Grounding the meaning of each symbol in math formulae is important for automated understanding of scientific documents. Generally speaking, the meanings of math symbols are not necessarily constant, and the same symbol is used in multiple meanings. Therefore, coreference relations between symbols need to be identified for grounding, and the task has aspects of both description alignment and coreference analysis. In this study, we annotated 15 papers selected from arXiv.org with the grounding information. In total, 12,352 occurrences of math identifiers in these papers were annotated, and all coreference relations between them were made explicit in each paper. The constructed dataset shows that regardless of the ambiguity of symbols in math formulae, coreference relations can be labeled with a high inter-annotator agreement. The constructed dataset enables us to achieve automation of formula grounding, and in turn, make deeper use of the knowledge in scientific documents using techniques such as math information extraction. The built grounding dataset is available at https://sigmathling.kwarc.info/resources/grounding- dataset/.

A large amount of scientific knowledge is represented within mixed forms of natural language texts and mathematical formulae. Therefore, a collaboration of natural language processing and formula analyses, so-called mathematical language processing, is necessary to enable computers to understand and retrieve information from the documents. However, as we will show in this project, a mathematical notation can change its meaning even within the scope of a single paragraph. This flexibility makes it difficult to extract the exact meaning of a mathematical formula. In this project, we will propose a new task direction for grounding mathematical formulae. Particularly, we are addressing the widespread misconception of various research projects in mathematical information retrieval, which presume that mathematical notations have a fixed meaning within a single document. We manually annotated a long scientific paper to illustrate the task concept. Our high inter-annotator agreement shows that the task is well understood for humans. Our results indicate that it is worthwhile to grow the techniques for the proposed task to contribute to the further progress of mathematical language processing.