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Natural Language Dialog with a Tutor System for Mathematical Proofs
 JOURNAL OF COMPUTER SCIENCE AND TECHNOLOGY
, 2007
"... Natural language interaction between a student and a tutoring or an assistance system for mathematics is a new multidisciplinary challenge that requires the interaction of (i) advanced natural language processing, (ii) flexible tutorial dialog strategies including hints, and (iii) mathematical dom ..."
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Cited by 8 (5 self)
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Natural language interaction between a student and a tutoring or an assistance system for mathematics is a new multidisciplinary challenge that requires the interaction of (i) advanced natural language processing, (ii) flexible tutorial dialog strategies including hints, and (iii) mathematical domain reasoning. This paper provides an overview on the current research in the multidisciplinary research project Dialog, whose goal is to build a prototype dialogenabled system for teaching to do mathematical proofs. We present the crucial subsystems in our architecture: the input understanding component and the domain reasoner. We present an interpretation method for mixedlanguage input consisting of informal and imprecise verbalization of mathematical content, and a proof manager that supports assertionlevel automated theorem proving that is a crucial part of our domain reasoning module. Finally, we briefly report on an implementation of a demo system.
A proofcentric approach to mathematical assistants
 Journal of Applied Logic: Special Issue on Mathematics Assistance Systems
, 2005
"... We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a f ..."
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Cited by 5 (1 self)
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We present an approach to mathematical assistants which uses readable, executable proof scripts as the central language for interaction. We examine an implementation that combines the Isar language, the Isabelle theorem prover and the IsaPlanner proof planner. We argue that this synergy provides a flexible environment for the exploration, certification, and presentation of mathematical proof.
ΩMEGA: Computer supported mathematics
 IN: PROCEEDINGS OF THE 27TH GERMAN CONFERENCE ON ARTIFICIAL INTELLIGENCE (KI 2004)
, 2004
"... The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated dedu ..."
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Cited by 3 (3 self)
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The year 2004 marks the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number” (with Martin Davis’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proofchecked by a computer. Classical theorem proving procedures of today are based on ingenious search techniques to find a proof for a given theorem in very large search spaces – often in the range of several billion clauses. But in spite of many successful attempts to prove even open mathematical problems automatically, their use in everyday mathematical practice is still limited. The shift
Redirecting proofs by contradiction
"... This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph, as produced by an automatic theorem prover (e.g., E, SPASS, Vampire, Z3); the output is a direct proof expressed in natural deduction extended with case analyses and nested subproofs. The algori ..."
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Cited by 2 (2 self)
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This paper presents an algorithm that redirects proofs by contradiction. The input is a refutation graph, as produced by an automatic theorem prover (e.g., E, SPASS, Vampire, Z3); the output is a direct proof expressed in natural deduction extended with case analyses and nested subproofs. The algorithm is implemented in Isabelle’s Sledgehammer, where it enhances the legibility of machinegenerated proofs. 1
System Description: A Dialogue Manager Supporting Natural Language Tutorial Dialogue on Proofs
 UITP 2005 PRELIMINARY VERSION
, 2005
"... The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Since the medium of communication is natural language dialogue, and since tutorial dialogues are by nature both flexible and unpredictable, it is essential to include a sophisticated, dedicated dialog ..."
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Cited by 1 (0 self)
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The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Since the medium of communication is natural language dialogue, and since tutorial dialogues are by nature both flexible and unpredictable, it is essential to include a sophisticated, dedicated dialogue manager to handle the interaction between student and the system modules. In this paper we present the design and implementation of the dialogue manager for the demonstrator system of the Dialog project. The dialogue manager forms the interface between the user and the system modules, including the automated theorem prover Ωmega–Core, the tutorial module and the linguistic analysis module.
A Dialogue Manager supporting Natural Language Tutorial Dialogue on Proofs
 ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
, 2006
"... The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Due to the flexible and unpredictable nature of tutorial dialogue in natural language it is essential to include a sophisticated, dedicated dialogue manager to handle the interaction between student a ..."
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Cited by 1 (1 self)
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The Dialog project investigates flexible natural language tutorial dialogue on mathematical proofs. Due to the flexible and unpredictable nature of tutorial dialogue in natural language it is essential to include a sophisticated, dedicated dialogue manager to handle the interaction between student and the system modules. In this paper we present the design and implementation of the dialogue manager for the demonstrator system of the Dialog project. The dialogue manager forms the interface between the user and the system modules, including the automated theorem prover Ωmega–Core, the tutorial module and the linguistic analysis module. We also give an evaluation of Rubin, the development platform for the dialogue manager.
Computer Supported Formal Work: Towards a Digital Mathematical Assistant
 STUDIES IN LOGIC, GRAMMAR AND RHETORIC
, 2007
"... The year 2004 marked the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number ” (with Martin Davis ’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated ..."
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Cited by 1 (1 self)
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The year 2004 marked the fiftieth birthday of the first computer generated proof of a mathematical theorem: “the sum of two even numbers is again an even number ” (with Martin Davis ’ implementation of Presburger Arithmetic in 1954). While Martin Davis and later the research community of automated deduction used machine oriented calculi to find the proof for a theorem by automatic means, the Automath project of N.G. de Bruijn – more modest in its aims with respect to automation – showed in the late 1960s and early 70s that a complete mathematical textbook could be coded and proofchecked by a computer. Roughly at the same time in 1973, the Mizar project started as an attempt to reconstruct mathematics based on computers. Since 1989, the most important activity in the Mizar project has been the development of a database for mathematics. International cooperation resulted in creating a database which includes more than 7000 definitions of mathematical concepts and more than 42000 theorems. The work by
Organization, Transformation, and Propagation of Mathematical Knowledge in Ωmega
"... Abstract. Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend. In this article we propose a component network architecture as a means to design and implement such systems. U ..."
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Abstract. Mathematical assistance systems and proof assistance systems in general have traditionally been developed as large, monolithic systems which are often hard to maintain and extend. In this article we propose a component network architecture as a means to design and implement such systems. Under this view a mathematical assistance system is an integrated knowledgebased system composed as a network of individual, specialized components. These components manipulate and mutually exchange different kinds of mathematical knowledge encoded within different document formats. Consequently, several units of mathematical knowledge coexist throughout the system within these components and this knowledge changes nonmonotonically over time. Our approach has resulted in a lean and maintainable system code and makes the system open for extensions. Moreover, it naturally decomposes the global and complex reasoning and truth maintenance task into local reasoning and truth maintenance tasks inside the system components. The interplay between neighboring components in the network is thereby realized by nonmonotonic updates over agreed interface representations encoding different kinds of mathematical knowledge. 1.