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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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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.
The Naproche Project Controlled Natural Language Proof Checking of Mathematical Texts
"... Abstract. This paper discusses the semiformal language of mathematics and presents the Naproche CNL, a controlled natural language for mathematical authoring. Proof Representation Structures, an adaptation of Discourse Representation Structures, are used to represent the semantics of texts written ..."
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Abstract. This paper discusses the semiformal language of mathematics and presents the Naproche CNL, a controlled natural language for mathematical authoring. Proof Representation Structures, an adaptation of Discourse Representation Structures, are used to represent the semantics of texts written in the Naproche CNL. We discuss how the Naproche CNL can be used in formal mathematics, and present our prototypical Naproche system, a computer program for parsing texts in the Naproche CNL and checking the proofs in them for logical correctness.
Premise Selection in the Naproche System
"... Abstract. Automated theorem provers (ATPs) struggle to solve problems with large sets of possibly superfluous axiom. Several algorithms have been developed to reduce the number of axioms, optimally only selecting the necessary axioms. However, most of these algorithms consider only single problems. ..."
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Abstract. Automated theorem provers (ATPs) struggle to solve problems with large sets of possibly superfluous axiom. Several algorithms have been developed to reduce the number of axioms, optimally only selecting the necessary axioms. However, most of these algorithms consider only single problems. In this paper, we describe an axiom selection method for series of related problems that is based on logical and textual proximity and tries to mimic a human way of understanding mathematical texts. We present first results that indicate that this approach is indeed useful. Key words: formal mathematics, automated theorem proving, axiom selection 1
Literate proving: presenting and documenting formal proofs
 4th Int. Conf. on Mathematical Knowledge Management, MKM 2005, LNCS 3863
, 2006
"... Abstract. Literate proving is the analogue for literate programming in the mathematical realm. That is, the goal of literate proving is for humans to produce clear expositions of formal mathematics that could even be enjoyable for people to read whilst remaining faithful representations of the actua ..."
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Abstract. Literate proving is the analogue for literate programming in the mathematical realm. That is, the goal of literate proving is for humans to produce clear expositions of formal mathematics that could even be enjoyable for people to read whilst remaining faithful representations of the actual proofs. This paper describes maze, a generic literate proving system. Authors markup formal proof files, such as Mizar files, with arbitary XML and use maze to obtain the selected extracts and transform them for presentation, e.g. as L ATEX. To aid its use, maze has built in transformations that include pretty printing and proof sketching for inclusion in L ATEX documents. These transformations challenge the concept of faithfulness in literate proving but it is argued that this should be a distinguishing feature of literate proving from literate programming. 1
Translating between Language and Logic: What Is Easy and What Is Difficult
"... Abstract. Natural language interfaces make formal systems accessible in informal language. They have a potential to make systems like theorem provers more widely used by students, mathematicians, and engineers who are not experts in logic. This paper shows that simple but still useful interfaces are ..."
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Abstract. Natural language interfaces make formal systems accessible in informal language. They have a potential to make systems like theorem provers more widely used by students, mathematicians, and engineers who are not experts in logic. This paper shows that simple but still useful interfaces are easy to build with available technology. They are moreover easy to adapt to different formalisms and natural languages. The language can be made reasonably nice and stylistically varied. However, a fully general translation between logic and natural language also poses difficult, even unsolvable problems. This paper investigates what can be realistically expected and what problems are hard.
Developing the System MathNat for Automatic Formalization of Mathematical texts
, 2012
"... Wide gap between the language of mathematics used in textbooks and the mathematics formalized in various theorem provers / proof assistants Developing the System MathNat ..."
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Wide gap between the language of mathematics used in textbooks and the mathematics formalized in various theorem provers / proof assistants Developing the System MathNat
unknown title
, 2007
"... Mathematical documents faithfully computerised: the grammatical and text & symbol aspects of the MathLang framework ..."
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Mathematical documents faithfully computerised: the grammatical and text & symbol aspects of the MathLang framework
Informal and Formal Representations in Mathematics
, 2007
"... In this paper we discuss the importance of good representations in mathematics and relate them to general design issues. Good design makes life easy, bad design difficult. For this reason experienced mathematicians spend a significant amount of their time on the design of their concepts. While many ..."
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In this paper we discuss the importance of good representations in mathematics and relate them to general design issues. Good design makes life easy, bad design difficult. For this reason experienced mathematicians spend a significant amount of their time on the design of their concepts. While many formal systems try to support this by providing a highlevel language, we argue that more should be learned from the mathematical practice in order to improve the applicability of formal systems.
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.