James F. Allen and George Ferguson, ``Actions and events in
interval temporal logic'', <I> J. Logic Computat.</I>, 1994, Vol. 4, No.
5, pp. 531--579.
<P>

The authors describe an interval-based temporal logic in which usual
non-temporal basic statements of the type $P(s)$ (``the property $P$
holds for objects $s$'') are replaced by temporal statements
$P(s,[t^-,t^+])$ (``the property $P$ holds for objects $s$ for all
moments of time $t\in [t^-,t^+]$''). The basic relation between
intervals is ``meets'': $[t^-,t^+]$ meets $[s^-,s^+]$ iff $t^+=s^-$.
All other ordering relations between intervals can be expressed in
terms of ``meets'': e.g., ``${\bf t}=[t^-,t^+]$ precedes ${\bf s}=[s^-,s^+]$''
(meaning $t^+<s^-$) is equivalent to 
$$\exists {\bf u}\,({\bf t}{\rm \ meets\ }{\bf u}\,\&\,
{\bf u}{\rm \ meets\ }{\bf s}).$$
The authors show how this logic can be used to represent expert
knowledge about actions, and how it can be used for prediction,
planning, and explanations. 
<P>
Alessandro Provetti