A.~Tansel, J.~Clifford, S.~Gadia, S.~Jajodia, A.d~Segev, and
R.~Snodgrass, Benjamin/Cummings Publishers, Database Systems and
Applications Series), a glossary on temporal database concepts and
terms was developed. The glossary also appears in the September 1992
issue of the SIGMOD Record. The terms and concepts from this glossary
are included here as an appendix in a dictionary-like format.
Evaluation criteria, to be used when proposing new glossary entries,
are also included in the appendix.

\section{New, Proposed Glossary Entries}
\label{sec:new}

\subsection{Temporal Data Type}
\label{sec:tem}

\entry{Definition} 
The user-defined temporal data type is a time representation specially
designed to meet the specific needs of the user.  For example, the
designers of a database used for class scheduling in a school might be
based on a ``Year:Term:Day:Period'' format.  Terms belonging to a
user-defined temporal data type get the same query language support as
do terms belonging to built-in temporal data types such as the DATE
data type.

\entry{Alternative Names}
User-defined temporal data type, auxiliary temporal data type.

\entry{Discussion}
The phrase ``user-defined temporal data type'' is uncomfortably similar
to the phrase ``user-defined time'', which is an orthogonal concept.
Nevertheless, it is an appropriate description for the intended usage
and we have used in our work.  If the notion of providing special
purpose temporal terms becomes more popular, I suspect the shorter
term ``Temporal Data Type'' will be sufficiently descriptive.

\subsection{Schema Evolution}

\entry{Definition}
A database system supports {\em schema evolution} if it permits
modification of the database schema without the loss of extant data.
No historical support for previous schemas is required.

\entry{Alternative Names}   
Schema versioning, data evolution.

\entry{Discussion}

While support for ``schema evolution'' indicates that an evolving
schema may be supported, the term ``schema versioning'' indicates that
previous versions of an evolving schema are also supported. Therefore,
``schema versioning'' is appropriate for a more restrictive concept.

The name ``data evolution'' is inappropriate because ``data'' refers
to the schema contents, i.e., the extension rather than the intension.
Data evolution is supported by conventional update operators.

While some confusion exists as to its exact definition, ``schema
evolution'' is an accepted name and is widely used already.

\subsection{Schema Versioning}

\entry{Definition}

A database system accomodates {\em schema versioning} if it allows the
querying of all data, both retrospectively and prospectively, through
user-definable version interfaces. While support for schema versioning
implies the support for schema evolution, the reverse is not true.

Support for schema versioning requires that a history of changes be
maintained to enable the retention of past schema definitions.

\entry{Alternative Names}   
Schema evolution, data evolution.

\entry{Discussion}
The name ``schema evolution'' does not indicate that previously
current versions of the evolving schema are also supported. It is thus
less precise that ``schema versioning.'' As schema evolution, schema
versioning is an intensional concept; ``data evolution'' has
extensional connotations and is inappropriate.

\subsection{Snapshot Equivalent}

\entry{Definition}         
Informally, two tuples are {\em snapshot equivalent\/} if the snapshots of the
tuples at all times are identical.

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, formally, tuples $x$ and $y$
are snapshot equivalent if 

\[ \forall t_1 \in D_1 \ldots \forall t_n \in D_n (
\tau^n_{t_n}( \ldots (\tau^1_{t_1}(x)) \ldots ) =
\tau^n_{t_n}( \ldots (\tau^1_{t_1}(y)) \ldots )) \;\; .\]

\noindent
Similarly, two relations are {\em snapshot equivalent\/} if at every time their
snapshots are equal.
{\em Snapshot equivalence\/} is a binary relation that can be applied to
tuples and to relations.

\entry{Alternative Names}   
Weakly equal, temporally weakly equal, weak equivalence.

\entry{Discussion}
Weak equivalence has been used by Ullman to relate two algebraic
expressions (Ullman, Principles of Database Systems, Second Edition,
page 309). Hence, ``temporally weakly equal'' is preferable to
``weakly equal'' (E7).

In comparing ``temporally weakly equal'' with ``snapshot equivalent'',
the former term is longer and more wordy, and is
somewhat awkward, in that it contains two adverbs ($-$E2). 
``Temporally weak'' is not intuitive---in what way is it weak?
Snapshot equivalent explicitly identifies the source of the
equivalence (+E8).

