Subject: about temporal indeterminacy

From: [email-masked] (Barbara Pernici)
Date: Mon, 3 May 93 1:06:56 GMT-1:00

Please find in the following some entries related to the previous
discussion about temporally indeterminate events.

Also, I would like to suggest as an alternative  name for 'period of
indeterminacy' the term 'admissibility interval'.
I think it is more intuitive (+E8) and we used this term in the
TSOS system (+E7).

Barbara Pernici
University of Udine

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\begin{document}

\subsection{Chronologically definite}

\entry{Definition}
Modifier indicating that a fact or an event has associated
a valid time at a given time-stamp granularity.

\entry{Alternative Names}

\entry{Discussion}
A chronologically defined event or fact has associated a
time (see also the discussion about 'temporally indeterminate') and that
this time does not depend on the time of other events or facts.
For instance: Mary's salary was raised on March 30, 1993.
The time associated to chronologically defined events has also
been called absolute time  in the literature.

\subsection{Chronologically indefinite}

\entry{Definition}
Modifier indicating that the time of a fact or an event is related
to the occurrence of another event.

\entry{Alternative Names}
imprecise, relative

\entry{Discussion}
Example are:
Mary's salary was raised yesterday. (here it depends on the
utterance time for the sentence).
Mary's salary was raised before Lucy's.
The time associated to chronologically indefinite events has also
been called relative time in the literature.

\subsection{Temporally determinate}

\entry{Definition}
Modifier indicating that the occurrence time of an event or fact
is precisely known.

\entry{Alternative Names}
precise

\entry{Discussion}
See Temporally indeterminate

\subsection{Temporally indeterminate}

\entry{Definition}
Modifier to indicate that a fact or event it is known to have occurred
but it is unknown precisely when.

\entry{Alternative Names}
vague, imprecise

\entry{Discussion}

There are (at least) two possible sources of
indeterminacy: (i) a discrepancy between the granularities of the temporal
qualification and the occurrence time; (ii) an  underspecification of the
occurrence time, when the granularities of the temporal qualification and the
occurrence time coincide.

The proposed
definition of {\em temporally-indeterminate} event is: ``a {\em
temporally-indeterminate} event is an event that is known to have occurred but
precisely when is unknown''. Reformulated in terms of statements it becomes:
``a {\em  temporally-indeterminate} statement is a statement that allows us to
conclude that an event has occurred but it does not tell us precisely when it
has occurred''.

Chronologically-indefinite statements are also temporally
indeterminate, but not vice versa: temporally-indeterminate statements can be
chronologically indefinite as well as chronologically definite.

The statements ``Jack  was killed on xx/xx/1990'' and ``Michelle was
born yesterday'' come within different categories with respect to the
chronological  definiteness/indefiniteness characterization, but they are both
temporally indeterminate.

As a first approximation, we can say that a statement is {\em temporally
indeterminate} if the granularity of its temporal qualification (in the
examples, the granularity of days) is coarser than the granularity of the time
at which the denoted events (instantaneously) occur. Notice that temporal
indeterminacy as well as chronological indefiniteness are mainly qualifications
of statements rather than of the events they denote (better, temporal
indeterminacy characterizes the relation between the granularities of the
statement temporal qualification and of the event occurrence time). Notice also
that it does not depend on the time at which the statement is evaluated. The
crucial, and critical, point is clearly the determination of the time
granularity of the event occurrence time.

Some problems could be avoided by adopting the following weaker notion of
temporally indeterminacy: a statement whose temporal qualification has
granularity G (to say, days) is temporally determinate with respect to every
coarser granularity (e.g., months) and temporally indeterminate with respect to
every finer granularity (e.g., seconds).

However, we do not like this solution, because it does not take into account
information about the denoted events. In particular, for each event
there exists a limit time granularity such that its occurrence time can be
specified at such a granularity and all coarser ones, but not at finer ones.
With respect to each finer granularity, the event as a whole does not make sense
at all and it must decomposed into a set of components (if possible).

Let us go back to the proposed definition of temporal indeterminacy to discuss
the following issue: does temporal indeterminacy always involve a discrepancy
between temporal qualification (expressed as a valid time)
and occurrence time granularities? Consider the
sentence: ``The  shop remained open on a Sunday in April 1990 all the day
long''. Clearly, the truth value of the statement does not depend on its
utterance time, that is, the statement is chronologically defined. Furthermore,
day is the granularity of both the temporal qualification and the occurrence
time. Nevertheless, we believe that this statement is {\em temporally
indeterminate}, because the precise day in which the shop remained open is
unknown (we only know that it belong to the set of Sunday days in April 1990).

These sources of indeterminacy are not exclusive and
they can jointly contribute to make a statement temporally indeterminate. This
is the case, for instance, in the sentence: ``Jack was killed on a Friday night
in 1990''.

\subsection{Temporal modality}

\entry{Definition}

{\em Temporal modality} concerns the way according to which a fact originally
associated with a time point or interval at a given granularity distributes itse
   lf over the
corresponding time points at finer granularities or within the
interval at the same level of granularity. We distinguish two basic
temporal modalities, namely {\em sometimes} and {\em always}.

The {\em sometimes temporal modality} states that the relevant fact is true in
at least one of the corresponding time points at the finer granularity for
time points, or in at least one of the time points of the interval
in case an interval is given.
For instance: ``The light was on yesterday afternoon'', meaning that it was
on at least for one minute in the afternoon (assuming minute as temporal
quantum).

The {\em always temporal modality} states that the relevant fact is true in
each corresponding time point at the finer granularity. This is
the case, for instance, of the sentence: ``The shop remained open on a
Sunday in April 1990 all the day long'' with respect to the granularity of
hour.

This issue is relate to  attributes varying within their validity intervals.

\end{document}

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