Explicit linguistic knowledge, encoded by resources such as rule-based morphological analyzers, continues to prove useful in downstream NLP tasks, especially for low-resource languages and dialects. Rules are an important asset in descriptive linguistic grammars. However, creating such resources is usually expensive and non-trivial, especially for spoken varieties with no written standard. In this work, we present a novel approach for automatically learning morphophonological rules of Arabic from a corpus. Motivated by classic cognitive models for rule learning, rules are generalized cautiously. Rules that are memorized for individual items are only allowed to generalize to unseen forms if they are sufficiently reliable in the training data. The learned rules are further examined to ensure that they capture true linguistic phenomena described by domain experts. We also investigate the learnability of rules in low-resource settings across different experimental setups and dialects.