\subsection{Snapshot-Equivalence Preserving Operator}

\entry{Definition}         

A unary operator $F$ is {\em snapshot-equivalence preserving\/} if
relation $r$ is snapshot equivalent to $r'$ implies $F(r)$ is snapshot
equivalent to $F(r')$. This definition may be extended to operators
that accept two or more argument relation instances.

\entry{Alternative Names}   
Weakly invariant operator, is invariant under weak binding of belongs to.

\entry{Discussion}
This definition does not rely on the term ``weak binding'' (+E7).

\subsection{Snapshot Equivalence Class}

\entry{Definition}         
A {\em snapshot equivalence class\/} is a set of relation instances that
are all snapshot equivalent to each other.

\entry{Alternative Names}   
Weak relation.

\entry{Discussion}
``Weak relation'' is not intuitive, as the concept identifies a set of relation
instances, not a single instance ($-$E8).

\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.

\subsection{Fixed Span}

\entry{Definition}
The duration of a span is either context-dependent or
context-independent. A {\em fixed span\/} has a context-independent
duration. For example, the span {\tt one hour} has a duration of 60
minutes and is therefore a fixed span.

\entry{Alternative Names}
Constant span.

\entry{Discussion}
Fixed span is short (+E2), precise (+E9), and has no conflicting
meanings (+E5).

``Constant'' appears more precise (+E8) and intuitive (+E9), but it is
also used as a keyword in several programming languages ($-$E5).

\subsection{Variable Span}

\entry{Definition}
A span that is not fixed is {\em variable\/}---the value of the span
is dependent on the context in which it appears. For example, the
span {\tt one month} represents a duration of between twenty-eight and
thirty-one days depending on the context in which it is used.

\entry{Alternative Names}
Moving span.

\entry{Discussion}
Variable span is intuitive (+E9), and precise (+E9).  

``Moving span'' is unintuitive ($-$E9) and has informal spatial
connotations ($-$E5).

\subsection{Physical Clock}

\entry{Definition}
A {\em physical clock\/} is a physical process coupled with a method
of measuring that process. Although the underlying physical process
is continuous, the physical clock measurements are discrete, hence a
physical clock is discrete.

\entry{Alternative Names}   
Clock.

\entry{Discussion}
A physical clock by itself does not measure time; it only measures the
process. For instance, the rotation of the earth measured in solar
days is a physical clock. Most physical clocks are based on cyclic
physical processes (such as the rotation of the earth). The modifier
``physical'' is used to distinguish this kind of clock from other
kinds of clocks, e.g., the time-line clock ($+$E9). It is also
descriptive in so far as physical clocks are based on recurring
natural or man-made phenomena ($+$E8).

\subsection{Time-line Clock}

\entry{Definition}
In the discrete model of time, a {\em time-line clock\/} is a set of
physical clocks coupled with some specification of when each physical
clock is authoritative. Each chronon in a time-line clock is a
chronon (or a regular division of a chronon) in an identified,
underlying physical clock. The time-line clock switches from one
physical clock to the next at a synchronization point. A
synchronization point correlates two, distinct physical clock
measurements. The time-line clock must be anchored at some chronon to
a unique physical state of the universe.

\entry{Alternative Names}   
Base-line clock, time-segment clock.

\entry{Discussion}

A time-line clock glues together a sequence of physical clocks to
provide a consistent, clear semantics for a discrete time-line. A
time-line clock provides a clear, consistent semantics for a discrete
time-line by gluing together a sequence of physical clocks. Since the
range of most physical clocks is limited, a time-line clock is usually
composed of many physical clocks. For instance, a tree-ring clock can
only be used to date past events, and the atomic clock can only be
used to date events since the 1950s. The term ``time-line'' has a
well-understood informal meaning, as does ``clock,'' which we coopt
for this definition ($+$E5). This concept currently has no name
($+$E7)($-$E3), but it is used for every timestamp (e.g., SQL2 uses
the mean solar day clock---the basis of the Gregorian calendar---as
its time-line clock). The modifier ``time-line'' distinguishes this
clock from other kinds of clocks ($+$E1). Time-line is more intuitive
than ``base-line'' ($+$E8), but less precise (mathematically) than
``time-segment,'' since the time-line clock usually describes a
segment rather than a line ($-$E9). We prefer time-line clock to
time-segment clock because the former term is more general ($+$E4) and
is intuitively appealing.

