Phonological processes tend to involve local dependencies, an observation that has been expressed explicitly or implicitly in many phonological theories, such as the use of minimal symbols in SPE and the inclusion of primarily strictly local constraints in Optimality Theory. I propose a learning-based account of local phonological processes, providing an explicit computational model. The model is grounded in experimental results that suggest children are initially insensitive to long-distance dependencies and that as their ability to track non-adjacent dependencies grows, learners still prefer local generalisations to non-local ones. The model encodes these results by constructing phonological processes starting around an alternating segment and expanding outward to incorporate more phonological context only when surface forms cannot be predicted with sufficient accuracy. The model successfully constructs local phonological generalisations and exhibits the same preference for local patterns that humans do, suggesting that locality can emerge as a computational consequence of a simple learning procedure.