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We discuss how the main features of high-energy `soft' and `semihard' ppcollisions may be described in terms of parton cascades and multi-Pomeronexchange. The interaction between Pomerons produces an effective infraredcutoff, k_sat, by the absorption of low k_t partons. This provides thepossibility of extending the parton approach, used for `hard' processes, toalso describe high-energy soft and semihard interactions. We outline a modelwhich incorporates these features. Finally, we discuss what the most recent LHCmeasurements in the soft domain imply for the model.

From hard to soft high-energy pp interactions