\subsection{Time-line Clock Granularity}

\entry{Definition}         
The {\em time-line clock granularity\/} is the uniform size of each
chronon in the time-line clock.

\entry{Alternative Names}   
None.

\entry{Discussion}
The modifier ``time-line'' distinguishes this kind of granularity from
other kinds of granularity ($+$E1) and describes precisely where this
granularity applies ($+$E9).

\subsection{Beginning}

\entry{Definition}         
The time-line supported by any temporal DBMS is, by necessity, finite
and therefore has a smallest and largest representable chronon. The
distinguished value {\em beginning\/} is a special valid-time event
preceding the smallest chronon on the valid-time line.  Beginning has
no transaction-time semantics.

\entry{Alternative Names}   
Start, begin, commencement, origin, negative infinity.

\entry{Discussion}
Beginning has the advantage of being intuitive (+E8), and does not
have conflicting meanings (+E5).

``Begin'' appears to be more straight-forward (+E8) but suffers from
conflicting meanings since it is a common programming language keyword
($-$E5).

``Start,'' ``commencement,'' and ``origin'' are awkward to use, e.g.,
``Start precedes the event,'' ``Commencement precedes the event,'' and
``Origin precedes the event.'' ($-$E8). Furthermore, choosing start
would require us to choose ``end'' for the opposite concept, and end
is a common programming language keyword ($-$E5). Origin also has a
conflicting meaning relative to calendars ($-$E5).

Lastly, ``negative infinity'' is longer ($-$E2) and slightly
misleading since it implies that time is infinite ($-$E9). This may
or may not be true depending on theories about the creation of the
universe. Also, negative infinity has a well-established mathematical
meaning ($-$E5).

\subsection{Forever}

\entry{Definition}         
The distinguished value {\em forever\/} is a special valid-time event
following the largest chronon on the valid-time line. Forever has no
transaction-time semantics.

\entry{Alternative Names}   
Infinity, positive infinity.

\entry{Discussion}
Forever has the advantage of being intuitive (+E8) and does not have
conflicting meanings (+E5).

``Infinity'' and ``positive infinity'' both appear to be more
straightforward but have conflicting mathematical meanings ($-$E5).
Furthermore, positive infinity is longer and would require us to
choose ``negative infinity'' for its opposite ($-$E2).

\subsection{Initiation}
The distinguished value {\em initiation\/} denotes the
transaction-time when the database was created, i.e., the chronon
during which the first update to the database occurred. Initiation
has no valid-time semantics.

\entry{Alternative Names}   
Start, begin, commencement, origin, negative infinity, beginning.

\entry{Discussion}
The arguments against ``start,'' ``begin,'' ``commencement,''
``origin,'' and ``negative infinity'' are as in the discussion of
beginning.

Initiation is preferred over beginning since transaction-time is
distinct from valid-time. Using different terms for the two concepts
avoids conflicting meanings (+E5).

\subsection{Timestamp Interpretation}

\entry{Definition}
In the discrete model of time, the {\em timestamp interpretation\/}
gives the meaning of each timestamp bit pattern in terms of some
time-line clock chronon (or group of chronons), that is, the time to
which each bit pattern corresponds. The timestamp interpretation is a
many-to-one function from time-line clock chronons to timestamp bit
patterns.

\entry{Alternative Names}  
None.

\entry{Discussion}  
Timestamp interpretation is a concise ($+$E2), intuitive ($+$E8),
precise ($+$E9) term for a widely-used but currently undefined concept
($+$E7).

\subsection{Timestamp Granularity}

\entry{Definition}         
In the discrete model of time, the {\em timestamp granularity\/} 
is the size of each chronon in a timestamp interpretation.
For instance, if the timestamp granularity is one second, then
the size of each chronon in the timestamp interpretation is one
second (and vice-versa).

\entry{Alternative Names}   
Time granularity.

