A Drt-based Approach for Formula Parsing in Textbook Proofs

Knowledge is essential for understanding discourse. Generally, this has to be common sense knowledge and therefore, discourse understanding is hard. For the understanding of textbook proofs, however, only a limited quantity of knowledge is necessary. In addition, we have gained something very essential: inference. A prerequisite for parsing textbook proofs is to being able to parse formulae that occur in these proofs. Parsing formulae alone in the empty context is trivial. But within the context of textbook proofs the task soon gets complex. Several kinds of references from the text to parts or sets of terms and formulae have to be handled. We describe some of the linguistic phenomena that occur in mathematical texts. The focus is on our treatment of term reference which is embedded in the DRT. 1 Motivation Knowledge is essential for understanding much discourse: knowledge about actions, causal-ity and goals and even common sense knowledge about everyday activities. Therefore, discourse understanding is hard. In order to limit the knowledge required to understand a discourse, most researchers restrict their discourses coming from certain domains, e.g., to articles from the Wall Street Journal and to UNIX handbooks. The domain we have chosen are textbook proofs. In doing so, we think that we have minimized the quantity of necessary knowledge and excluded common sense knowledge. In addition, we have gained something very essential: inference. Our long-range goal is to implement a program for the machine veriication of textbook proofs. This program will read textbook proofs and is able to communicate its knowledge about what it has read. This proof understander is able to recognize the proof structure as well as obvious deenitorial and logical dependencies. It answers questions about the proof accurately and is perhaps even capable to identify gaps or aws in the argumentation line. The proof system ooers a high-level analysis of the proof as well as a technical low-level access to details of the proof.