Subject: Even more terms defined

From: "Curtis E. Dyreson" <curtis>
Date: Thu, 11 Mar 1993 14:59:55 -0700 (MST)

\subsection{Temporally-indeterminate event}

\entry{Definition}

A {\em temporally-indeterminate event} (or just {\em indeterminate event}, 
when the context is clear) is an event that is known to have occurred 
but precisely when is unknown.  The times when the event might have 
occurred must be contiguous; non-contiguous times can be modeled by 
an exclusive-or disjunction of indeterminate events.

\entry{Alternative Names}

Temporally-incomplete event, temporally-fuzzy event, temporally-imprecise event.

\entry{Discussion}

``Michelle was born yesterday'' is a typical indeterminate event.
An indeterminate event is composed of an event (e.g., ``Michelle was born'')
and some indeterminate temporal information (e.g., ``yesterday'').

Note that an event with noncontiguous temporally-indeterminate information, 
such as ``Jack was killed on a Friday night in 1990,'' is not an 
indeterminate event since the times when the event might have occurred 
are non-contiguous.  The incomplete temporal information could be more 
substantial.  For instance, an indeterminate event could have an 
associated probability mass function which gives the probability 
that the event occurred during each chronon on a time-line.

Currently, there is no name used in the literature to describe the 
incomplete temporal information associated with an event.  The modifier 
``incomplete'' is too vague (-E9), while ``fuzzy'' has unwanted 
connotations (i.e., with fuzzy sets) (-E9).  ``Indeterminate'' is more 
general than ``imprecise;'' imprecise commonly refers to measurements, 
but imprecise clock measurements are only one source of indeterminate 
events.

\subsection{Upper support chronon}

\entry{Definition}

In the discrete model of time, the {\em upper support chronon} is the 
latest chronon during which an indeterminate event might have occurred.

\entry{Alternative Names}

Upper bound.

\entry{Discussion}

The upper support chronon is an upper bound on the possible times when
an indeterminate event might have occurred.  The noun ``support'' is 
preferred to ``bound'' because the use of the former term is consistent 
with probability theory (+E9).  For an indeterminate event, a probability 
mass function gives the probability that the event occurred during each
chronon.  The probability that the event occurred sometime after the 
upper support chronon is zero.

\subsection{Lower support chronon}

\entry{Definition}

In the discrete model of time, the {\em lower support chronon} is the 
earliest chronon during which an indeterminate event might have occurred.

\entry{Alternative Names}

Lower bound.

\entry{Discussion}

The lower support chronon is a lower bound on the possible times when
an indeterminate event might have occurred.  The noun ``support'' is 
preferred to ``bound'' because the use of the former term is consistent 
with probability theory (+E9).  For an indeterminate event, a probability 
mass function gives the probability that the event occurred during each 
chronon.  The probability that the event occurred sometime before the 
lower support chronon is zero.

\subsection{Temporally indeterminate interval}

\entry{Definition}

A {\em temporally-indeterminate interval} (or just {\em indeterminate 
interval} when the context is clear) is an interval bounded by at least 
one temporally-indeterminate event.  Since an interval cannot end before 
it starts, the possible times associated with the bounding events can 
overlap on only a single chronon.

\entry{Alternative Names}

Temporally-incomplete interval, temporally-fuzzy interval, temporally-imprecise interval.

\entry{Discussion}

Currently, there is no name used in the literature to describe the 
incomplete temporal information associated with an interval.  The modifier 
``incomplete'' is too vague (-E9), while ``fuzzy'' has unwanted 
connotations (i.e., with fuzzy sets) (-E9).  ``Indeterminate'' is more 
general than ``imprecise;'' imprecise commonly refers to measurements, 
but imprecise clock measurements are only one source of indeterminate 
intervals.