\entry{Discussion}
Timestamp granularity is not an issue in the continuous model of time.
The adjective ``timestamp'' is used to distinguish this kind of
granularity from other kinds of granularity, such as the granularity
of non-timestamp attributes ($+$E9,$+$E1). ``Time granularity'' is
much too vague a term since there is a different granularity
associated with temporal constants, timestamps, physical clocks, and
the time-line clock although all these concepts are time-related.
Each time dimension has a separate timestamp granularity. A time,
stored in a database, must be stored in the timestamp granularity
regardless of the granularity of that time (e.g., the valid-time date
January 1st, 1990 stored in a database with a valid-time timestamp
granularity of a second must be stored as a particular second during
that day, perhaps midnight January 1st, 1990). If the context is
clear, the modifier ``timestamp'' may be omitted, for example,
``valid-time timestamp granularity'' is equivalent to ``valid-time
granularity'' ($+$E2).

\subsection{Time Indeterminacy}

\entry{Definition}
Information that is {\em time indeterminate\/} can be characterized as
``don't know when'' information, or more precisely, ``don't know {\em
exactly\/} when'' information. The most common kind of time
indeterminacy is valid-time indeterminacy or user-defined time
indeterminacy. Transaction-time indeterminacy is rare because
transaction times are always known exactly.

\entry{Alternative Names}  
Fuzzy time, time imprecision, time incompleteness.

\entry{Discussion}

Often a user knows only approximately when an event happened, when an
interval began and ended, or even the duration of a span. For
instance, she may know that an event happened ``between 2 PM and 4
PM,'' ``on Friday,'' ``sometime last week,'' or ``around the middle of
the month.'' She may know that a airplane left ``on Friday'' and
arrived ``on Saturday.'' Or perhaps, she has information that
suggests that a graduate student takes ``four to fifteen'' years to
write a dissertation. These are examples of time indeterminacy. The
adjective ``time'' allows parallel kinds of indeterminacy to be
defined, such as spatial indeterminacy ($+$E1). We prefer ``time
indeterminacy'' to ``fuzzy time'' since fuzzy has a specific, and
different, meaning in database contexts ($+$E8). There is a subtle
difference between indeterminate and imprecise. In this context,
indeterminate is a more general term than imprecise since precision is
commonly associated with making measurements. Typically, a precise
measurement is preferred to an imprecise one. Imprecise time
measurements, however, are just one source of time indeterminate
information ($+$E9). On the other hand, ``time incompleteness'' is
too general. Time indeterminacy is a specific kind of time incomplete
information.

\subsection{Period of Indeterminacy}

\entry{Definition}
The {\em period of indeterminacy\/} is either an anchored duration
associated with an indeterminate event or a duration associated with
an indeterminate span, that delimits the range of possible times
represented by the event or span.

\entry{Alternative Names} 
Interval of indeterminacy, fuzzy interval.

\entry{Discussion}
The period of indeterminacy associated with an indeterminate event is
an anchored duration that delimits the range of possible times during
which the event occurred. The event happened sometime during the
period of indeterminacy but it is unknown exactly when. An anchored
duration is usually referred to as an interval, however, in this
context, we prefer to call it a period because the syntactic
difference between an ``indeterminate interval'' and an ``interval of
indeterminacy'' is slight, while the semantic difference is great.
Hence, while using ``interval of indeterminacy'' might be more precise
($+$E9), it would also be more confusing ($-$E8). Using ``fuzzy
interval'' would also be confusing due to the influence of fuzzy
databases ($+$E5).

\subsection{Temporal Specialization}

\entry{Definition}

{\em Temporal specialization} denotes the restriction of the
interrelationship between otherwise independent (implicit or explicit)
timestamps in relations. An example is a relation where facts are
always inserted after they were valid in reality. In such a relation,
the transaction time would always be after the valid time. Temporal
specialization may be applied to relation schemas, relation instances,
and individual tuples.

\entry{Alternative Names}   

Temporal restriction.

\entry{Discussion}

Data models exist where relations are required to be specialized, and
temporal specializations often constitute important semantics about
temporal relations that may be utilized for, e.g., query optimization
and processing purposes.

The chosen name is more widely used than the alternative name (+E3).
The chosen name is new (+E5) and indicates that specialization is done
with respect to the temporal aspects of facts (+E8). Temporal
specialization seems to be open-ended (+E4). Thus, an opposite
concept, temporal generalization, has been defined. ``Temporal
restriction'' has no obvious opposite name ($-$E4).

