Definition Extraction from Mathematical Texts on Graph Theory in German and English

Definition Extraction from Mathematical Texts on Graph Theory in German and English Theresa Kruse University of Hildesheim Universit¨atsplatz 1 31141 Hildesheim, Germany kruset@uni-hildesheim.de Fritz Kliche University of Hildesheim Universit¨atsplatz 1 31141 Hildesheim, Germany kliche@uni-hildesheim.de Abstract We extract definitions from text books and sci- entific publications on mathematics in both, German and English, from the sub-domain of graph theory. Mathematical texts differ from other domains because sentences which appear as definitions from a linguistic perspective are not necessarily definitions in the mathematical sense. For the English texts we train a neu- ral network on existing training data (Vanetik et al., 2020). For the German texts we semi- automatically generate training data using pat- terns for the extraction of definitions. We show that this is a feasible approach for the domain of mathematical texts which generally makes extensive use of formalized language patterns. We measure precision and recall on a random sample to evaluate our results. The F-Score is similar for both languages but precision and recall are closer to each other for the German data. Further comparisons are made with a term list automatically extracted from the data. We conclude that our approach can be used to extract candidate sentences for further postpro- cessing. 1 Introduction In this paper, we combine two domains where def- initions play a significant role: lexicography and mathematics. In lexicography, definitions provide dictionary users with information about a term. In mathematics, definitions are crucial to ensure a common understanding of the domain’s concepts. We extract definitions from texts on graph theory to use them in a domain-specific dictionary. In Section 2, we give an overview of related work on types and forms of definitions and on extrac- tion methods. In Section 3.1, we describe our data. Sections 3.2 and 3.3 present our method for the extraction of definitions from the English and the German data. Section 4.1 gives a qualitative anal- ysis of the results and Section 4.2 a quantitative evaluation. We conclude in Section 5. 2 Background and Related Work 2.1 Definitions in Mathematical Texts Mathematical texts consist of corollaries, lem- mas, propositions, theorems, proofs and definitions (Solow, 1990). Usually, a numbering indicates the types (e.g. Theorem 2.1) but this is not necessar- ily the case for definitions. Some authors include them in the numbering and others simply give them in the text. Some authors highlight defined terms, e.g. by means of italics. Kruse and Heid (2020) analyze mathematical definitions for lexicographic purposes. They conclude that analytical definitions (or logical definitions as they are also called) in the Aristotelian scheme are mostly used. Single-clause when-definitions appear to define adjectives and verbs, contrary to usual practice in dictionaries for general language, as Dziemianko and Lew (2006) proposed. For definition extraction, however, it is more relevant to distinguish a definition from a non-definition rather than paying attention to the different types of definitions. Nevertheless, some sentences are definitions from a linguistic perspec- tive but not from a mathematical perspective in content. This constitutes a special challenge for …

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