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Human language relies on a finite lexicon to express a potentially infinite set of ideas. A key result of this tension is that words acquire novel senses over time. However, the cognitive processes that underlie the historical emergence of new word senses are poorly understood. Here, we present a computational framework that formalizes competing views of how new senses of a word might emerge by attaching to existing senses of the word. We test the ability of the models to predict the temporal order in which the senses of individual words have emerged, using an historical lexicon of English spanning the past millennium. Our findings suggest that word senses emerge in predictable ways, following an historical path that reflects cognitive efficiency, predominantly through a process of nearest-neighbor chaining. Our work contributes a formal account of the generative processes that underlie lexical evolution. [ABSTRACT FROM AUTHOR]