\subsection{Specialized Bitemporal Relationship}

\entry{Definition}

A temporal relation schema exhibits a {\em specialized bitemporal
relationship} if all instances obey some given specialized
relationship between the (implicit or explicit) valid and transaction
times of the stored facts. Individual instances and tuples may also
exhibit specialized bitemporal relationships. As the transaction times
of tuples depend on when relations are updated, updates may also be
characterized by specialized bitemporal relationships.

\entry{Alternative Names}

Restricted bitemporal relationship.

\entry{Discussion}

The primary reason for the choice of name is consistency with the
naming of temporal specialization (+E1). For additional discussions,
see temporal specialization.

\subsection{Retroactive Bitemporal Relation}

\entry{Definition}

A bitemporal relation schema is {\em retroactive} if each stored fact
of any instance is always valid in the past. The concept may be
applied to bitemporal relation instances, individual tuples, and to
updates.

\entry{Alternative Names}

None.

\entry{Discussion}

The name is motivated by the observation that a retroactive bitemporal
relation contains only information concerning the past (+E8).

\subsection{Predictive Temporal Relation}

\entry{Definition}

A temporal relation schema including at least valid time is {\em
predictive} if each fact of any relation instance is valid in the
future when it is being stored in the relation. The concept may be
applied to temporal relation instances, individual tuples, and to
updates.

\entry{Alternative Names}   

Proactive bitemporal relation.

\entry{Discussion}

Note that the concept is applicable only to relations which support
valid time, as facts valid in the future cannot be stored otherwise.

The choice of ``predictive'' over ``proactive'' is due to the more
frequent every-day use of ``predictive,'' making it a more intuitive
name (+E8). In fact, ``proactive'' is absent from many dictionaries.
Tuples inserted into a predictive bitemporal relation instance are, in
effect, predictions about the future of the modeled reality.  Still,
``proactive'' is orthogonal to ``retroactive'' ($-$E1).

\subsection{Degenerate Bitemporal Relation}

\entry{Definition}

A bitemporal relation schema is {\em degenerate} if updates to it's
relation instances are made immediately when something changes in
reality, with the result that the values of the valid and transaction
times are identical. The concept may be applied to bitemporal relation
instances, individual tuples, and to updates.

\entry{Alternative Names}

None.

\entry{Discussion}

``Degenerate bitemporal relation'' names a previously unnamed concept
that is frequently used. A degenerate bitemporal relation resembles a
transaction-time relation in that only one timestamp is necessary.
Unlike a transaction-time relation, however, it is possible to pose
both valid-time and transaction-time queries on a degenerate
bitemporal relation.

The use of ``degenerate'' is intended to reflect that the two time
dimensions may be represented as one, with the resulting limited
capabilities.

\subsection{Tick}

\entry{Definition}     
Same as definition of ``chronon''.

\entry{Alternative Names}   
Chronon, instant, atomic time unit, time unit.

\entry{Discussion}
Tick is concise, intuitive, and unpretentious.

\appendix

\section{Relevance Criteria for Concepts}
\label{sec:rel}

It must be attempted to name only concepts that fulfill the following four
requirements.
\begin{description}
    \item [R1] The concept must be specific to temporal databases.
          Thus, concepts used more generally are excluded.
    \item [R2] The concept must be well-defined. Before attempting to name
          a concept, it is necessary to agree on the definition of the
          concept itself.
    \item [R3] The concept must be well understood. We have attempted
          to not name a concept if a clear understanding of the
          appropriateness, consequences, and implications of the
          concept is missing. Thus, we avoid concepts from research
          areas that are currently being explored.
    \item [R4] The concept must be widely used. We have avoided concepts
          used only sporadically within the field.
\end{description}

\section{Evaluation Criteria for Naming Concepts}
\label{sec:eva}

Below is a list of criteria for what is a good name. These criteria
should be referenced when proposing a glossary entry. The criteria are
sometimes conflicting, making the choice of names a difficult and
challenging task. While this list is comprehensive, it is not complete.

