Automated Discovery of Mathematical Definitions in Text

Proceedings of the 12th Conference on Language Resources and Evaluation (LREC 2020), pages 2086–2094 Marseille, 11–16 May 2020 c⃝ European Language Resources Association (ELRA), licensed under CC-BY-NC 2086 Automated Discovery of Mathematical Definitions in Text Natalia Vanetik, Marina Litvak, Sergey Shevchuk and Lior Reznik Department of Software Engineering Shamoon College of Engineering, Beer Sheva, Israel {natalyav,marinal,sergesh}@sce.ac.il, liorrezn@gmail.com Abstract Automatic definition extraction from texts is an important task that has numerous applications in several natural language processing fields such as summarization, analysis of scientific texts, automatic taxonomy generation, ontology generation, concept identification, and question answering. For definitions that are contained within a single sentence, this problem can be viewed as a binary classification of sentences into definitions and non-definitions. Definitions in scientific literature can be generic (Wikipedia) or more formal (mathematical articles). In this paper, we focus on automatic detection of one-sentence definitions in mathematical texts, which are difficult to separate from surrounding text. We experiment with several data representations, which include sentence syntactic structure and word embeddings, and apply deep learning methods such as convolutional neural network (CNN) and recurrent neural network (RNN), in order to identify mathematical definitions. Our experiments demonstrate the superiority of CNN and its combination with RNN, applied on the syntactically-enriched input representation. We also present a new dataset for definition extraction from mathematical texts. We demonstrate that the use of this dataset for training learning models improves the quality of definition extraction when these models are then used for other definition datasets. Our experiments with different domains approve that mathematical definitions require special treatment, and that using cross-domain learning is inefficient. Keywords: definition extraction, deep learning 1. Introduction Definitions have a very important role in scientific literature because they define the major concepts an article operates with. They are basic building blocks of a scientific article that are used to properly describe hypotheses, experiments and analyses. Definitions are used in many automatic text analysis tasks, such as question answering, ontology match- ing and construction, formal concept analysis and structural text summarization. Therefore, automatic definition extrac- tion (DE) is an important field in natural language process- ing and can be used for better text analysis and search. Definitions play a key role in mathematics, but their creation and use differs from those of "everyday language" defini- tions (a comprehensive study is given in series of works by Edwards and Ward in (Edwards and Ward, 2008; Ed- wards and Ward, 2004; Edwards, 1998) inspired by writ- ings of Richard Robinson (Robinson, 1962) and lexicog- rapher Sidney Landau (Landau, 2001)). They distinguish between extracted definitions report usage and have a truth value (Edwards and Ward, 2004), while stipulated defini- tions create usage, indeed create concepts, by decree but have no truth value. Mathematical definitions frequently do have a history as they evolve over time. The definition we use for function, for instance, may not be the one that was used a hundred years ago. The concept of connectiv- ity has two definitions, path-connected and set-theoretically connected (Edwards and …

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