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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. 1
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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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.
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...
MATHRESS: A MATHEMATICAL RESEARCH SYSTEM Principal Investigator: Arnold Neumaier Funding Period: 5 years
"... This project creates foundations for an automatic system that combines the reliability and speed of a computer with the ability to perform at the level of a good mathematics student. The acronym MATHRESS abbreviating the project title, which may be pronounced “mattress”, indicates that the project s ..."
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This project creates foundations for an automatic system that combines the reliability and speed of a computer with the ability to perform at the level of a good mathematics student. The acronym MATHRESS abbreviating the project title, which may be pronounced “mattress”, indicates that the project serves to provide a good, comfortable foundation for the development of an automatic mathematical research system. The MATHRESS project creates the MATHRESS system that will itself be the foundation on which people will rely for mathematical support. VISION and OBJECTIVES. The ambitious longterm vision for our project is the creation of an expert system that supports mathematicians and scientists dealing with mathematics in: – checking their own work for correctness; – improving the quality of their presentations; – decreasing the time needed for routine work in the preparation of publications; – quickly and reliably reminding them of work done by others; – producing multiple language versions of their manuscripts; – quickly disseminating partially checked results to other users of the system; – intelligently searching a universal database of mathematical knowledge; – learning like a student from the experience accumulated during interaction with the user.
A modeling system for mathematics
"... This project aims at the development of a flexible modeling system for the specification of models for largescale numerical work in optimization, data analysis, and partial differential equations. Its input should be provided in a form natural for the working mathematician, while the choice of the ..."
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This project aims at the development of a flexible modeling system for the specification of models for largescale numerical work in optimization, data analysis, and partial differential equations. Its input should be provided in a form natural for the working mathematician, while the choice of the numerical solvers and the transformation to the format required by the solvers is done by the interface system. The input format should combine the simplicity of LaTeX source code with the semantic conciseness and modularity of current modeling languages such as AMPL, and it should be as close as possible to the mathematical language people use to explain and communicate their models in publications and lectures. In order that the system is useful for the intended applications, interfaces translating the model formulated in the proposed system into the input required for current state of the art solvers, and into the dominant current modeling languages are needed and shall be provided. Moreover, certain shortcomings of the current generation of modeling languages, such as the lack of support for the correct treatment of uncertainties and rounding errors, shall be overcome. The experience gained in this project will be useful in future work in the more general context
Systems related to the FMathL vision
, 2010
"... There are already many automatic mathematical assistants that provide expert help in specialized domains. Known classes include computer algebra systems, automated deduction systems, modeling systems, matrix packages, numerical prototyping languages, decision trees for scientific computing software, ..."
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There are already many automatic mathematical assistants that provide expert help in specialized domains. Known classes include computer algebra systems, automated deduction systems, modeling systems, matrix packages, numerical prototyping languages, decision trees for scientific computing software, etc.. Such existing tools already provide partial functionality of the kind to be created in the project but only tied to specific applications, or with a limited scope. This document describes a number of current systems related to the FMathL vision, and some of their limitations when viewed in the light of this vision. The PI’s website (www.mat.univie.ac. at/~neum/FMathL.html) contains a large selection of additional resources and references to existing related systems. L ATEX