Results 1 
3 of
3
A DRTbased approach for formula parsing in textbook proofs
 IN THIRD INTERNATIONAL WORKSHOP ON COMPUTATIONAL SEMANTICS (IWCS3
, 1999
"... 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 essent ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
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.
Checking Textbook Proofs
 Int. Workshop on FirstOrder Theorem Proving (FTP'98), Technical Report E1852GS981
, 1998
"... . Our longrange goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and deduction perspective and give an indepth analysis for a sample textbook proof. A three phase model for proof understanding is developed: parsing, str ..."
Abstract
 Add to MetaCart
. Our longrange goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and deduction perspective and give an indepth analysis for a sample textbook proof. A three phase model for proof understanding is developed: parsing, structuring and refining. It shows that the combined application of techniques from both NLP and AR is quite successful. Moreover, it allows to uncover interesting insights that might initiate progress in both AI disciplines. Keywords: automated reasoning, natural language processing, discourse analysis 1 Introduction In [12], John McCarthy notes that "Checking mathematical proofs is potentially one of the most interesting and useful applications of automatic computers". In the first half of the 1960s, one of his students, namely Paul Abrahams, implemented a Lisp program for the machine verification of mathematical proofs [1]. The program, named Proofchecker, "was primarily directed towar...
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 welldefined and wellunderstood domain, thus offering an ideal domain for discourse analysis. Because ..."
Abstract
 Add to MetaCart
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 welldefined and wellunderstood 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 realworld 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...