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**1 - 3**of**3**### Structuring Textbook Proofs

, 1999

"... We propose a promising research problem, the machine verification of textbook proofs. It shows that textbook proofs are a sufficiently complex and highly structured form of discourse, embedded in a well-defined and well-understood domain, thus offering an ideal domain for discourse analysis. Because ..."

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We propose a promising research problem, the machine verification of textbook proofs. It shows that textbook proofs are a sufficiently complex and highly structured form of discourse, embedded in a well-defined and well-understood domain, thus offering an ideal domain for discourse analysis. Because recognizing the structure of a proof is a prerequisite for verifying the correctness of a given mathematical argument, we define a four component model of discourse segmentation. 1 Introduction In order to advance our knowledge of discourse understanding, we have to 1. tackle real-world problems, that is study discourse that is sufficiently complex; 2. build ontologies and formalize knowledge about the domain of discourse; 3. seriously address representation issues; 4. apply reasoning techniques. This is nothing new. But did you ever see a natural language system where each of these four issues has been successfully addressed? Contrarily, many research resources has been spent on a family...

### On the Relationship Between Structure and Reference in Mathematical Discourse

"... We study the relationship between the structure of discourse and the use of referring expressions in the mathematical domain. We address linguistic, algorithmic as well as representation issues. We show how referential expressions refer to mathematical statements and how a knowledge intensive approa ..."

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We study the relationship between the structure of discourse and the use of referring expressions in the mathematical domain. We address linguistic, algorithmic as well as representation issues. We show how referential expressions refer to mathematical statements and how a knowledge intensive approach, domain reasoning with the use of proof plans, are used for discourse understanding. We propose to represent discourse plans as underspecified discourse representation structures being selected and instantiated during discourse processing. Our main emphasis is on the handling of abstract discourse entities. 1 Motivation We have the following practical application in mind: the automatic verification of mathematical textbook proofs. Imagine a program that understands mathematical discourse. Such a device reads proofs, say mathematical arguments taken from textbooks on elementary mathematics, and is then able to communicate its knowledge about what it has read and analyzed. It answers ques...