Subject: Some more temporal concepts defined

From: "Curtis E. Dyreson" <curtis>
Date: Tue, 24 Nov 1992 15:39:24 MST

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\begin{document}

\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{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{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 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{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{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).

\end{document}