In this paper, we present the first statistical parser for Lambek categorial grammar (LCG), a grammatical formalism for which the graphical proof method known as *proof nets* is applicable. Our parser incorporates proof net structure and constraints into a system based on self-attention networks via novel model elements. Our experiments on an English LCG corpus show that incorporating term graph structure is helpful to the model, improving both parsing accuracy and coverage. Moreover, we derive novel loss functions by expressing proof net constraints as differentiable functions of our model output, enabling us to train our parser without ground-truth derivations.

In CCG and other highly lexicalized grammars, supertagging a sentence’s words with their lexical categories is a critical step for efficient parsing. Because of the high degree of lexicalization in these grammars, the lexical categories can be very complex. Existing approaches to supervised CCG supertagging treat the categories as atomic units, even when the categories are not simple; when they encounter words with categories unseen during training, their guesses are accordingly unsophisticated. In this paper, we make use of the primitives and operators that constitute the lexical categories of categorial grammars. Instead of opaque labels, we treat lexical categories themselves as linear sequences. We present an LSTM-based model that replaces standard word-level classification with prediction of a sequence of primitives, similarly to LSTM decoders. Our model obtains state-of-the-art word accuracy for single-task English CCG supertagging, increases parser coverage and F1, and is able to produce novel categories. Analysis shows a synergistic effect between this decomposed view and incorporation of prediction history.