What are the constraints, cues, and mechanisms that help learners create successful word-meaning mappings? This study takes up linguistic disjunction and looks at cues and mechanisms that can help children learn the meaning of "or." We first used a large corpus of parent-child interactions to collect statistics on "or" uses. Children started producing "or" between 18-30 months and by 42 months, their rate of production reached a plateau. Second, we annotated for the interpretation of disjunction in child-directed speech. Parents used "or" mostly as exclusive disjunction, typically accompanied by rise-fall intonation and logically inconsistent disjuncts. But when these two cues were absent, disjunction was generally not exclusive. Our computational modeling suggests that an ideal learner could successfully interpret an English disjunction (as exclusive or not) by mapping forms to meanings after partitioning the input according to the intonational and logical cues available in child-directed speech.