This paper conjectures a computational account of how children might learn the meanings of words in their native language. First, a simplified version of the lexical acquisition task faced by children is modeled by a precisely specified formal problem. Then, an implemented algorithm for solving this formal problem is presented. Key advances of this algorithm over previously proposed algorithms are its ability to learn homonymous word senses in the presence of noisy input and its ability to scale up to problems of the size faced by real children.