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This chapter introduces weighted bilexical grammars, a formalism in which individual lexical items, such as verbs and their arguments, can have idiosyncratic selectional influences on each other. Such ‘bilexicalism’ has been a theme of much current work in parsing. The new formalism can be used to describe bilexical approaches to both dependency and phrase-structure grammars, and a slight modification yields link grammars. Its scoring approach is compatible with a wide variety of probability models.

The obvious parsing algorithm for bilexical grammars (used by most previous authors) takes time O(n ⁵). A more efficient O(n ³) method is exhibited. The new algorithm has been implemented and used in a large parsing experiment Eisner, 1996b). We also give a useful extension to the case where the parser must undo a stochastic transduction that has altered the input.