State-of-the-art parsers suffer from incomplete lexicons, as evidenced by the fact that they all contain built-in methods for dealing with out-of-lexicon items at parse time. Since new labelled data is expensive to produce and no amount of it will conquer the long tail, we attempt to address this problem by leveraging the enormous amount of raw text available for free, and expanding the lexicon offline, with a semi-supervised word learner. We accomplish this with a method similar to self-training, where a fully trained parser is used to generate new parses with which the next generation of parser is trained. This thesis introduces Chart Inference (CI), a two-phase word-learning method with Combinatory Categorial Grammar (CCG), operating on the level of the partial parse as produced by a trained parser. CI uses the parsing model and lexicon to identify the CCG category type for one unknown word in a context of known words by inferring the type of the sentence using a model of end punctuation, then traversing the chart from the top down, filling in each empty cell as a function of its mother and its sister. We first specify the CI algorithm, and then compare it to two baseline wordlearning systems over a battery of learning tasks. CI is shown to outperform the baselines in every task, and to function in a number of applications, including grammar acquisition and domain adaptation. This method performs consistently better than self-training, and improves upon the standard POS-backoff strategy employed by the baseline StatCCG parser by adding new entries to the lexicon. The first learning task establishes lexical convergence over a toy corpus, showing that CI’s ability to accurately model a target lexicon is more robust to initial conditions than either of the baseline methods. We then introduce a novel natural language corpus based on children’s educational materials, which is fully annotated with CCG derivations. We use this corpus as a testbed to establish that CI is capable in principle of recovering the whole range of category types necessary for a wide-coverage lexicon. The complexity of the learning task is then increased, using the CCGbank corpus, a version of the Penn Treebank, and showing that CI improves as its initial seed corpus is increased. The next experiment uses CCGbank as the seed and attempts to recover missing question-type categories in the TREC question answering corpus. The final task extends the coverage of the CCGbank-trained parser by running CI over the raw text of the Gigaword corpus. Where appropriate, a fine-grained error analysis is also undertaken to supplement the quantitative evaluation of the parser performance with deeper reasoning as to the linguistic points of the lexicon and parsing model.