  \begin{description}
    \item [E1] The naming of concepts should be orthogonal. Parallel
          concepts should have parallel names.
    \item [E2] Names should be easy to write, i.e., they should be
          short or possess a short acronym, should be easily
          pronounced (the name or its acronym), and should be
          appropriate for use in subscripts and superscripts.
    \item [E3] Already widely accepted names are preferred over new
          names.
    \item [E4] Names should be open-ended in the sense that the name
          of a concept should not prohibit the invention of a parallel
          name if a parallel concept is defined.
    \item [E5] We have avoided creating homographs and homonyms. Names
          with an already accepted meaning, e.g., an informal meaning,
          should not be given an additional meaning.
    \item [E6] We have striven to be conservative when naming
          concepts. No name is better than a bad name.
    \item [E7] New names should be consistent with related and already
          existing and accepted names.
    \item [E8] Names should be intuitive.
    \item [E9] Names should be precise.
  \end{description}

\section{Overview of Existing Terms}
\label{sec:ove}

The following list of temporal database terms appeared as complete
glossary entries in ``Jensen, C.~S., J.~Clifford, S.~K.~Gadia,
A.~Segev, and R.~T.~Snodgrass: {\em A Glossary of Temporal Database
Concepts,} {\it ACM SIGMOD Record\/}, Vol.~21, No.~3, September 1992,
pp.~35--43.

\dicstart
\name{bitemporal relation}
A {\em bitemporal relation\/} is a relation with exactly one system
supported valid time and exactly one system-supported transaction
time.

\name{chronon}
A {\em chronon} is the shortest duration of time supported by a
temporal DBMS---it is a nondecomposable unit of time. A particular
chronon is a subinterval of fixed duration on time-line.

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.''

\name{event}
An {\em event} is an isolated instant in time. An event is said to
occur at time $t$ if it occurs at any time during the chronon
represented by $t$.

\name{interval}
An {\em interval} is the time between two events. It may be
represented by a set of contiguous chronons.

\name{lifespan}
The {\em lifespan} of a database object is the time over which it is
defined. The valid-time lifespan of a database object refers to the
time when the corresponding object exists in the modeled reality,
whereas the transaction-time lifespan refers to the time when the
database object is current in the database.

If the object (attribute, tuple, relation) has an associated timestamp
then the lifespan of that object is the value of the timestamp. If
components of an object are timestamped, then the lifespan of the
object is determined by the particular data model being employed.

\name{snapshot relation}
Relations of a conventional relational database system incorporating
neither valid-time nor trans\-action-time timestamps are {\em snapshot
relations\/}.

\name{snapshot, valid- and transaction-time, and bitemporal as
modifiers}
The definitions of how ``snapshot,'' ``valid-time,''
``transaction-time,'' and ``bitemporal'' apply to relations provide
the basis for applying these modifiers to a range of other concepts.
Let $x$ be one of snapshot, valid-time, transaction-time, and
bitemporal. Twenty derived concepts are defined as follows (+E1).

  \begin{description}
    \item [relational database] An $x$ relational database contains
          one or more $x$ relations.
    \item [relational algebra] An $x$ relational algebra has relations
          of type $x$ as basic objects.
    \item [relational query language] An $x$ relational query language
          manipulates any possible $x$ relation. Had we used
          ``some'' instead of ``any'' in this definition, the
          defined concept would be very imprecise ($-$E9).
    \item [data model] An $x$ data model has an $x$ query language and
          supports the specification of constraints on any $x$
          relation.
    \item [DBMS] An $x$ DBMS supports an $x$ data model.
  \end{description}

The two model-independent terms, data model and DBMS, may be
replaced by more specific terms. For example, ``data model'' may be
replaced by ``relational data model'' in ``bitemporal data model.''

\name{span}
A {\em span} is a directed duration of time. A duration is an amount
of time with known length, but no specific starting or ending
chronons.  For example, the duration ``one week'' is known to have a
length of seven days, but can refer to any block of seven consecutive
days. A span is either positive, denoting forward motion of time, or
negative, denoting backwards motion in time.

\name{temporal as modifier}
The modifier {\em temporal\/} is used to indicate that the modified
concept concerns some aspect of time.

\name{temporal database}
A {\em temporal} database supports some aspect of time, not counting
user-defined time.

\name{temporal element}
A {\em temporal element} is a finite union of $n$-dimensional time
boxes. Temporal elements are closed under the set theoretic operations
of union, intersection and complementation.

