This thesis presents and tests an incremental theory of Lexical Functional Grammar (LFG) in an attempt to support researchers in formal grammar to engage with questions raised by experimental findings on language processing and artificial intelligence. Previous work on the incremental building of syntactic structure has concentrated on constituent structure, considering interactions between word class and phrase-structure rules. However, syntax in LFG is represented not only as constituent structure, but also as functional structure: a universal set of grammatical functions is included within the primitives of the theory. The incremental theory presented here explores the role of grammatical functions as well as category and phrase-structur...