The Problem of Coincidence in A Theory of Temporal Multiple Recurrence
  Logical theories have been developed which have allowed temporal reasoning
about eventualities (a la Galton) such as states, processes, actions, events,
processes and complex eventualities such as sequences and recurrences of other
eventualities. This paper presents the problem of coincidence within the
framework of a first order logical theory formalising temporal multiple
recurrence of two sequences of fixed duration eventualities and presents a
solution to it The coincidence problem is described as: if two complex
eventualities (or eventuality sequences) consisting respectively of component
eventualities x0, x1,....,xr and y0, y1, ..,ys both recur over an interval k
and all eventualities are of fixed durations, is there a sub-interval of k over
which the incidence xt and yu for t between 0..r and s between 0..s coincide.
The solution presented here formalises the intuition that a solution can be
found by temporal projection over a cycle of the multiple recurrence of both
sequences.