Temporal elements may be used as timestamps. Special cases of
temporal elements occur as timestamps in valid-time relations,
transaction-time relations, and bitemporal relations. These special
cases are termed {\em valid-time elements}, {\em transaction time
elements}, and {\em bitemporal elements}. They are defined as finite
unions of valid-time intervals, transaction-time intervals, and
bitemporal rectangles, respectively.

\name{temporal expression}
A {\em temporal expression\/} is a syntactic construct used in a query
that evaluates to a temporal value, i.e., an event, an interval, a
span, or a temporal element.

In snapshot databases, expressions evaluate to relations and therefore
they may be called relational expressions to differentiate them from
temporal expressions. All approaches to temporal databases allow
relational expressions. Some only allow relational expressions, and
thus they are unisorted. Some allow relational expressions, temporal
expressions and also possibly boolean expressions. Such expressions
may defined through mutual recursion.

\name{temporally homogeneous}
A temporal tuple is {\em temporally homogeneous\/} if the lifespan
of all attribute values within it are identical. A temporal relation is
said to be temporally homogeneous if its tuples are temporally
homogeneous. A temporal database is said to be temporally homogeneous
if all its relations are temporally homogeneous. In addition to being
specific to a type of object (tuple, relation, database), homogeneity
is also specific to some time dimension, as in ``temporally
homogeneous in the valid-time dimension'' or ``temporally homogeneous
in the transaction-time dimension.''

The motivation for homogeneity arises from the fact that no timeslices
of a homogeneous relation produce null values. Therefore a homogeneous
relational model is the temporal counterpart of the snapshot
relational model without nulls. Certain data models assume temporal
homogeneity. Models that employ tuple timestamping rather than
attribute value timestamping are necessarily temporally
homogeneous---only temporally homogeneous relations are possible.

\name{time-invariant attribute}
A {\em time-invariant attribute} is an attribute whose value is
constrained to not change over time. In functional terms, it is a
constant-valued function over time.

\name{timestamp}
A {\em timestamp\/} is a time value associated with some time-stamped
object, e.g., an attribute value or a tuple. The concept may be
specialized to valid timestamp, transaction timestamp, interval
timestamp, event timestamp, bitemporal element timestamp, etc.

\name{transaction time}
A database fact is stored in a database at some point in time, and
after it is stored, it may be retrieved. The {\em transaction time\/}
of a database fact is the time when the fact is stored in the
database. Transaction times are consistent with the serialization
order of the transactions. Transaction time values cannot be after the
current time. Also, as it is impossible to change the past,
transaction times cannot be changed. Transaction times may be
implemented using transaction commit times.

\name{transaction-time relation}
A {\em transaction-time relation\/} is a relation with exactly one
system supported transaction time. As for valid-time relations, there
are no restrictions as to how transaction times may be associated with
the tuples.

\name{transaction timeslice operator}
The {\em transaction timeslice operator\/} may be applied to any
relation with a transaction time. It also takes as argument a time
value not exceeding the current time, {\em NOW\/}. It returns the
state of the argument relation that was current at the time specified
by the time argument.

\name{user-defined time}
{\em User-defined time\/} is an uninterpreted attribute domain of date
and time. User-defined time is parallel to domains such as ``money''
and integer---unlike transaction time and valid time, it has no
special query language support. It may be used for attributes such as
``birth day'' and ``hiring date.''

Conventional database management systems generally support a time
and/or date attribute domain. The SQL2 standard has explicit support
for user-defined time in its {\tt datetime} and {\tt interval} types.

\name{valid time}
The {\em valid time\/} of a fact is the time when the fact is true in
the modeled reality. A fact may have associated any number of events
and intervals, with single events and intervals being important
special cases.

\name{valid-time relation}
A {\em valid-time relation\/} is a relation with exactly one system
supported valid time. In agreement with the definition of valid time,
there are no restrictions on how valid times may be associated with
the tuples (e.g., attribute value time stamping may be employed).

\name{valid timeslice operator}
The {\em valid timeslice operator\/} may be applied to any relation
with a valid time. It takes as argument a time value. It returns
the state of the argument relation that was valid at the time of the
time argument.
\dicend

\end{document}