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Logical theories have been developed which have allowed temporal reasoningabout eventualities (a la Galton) such as states, processes, actions, events,processes and complex eventualities such as sequences and recurrences of othereventualities. This paper presents the problem of coincidence within theframework of a first order logical theory formalising temporal multiplerecurrence of two sequences of fixed duration eventualities and presents asolution to it The coincidence problem is described as: if two complexeventualities (or eventuality sequences) consisting respectively of componenteventualities x0, x1,....,xr and y0, y1, ..,ys both recur over an interval kand all eventualities are of fixed durations, is there a sub-interval of k overwhich 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 befound by temporal projection over a cycle of the multiple recurrence of bothsequences.

The Problem of Coincidence in A Theory of Temporal Multiple Recurrence