To be or not to be an Integer? Encoding Variables for Mathematical Text

Findings of the Association for Computational Linguistics: ACL 2022, pages 938 - 948 May 22-27, 2022 c⃝2022 Association for Computational Linguistics To be or not to be an Integer? Encoding Variables for Mathematical Text Deborah Ferreira1, Mokanarangan Thayaparan1,2, Marco Valentino1,2, Julia Rozanova1, Andre Freitas1,2 Department of Computer Science, University of Manchester, United Kingdom 1 Idiap Research Institute, Switzerland 2 deborah.ferreira@manchester.ac.uk Abstract The application of Natural Language Inference (NLI) methods over large textual corpora can fa- cilitate scientific discovery, reducing the gap be- tween current research and the available large- scale scientific knowledge. However, contem- porary NLI models are still limited in interpret- ing mathematical knowledge written in Natural Language, even though mathematics is an inte- gral part of scientific argumentation for many disciplines. One of the fundamental require- ments towards mathematical language under- standing is the creation of models able to mean- ingfully represent variables. This problem is particularly challenging since the meaning of a variable should be assigned exclusively from its defining type, i.e., the representation of a variable should come from its context. Recent research has formalised the variable typing task, a benchmark for the understanding of abstract mathematical types and variables in a sentence. In this work, we propose VarSlot, a Variable Slot-based approach, which not only delivers state-of-the-art results in the task of variable typing, but is also able to create context-based representations for variables. 1 Introduction The articulation of mathematical arguments is a fundamental part of scientific reasoning and com- munication. Across many scientific disciplines, ex- pressing relations and inter-dependencies between quantities is at the centre of its argumentation. One of the particular linguistic elements used for such argumentation is variables: they are essential for expressing complex mathematical ideas, allowing scientists to refer to a set of values compactly and rigorously. Given the essential nature of variables, models that perform inference over scientific and mathematical text should be able to meaningfully represent and leverage such elements to understand mathematical language and improve downstream inference performance. While there is still debate on a universally ac- cepted definition for variables, their functional as- pects within mathematical text are well established. A variable is usually defined as a symbol standing as a referent for a set consisting of at least two elements (Philipp, 1992). Given their nature of ab- stract and dynamic referents, two aspects make the representation of variables particularly challenging in the field of NLP: (i) The meaning of a variable is exclusively determined by its context (Schoenfeld and Arcavi, 1988), a variable carries no meaning when considered in isolation, behaving unlike any word in English; (ii) The same variable symbol (e.g., the variable x) can be reused in an unlim- ited number of sentences and expressions, possibly assuming different meanings and referring to dif- ferent sets of values while keeping the same name. While a similar problem can also be found for the representation of words (i.e., word sense disam- biguation), the scale of ambiguity is more marked, due to the fact that variable names, …

Content truncated to 500 words