This spillover processing effect is simply a matter of modeling convenience: without it, we would have to compute Surprisal probabilities over regions rather than individual words.
the overall prefix probability can be computed as: P (w) = p,c,t P prag (p|w, t, c)P coref (c|w, t)P parser (w, t), which is then substituted in Equation (1) to get a Surprisal prediction for the current word.