Problem model

There's probably several ways to put the underlying problematic in a mathematical object. I, for one, tend to prefer the graph approach than the full probabilistic one.

Let's define the finite set of historical facts .
$ \forall i \in \{1,\dots,n\},

\begin{array}{lrcl}

f: & \mathcal{F} & \longrightarrow & \{0,1\} \\
& f_{i} & \stackrel{f}{\longmapsto} & f(f_{i}) = \left\{
\begin{array}{rl} 0 & \quad si\,f_{i}\,est\,arrivé \\
1 & \quad si\,f_{i}\,est\,n'est\,pas\,arrivé
\end{array}
\right

\end{array} $

The set is mean to be a complete set of all facts that might happen or not. The function is only here to cope with the complexity associated to build a reduction of the list of facts to simple logical fact that only exist or not in the history line we want to model.