Natural Language Processing of Mathematical Texts in mArachna

Abstract

mArachna is a technical framework designed for the extraction of mathematical knowledge from natural language texts. mArachna avoids the problems typically encountered in automated-reasoning based approaches through the use of natural language processing techniques taking advantage of the strict formalized language characterizing mathematical texts. Mathematical texts possess a strict internal structuring and can be separated into text elements (entities) such as definitions, theorems etc. These entities are the principal carriers of mathematical information. In addition, Entities show a characteristic coupling between the presented information and their internal linguistic structure, well suited for natural language processing techniques. Taking advantage of this structure, mArachna extracts mathematical relations from texts and integrates them into a knowledge base. Identifying sub elements within new elements of information with already stored mathematical concepts defines the structure of the knowledge base. As a result, mArachna generates an ontology of the analyzed mathematical texts. In response to user queries, parts of the knowledge base are visualized using OWL. In particular, mArachna aims to provide an overview of single fields of mathematics, as well as showing intra-field relations between mathematical objects and concepts. The following paper gives an overview of the theoretical basis and the technologies applied within the mArachna framework.