290 Chapter 13 Time for Planning
13.3 Qualitative Temporal Relations
This section is concerned with qualitative temporal constraints. Two approaches will
be considered, point algebra (PA) and interval algebra (IA), dealing with qualitative
constraints on, respectively, time points and intervals. A geometric interpretation
of the latter will then be introduced, enabling us to relate the two representations.
13.3.1 Point Algebra
Point algebra (PA) is a symbolic calculus that enables us to relate in time a set of
instants with qualitative constraints without necessarily ordering them.
Two instants t
1
and t
2
that are set in time, with real values, can be related in only
three possible ways: [t
1
<t
2
], [t
1
>t
2
], or [t
1
= t
2
]. Two instants whose values
are not