[Crm-sig] A question about relations between time intervals with fuzzy borders
c.e.s.ore at iln.uio.no
Mon Aug 24 12:04:22 EEST 2009
It is correct that in his 1983 paper Allen argues that one should
represent temporal entities as intervals with non-fuzzy boarders. In
the paper he discusses a system where the intervals/temporal entities
are atoms without any internal structure. In the system a set of
relations between these atoms together with transitivity rules are
defined. These are used to reason about relations between temporal
entities and connected propositions.
In the CRM the E2 temporal entities and the properties P114-P140
correspond to the temporal entities and the relations in Allen’s paper.
It is important to note that the CRM is an ontology and contains
absolutely no rules for deduction or inference. Thus E2 and P114-P140
define a static model for Allen’s temporal entities and thus an
architecture for structures for storing this information, relations and
abut no deduction system.
As I understand CRM, the class E53 time-span describes the knowledge
categories we (may) use to describe approximations to some ideal real
world time-spans (in which temporal entities take place). Since the
idea behind time-spans is that they are approximations, time-spans
should not be connected with fixed start or end points in some system of
time primitives, that is, a concrete implementation. Instead we have
two facts expressed by P81 and P82, which can typically be expressed as
an inner ‘interval’ and an outer ‘interval’ on a numeric time-line. On
a time-line these two intervals will be expressed as four points. The
start points define an interval corresponding to an approximation of
the start point of the time-span based on our given knowledge.
(correspondingly for the end point). The intervals in the
time-primitive-structure for the start and end points of a time-span can
be seen as fuzzy (underspecified) points on the timeline. There is no
infinite recursion in the model since these intervals are not connected
to a E53 time-span and E2 temporal entity.
If the length of such an interval is zero, then we have knowledge about
exact when the time-span started. Thus in the Erlangen version with its
extra properties it is claimed that we usually can know exactly when a
time span starts.
Martin Scholz’s diagram:
Allen’s view of temporal entities as atoms and relations corresponds to
the E2, P114-140 part of the CRM. As I mentioned above the CRM contains
no deduction rules. In a deduction system based on CRM-compliant
structures, we have to add the transitivity rules etc from Allen’s
paper, to do any reasoning about the relations between instances of E2.
The information is simply a graph. One may very well express a
discrete time line down to nanoseconds in this structure. So far there
is no fuzziness at all.
In the CRM the time-span+time primitive is an alternative model to the
Allen approach. The scope note for E59 is “This class comprises
instances of E59 Primitive Value for time that should be implemented
with appropriate validation, precision and interval logic to express
date ranges relevant to cultural documentation.” In a consistent
instantiation temporal facts about instances of E2 expressed in
time-span+time primitive have to be consistent with facts expressed via
Martin Schlolz writes “Even for X1 and X2 three properties --- P118
overlaps in with, P119 meets in time with and P120 occurs before ---
(may) hold, depending on the view on the fuzzy borders. Allen's
relations, though, are thought of as mutually exclusive.” That is
correct and unproblematic in the CRM since the time primitive structure
(with fuzzy borders) needs not to be a model or implementation of the
Allen calculus. One can however use this in a deduction system.
Assume that we have the X1 and X2 situation, then we can deduce that one
and at most one of “P118 overlaps in with, P119 meets in time with and
P120 occurs before“ holds. If another fact, say P116 is equal in time
with, then this will cause an impossible situation. In this case one
has to check the premises and the deduction chains to see which fact(s)
caused the inconsistency.
Why use both Allen time capsules and (fuzzy) approximations?
The Allen system expresses information as a multi-dimensional graph and
the time-span + time-primitive system expresses (in our use) the
information as pair of intervals on a one-dimensional time line. The
Allen system is excellent to store relative temporal facts. It is
possible to define a mapping of the information in an Allen structure
onto the time line as pairs of inner and outer intervals or equivalent
as intervals with fuzzy start and end points. In many cases it is
handier to reason with such under-determined points. In the opposite
direction the pairs of intervals (approximations) define sets of
constrains on the Allen structure. Jon Holmen and I have worked on this
in connection with a CIDOC-CRM based temporal deduction system for
Allen and fuzzyness:
There is a rather mathematical paper on this
Temporal Integrity Constraints with Indeterminacy
Proceedings of the 26th International Conference on Very Large Data Bases
Pages: 441 - 450
Year of Publication: 2000
Authors Wes Cowley ,Dimitris Plexousakis
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