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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.
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.
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
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
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
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