[Crm-sig] A question about relations between time intervals with fuzzy borders

martin martin at ics.forth.gr
Sat Aug 1 14:44:35 EEST 2009

Dear Martin,

Thank you for this contribution.

Bernhard Schiemann wrote:
> Dear all,
>  In CRM, E2 Temporal Entities are located on the timeline by E53
>  Time-Spans, which may have fuzzy borders.  At the same time, Allen's
>  interval relations are defined on E2 through the properties
>  P114-P120, and in their scope notes it is stated that they "can be
>  calculated".  However, Allen's interval relations and inference rules
>  are only well-defined on intervals with "clear cut" borders, not with
>  fuzzy ones.
>  Currently there seems to be some unclarity and ambiguity regarding
>  the right classification of and inferencing over E2 and P114-P120.
>  Some examples are illustrated in the attached figure: While the
>  relationship between X2 and X3 can be clearly classified as P117(I)
>  occurs during, the situation is totally unclear in the case of X4 and
>  X5.  Even for X1 and X2 three properties --- P118 overlaps in time
>  with, P119 meets in time with and P120 occurs before --- (may) hold,
>  dependending on the the view on the fuzzy borders.  Allen's
>  relations, though, are thought of as mutually exclusive.

The problem is not the CRM, the problem is the nature of our knowledge
about reality, and reality itself. If we accept that our knowledge is
imprecise, and that physical processes do not start or end on well-defined
points in time, there are obviously relationships of type Allen's, which
cannot always be decided. Such problems do not occur, for instance, in engineering
environments that can work with discrete time models of any granularity.
The CRM however tries to deal with statements about a reality that is not bound
to such constraints. However, given two P81, P82 intervals, there are
some unions of Allen's relationships (OR) that can always be calculated.

>  Obviously, the problem lies in the interaction of the fuzzy borders
>  and Allen's relations: which temporal extent should be used for
>  calculation?  The minimal or the maximal extent or something in
>  between?
Any such solution must be based on an assumption of a tolerable error,
which we cannot make for the CRM in general. Any such solution would mean
to "bend reality" for sake of decidability.
>  One possible solution could be to ignore the fuzziness of E52
>  Time-spans and just annotate the relations which can be trusted
>  (minimal extent). 

This is not a solution, since Allen's relations make stronger commitments.
But what I suggested above is quite similar: For instance, if the outer bounds
of two time-spans are disjoint, "P120 occurs before" can always be answered.
Similarly, "P118 overlaps in time with", can be answered in some cases
with a combination of inner and outer bounds.

> Has anybody an idea about a best practice about
>  the P114-P120 relations?

The problematic Allen relations are the ones that relate two time-spans
with one common point in time. In the sense of physics, such relations
cannot be observed, and can happen only if the processes are not independent.
There is an archaeological reality to these relationships for subdevided periods, or
there are examples where an event such as the death of a king automatically starts
the next ruling period by definition.
In these cases, p114, p115, p116, p117 hold by definition, and are necessary
as such.

Actually, P114 can be regarded as shortcut to sharing the same time-span.

Only the Allen relations P118, P120, P121 can be observed and calculated from
appropriate time-span descriptions.

This sums up I see two problems with the CRM text:
A) The stereotype phrase in the scope notes "This property is only necessary if
the relevant time spans are unknown (otherwise the relationship can be calculated)."
is strictly speaking wrong.

Actually, the intention of this phrase in the CRM is to discourage people from
using Allen operators once the timespans are absolutely known with any precision.
The principle would be to store in the CRM the primary information, in order not to cause
confusion between deductions and primary knowledge.

If the Allen relation is primary knowledge, and one timespan is known, boundaries for
the other timespan can be calculated. If timespans are primary knowledge, it may be possible to
calculate some Allen relations.

If timespans are the only primary knowledge, there is no need to use Allen relations,
because any relation that holds or may hold can be calculated, even relations not foreseen
by Allen.

If timespans and Allen relations are primary knowledge, refined timespans may be calculated.

I propose to modify the CRM scope note accordingly.

B) The Allen relations are not the appropriate set to deal monotonically with
incomplete temporal knowledge. There are stages of knowledge such as: "P120 OR P118
OR P119", which may later be refined, for instance into "P118", without invalidating
the former proposition. I am not aware of any  publication dealing with that.
The CRM intends to allow for monotonical reasoning.

I am not sure, if it makes any sense to model these relations as properties in the
CRM, if they are not possible primary knowledge, either by definition (Early Minoan
starts Minoan etc.) or by observation, once the set of ass-ase-aes-aee boundaries is
more expressive than Allen's.

Anyone could extend the CRM on this base to his liking.

Does anyone see a relationship such as "P120 OR P118 OR P119" (before or overlaps) to
be a result of primary observation without absolute time knowledge? In that case we
may like to extend the CRM with other relationships than Allen's.

In our paper about the time primitive we have shown that the set relations to query
indeterminacy intervals is somehow orthogonal to Allen's.

C) The example for P114 is problematic. It assumes a certain tolerable error.
Are there communities that would need a notion of Allen's relations with a well
defined "tolerable error", such as "virtually meets in time", based on observation,
and what would that mean? Can it be objectified? Currently, the CRM text leaves
this interpretation delibarately open.

>  So, to sum up, the main problem is to compute Allen's relations on
>  time-spans with fuzzy borders. To the best of our knowledge Allen
>  himself did not make a suggestion for this kind of problem.  Does
>  anybody someone know about publications on this problem?

Right. To my understanding, in case of conflict, the CRM is committed to a fuzzy reality,
and not to mutual exclusivity of temporal relations.


> Best regards,
> Martin Scholz, Dipl-Inf.
>  Artificial Intelligence Division
>  Department of Computer Science
>  University of Erlangen-Nuremberg
>  Haberstr. 2
>  91058 Erlangen
>  martin.scholz at informatik.uni-erlangen.de
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