In syntactic parsing, *proof nets* are graphical structures that have the advantageous property of invariance to spurious ambiguities. Semantically-equivalent derivations correspond to a single proof net. Recent years have seen fresh interest in statistical syntactic parsing with proof nets, including the development of methods based on neural networks. However, training of statistical parsers requires corpora that provide ground-truth syntactic analyses. Unfortunately, there has been a paucity of corpora in formalisms for which proof nets are applicable, such as Lambek categorial grammar (LCG), a formalism related to combinatory categorial grammar (CCG). To address this, we leverage CCGbank and the relationship between LCG and CCG to develop LCGbank, an English-language corpus of syntactic analyses based on LCG proof nets. In contrast to CCGbank, LCGbank eschews type-changing and uses only categorial rules; the syntactic analyses thus provide fully compositional semantics, exploiting the transparency between syntax and semantics that so characterizes categorial grammars.

In statistical parsing with CCG, the standard evaluation method is based on predicate-argument structure and evaluates dependencies labelled in part by lexical categories. When a predicate has multiple argument slots that can be filled, the same lexical category is used for the label of multiple dependencies. In this paper, we show that this evaluation can result in disproportionate penalization of supertagging errors and obfuscate the truly erroneous dependencies. Enabled by the compositional nature of CCG lexical categories, we propose *decomposed scoring* based on subcategorial labels to address this. To evaluate our scoring method, we engage fellow categorial grammar researchers in two English-language judgement tasks: (1) directly ranking the outputs of the standard and experimental scoring methods; and (2) determining which of two sentences has the better parse in cases where the two scoring methods disagree on their ranks. Overall, the judges prefer decomposed scoring in each task; but there is substantial disagreement among the judges in 24% of the given cases, pointing to potential issues with parser evaluations in general.

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.