Temporal Reasoning with Probabilities
  In this paper we explore representations of temporal knowledge based upon the
formalism of Causal Probabilistic Networks (CPNs). Two different
?continuous-time? representations are proposed. In the first, the CPN includes
variables representing ?event-occurrence times?, possibly on different time
scales, and variables representing the ?state? of the system at these times. In
the second, the CPN describes the influences between random variables with
values in () representing dates, i.e. time-points associated with the
occurrence of relevant events. However, structuring a system of inter-related
dates as a network where all links commit to a single specific notion of cause
and effect is in general far from trivial and leads to severe difficulties. We
claim that we should recognize explicitly different kinds of relation between
dates, such as ?cause?, ?inhibition?, ?competition?, etc., and propose a method
whereby these relations are coherently embedded in a CPN using additional
auxiliary nodes corresponding to "instrumental" variables. Also discussed,
though not covered in detail, is the topic concerning how the quantitative
specifications to be inserted in a temporal CPN can be learned from specific
data.
