Mathematics is a highly specialized domain with its own unique set of challenges. Despite this, there has been relatively little research on natural language processing for mathematical texts, and there are few mathematical language resources aimed at NLP. In this paper, we aim to provide annotated corpora that can be used to study the language of mathematics in different contexts, ranging from fundamental concepts found in textbooks to advanced research mathematics. We preprocess the corpora with a neural parsing model and some manual intervention to provide part-of-speech tags, lemmas, and dependency trees. In total, we provide 182397 sentences across three corpora. We then aim to test and evaluate several noteworthy natural language processing models using these corpora, to show how well they can adapt to the domain of mathematics and provide useful tools for exploring mathematical language. We evaluate several neural and symbolic models against benchmarks that we extract from the corpus metadata to show that terminology extraction and definition extraction do not easily generalize to mathematics, and that additional work is needed to achieve good performance on these metrics. Finally, we provide a learning assistant that grants access to the content of these corpora in a context-sensitive manner, utilizing text search and entity linking. Though our corpora and benchmarks provide useful metrics for evaluating mathematical language processing, further work is necessary to adapt models to mathematics in order to provide more effective learning assistants and apply NLP methods to different mathematical domains.

We investigate different systems for extracting mathematical entities from English texts in the mathematical field of category theory as a first step for constructing a mathematical knowledge graph. We consider four different term extractors and compare their results. This small experiment showcases some of the issues with the construction and evaluation of terms extracted from noisy domain text. We also make available two open corpora in research mathematics, in particular in category theory: a small corpus of 755 abstracts from the journal TAC (3188 sentences), and a larger corpus from the nLab community wiki (15,000 sentences)

Sentences with presuppositions are often treated as uninterpretable or unvalued (neither true nor false) if their presuppositions are not satisfied. However, there is an open question as to how this satisfaction is calculated. In some cases, determining whether a presupposition is satisfied is not a trivial task (or even a decidable one), yet native speakers are able to quickly and confidently identify instances of presupposition failure. I propose that this can be accounted for with a form of possible world semantics that encapsulates some reasoning abilities, but is limited in its computational power, thus circumventing the need to solve computationally difficult problems. This can be modeled using a variant of the framework of finite state semantics proposed by Rooth (2017). A few modifications to this system are necessary, including its extension into a three-valued logic to account for presupposition. Within this framework, the logic necessary to calculate presupposition satisfaction is readily available, but there is no risk of needing exceptional computational power. This correctly predicts that certain presuppositions will not be calculated intuitively, while others can be easily evaluated.