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Understanding Mathematical Discourse
 DIALOGUE. AMSTERDAM UNIVERSITY
, 1999
"... Discourse Understanding is hard. This seems to be especially true for mathematical discourse, that is proofs. Restricting discourse to mathematical discourse allow us, however, to study the subject matter in its purest form. This domain of discourse is rich and welldefined, highly structured, offers ..."
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Cited by 7 (6 self)
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Discourse Understanding is hard. This seems to be especially true for mathematical discourse, that is proofs. Restricting discourse to mathematical discourse allow us, however, to study the subject matter in its purest form. This domain of discourse is rich and welldefined, highly structured, offers a welldefined set of discourse relations and forces/allows us to apply mathematical reasoning. We give a brief discussion on selected linguistic phenomena of mathematical discourse, and an analysis from the mathematician’s point of view. Requirements for a theory of discourse representation are given, followed by a discussion of proofs plans that provide necessary context and structure. A large part of semantics construction is defined in terms of proof plan recognition and instantiation by matching and attaching.
Bidirectional Natural Deduction
 AI*IA Notizie
, 1993
"... The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. Thi ..."
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Cited by 4 (2 self)
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The goal of this paper is to present a theorem prover able to perform both forward and backward reasoning supported by a well defined formal system. This system for bidirectional reasoning has been proved equivalent to Gentzen's classical system of propositional natural deduction. This paper, primarily aimed at developing a deeper theoretical understanding of bidirectional reasoning, provides basic concepts to be incorporated into an innovative theorem prover to support interactive proofs construction in general domains. 1
Verifying textbook proofs
 Technische Universität
, 1998
"... In the first half of the 1960s, Paul Abrahams implemented a Lisp program for the machine verification of mathematical proofs [1]. The program, named Proofchecker, “was primarily directed towards the verification of textbook proofs, i.e., proofs resembling those that normally appear in mathematical t ..."
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Cited by 3 (3 self)
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In the first half of the 1960s, Paul Abrahams implemented a Lisp program for the machine verification of mathematical proofs [1]. The program, named Proofchecker, “was primarily directed towards the verification of textbook proofs, i.e., proofs resembling those that normally appear in mathematical textbooks and journals”. Abrahams did not succeed. If, so Abrahams, “a computer were to check a textbook proof verbatim, it would require far more intelligence than is possible with the current state of the programming art”. Therefore, so Abrahams, “the user must create a rigorous, i.e., completely formalised, proof that he believes represents the intent of the author of the textbook proof, and use the computer to check this rigorous proof”. Abrahams points further out that “it it a trivial task to program a computer to check a rigorous proof; however, it it not a trivial task to create such a proof from a textbook proof”. Abrahams was right. In all later projects, proofs had to be written in a formal language in order to verify them. One wellknown example is the the Automath project: van BenthemJutting formalised a whole textbook of Landau, the ‘Grundlagen der Analysis’, into a formal language, autqe [8]. A second example is the Mizar project [5]: proofs have
Towards the Mechanical Verification of Textbook Proofs
 In Proceedings of the 7th. Workshop on Logic, Language, Information and Computation (WOLLIC2000
, 2000
"... 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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Cited by 1 (1 self)
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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.
Computing Presuppositions and Implicatures in Mathematical Discourse
 In Proceedings of the 2nd. Workshop on Inference in Computational Semantics (ICoS2
, 2000
"... 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 effectively interpret them. Our approac ..."
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Cited by 1 (1 self)
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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 effectively 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. 1
unknown title
, 2009
"... Let me know if you find any mistakes or have any suggestions for improvement. These notes may NOT be duplicated without seeking express permission. Contents 0 Prelude xvi I The craft of translator writing 1 1 A model for translator software 4 1.1 Common front end................................ 6 ..."
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Let me know if you find any mistakes or have any suggestions for improvement. These notes may NOT be duplicated without seeking express permission. Contents 0 Prelude xvi I The craft of translator writing 1 1 A model for translator software 4 1.1 Common front end................................ 6
A Brief Introduction to Proofs
, 2010
"... Proofs are perhaps the very heart of mathematics. Unlike the other sciences, ..."
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Proofs are perhaps the very heart of mathematics. Unlike the other sciences,