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Computing Presuppositions and Implicatures in Mathematical Discourse
"... In any wellwritten mathematical discourse a certain amount of mathematical and metamathematical knowledge is presupposed and implied. We give an account on presuppositions and implicatures in mathematical discourse and describe an architecture that allows to e ectively interpret them. Our approach ..."
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In any wellwritten mathematical discourse a certain amount of mathematical and metamathematical knowledge is presupposed and implied. We give an account on presuppositions and implicatures in mathematical discourse and describe an architecture that allows to e ectively interpret them. Our approach heavily relies on proof methods that capture common patterns of argumentation in mathematical discourse. This pragmatic information provides a highlevel strategic discourse understanding and allows to compute the presupposed and implied information.
Towards the Mechanical Verification of Textbook Proofs
"... Our goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and automated reasoning perspective and give an indepth analysis for a sample textbook proof. We propose a framework for natural language proof understanding that extends ..."
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Our goal is to implement a program for the machine verification of textbook proofs. We study the task from both the linguistics and automated reasoning perspective and give an indepth analysis for a sample textbook proof. We propose a framework for natural language proof understanding that extends and integrates stateoftheart technologies from Natural Language Processing (Discourse Representation Theory) and Automated Reasoning (Proof Planning) in a novel and promising way, having the potential to initiate progress in both of these disciplines.
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 ..."
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. 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...
An Intelligent Tutoring System for Induction Proofs
"... interfaces. We will specify and implement abstract interfaces for the student model, the dialogue history and the problem state. 4 Diagnosis and Therapy. We will view the diagnosis task as a plan recognition problem. We will explore the possibilities (i) of using proof plans and Oyster/Clam's proof ..."
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interfaces. We will specify and implement abstract interfaces for the student model, the dialogue history and the problem state. 4 Diagnosis and Therapy. We will view the diagnosis task as a plan recognition problem. We will explore the possibilities (i) of using proof plans and Oyster/Clam's proof planning facility to support the diagnosis and therapy task; (ii) of adapting a probabilistic plan recognition approach using Bayes's belief networks. This is the approach taken in Andes, a physics tutoring system [GCV98] with similar domain properties. Since specifying and implementing the diagnosis and therapy module of Intuition will be a significant project in itself, we will recruit a PhD student who will concentrate his research efforts solely on these components: 4.1 Knowledge acquisition (6pm), literature survey (3pm), and summarisation of intermediate results (1pm). 4.2 Diagnosis module (9pm), and summarisation of intermediate results (1pm). 4.3 Therapy module (9pm), and summar...