An annotated corpus and a grammar model of theorem description.pdfVIP

An Annotated Corpus and a Grammar Model of Theorem Description Yusuke Baba1 and Masakazu Suzuki2 1 Graduate School of Mathematics, Kyushu University 2 Faculty of Mathematics, Kyushu University 6-10-1 Hakozaki, Higashi-ku, Fukuoka, 812-8581 Japan {ma201040,suzuki}@math.kyushu-u.ac.jp Abstract. Digitizing documents is becoming increasingly popular in various fields, and training computers to understand the contents of dig- itized documents is of growing interest. Since the early 90’s, research of natural language processing using large annotated corpora such as the Penn TreeBank has developed. Applying the methods of corpus-based research, we built a syntactically annotated corpus of theorem descrip- tions, using a book of set theory, and extracted a grammar model of theorems from the obtained corpus, as the first step to understanding mathematical documents by computer. 1 Introduction In recent years, digitizing documents has become increasingly popular in various fields, for example, in mathematics[1][2][3][4]. In connection with this movement, understanding the contents of digitized documents by computer is of growing interest[5][6]. The technology of understanding documents is applicable to useful systems such as machine translation, summarization and search. In mathematics, there are also particular application ideas of application e.g. the a system that trans- lates descriptions of a proof into a language of proof-checker. The fundamental technology of understanding documents by computer is parsing. The effectiveness of the above-mentioned systems depends heavily on the accuracy of the parser. Generally, parsing is complicated by the characteristics of natural language such as ambiguity, omission and inversion. On the other hand, since mathematical documents are written in logical and precise expressions, we can expect that the typical methods of parsing for natural language give more accurate results for mathematical documents. The availability of large, syntac