### 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

### unknown title

"... DISSERTATION Titel der Dissertation Foundations for a self-reflective, context-aware semantic representation of mathematical specifications ..."

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DISSERTATION Titel der Dissertation Foundations for a self-reflective, context-aware semantic representation of mathematical specifications

### 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

### Closing the Gap Between Formal and Digital Libraries of Mathematics

"... Abstract. The representational gap between formal mathematics and most users of digital mathematics resources is a challenge for any approach to mathematical knowledge management which aims to combine the benefits of formal and informal mathematics. In this chapter we study this gap in the context o ..."

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Abstract. The representational gap between formal mathematics and most users of digital mathematics resources is a challenge for any approach to mathematical knowledge management which aims to combine the benefits of formal and informal mathematics. In this chapter we study this gap in the context of a digital library of mathematics based on the Mizar Mathematical Library and make recommendations for improving such formal systems support for MKM. 1

### 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

### Granularity Judgments in Proof Tutoring ⋆

"... The SFB 378 project Dialog [2] investigates natural tutorial dialog between a ..."

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The SFB 378 project Dialog [2] investigates natural tutorial dialog between a

### STUDIES IN LOGIC, GRAMMAR AND RHETORIC 10 (23) 2007 Closing the Gap Between Formal and Digital Libraries of Mathematics

"... Abstract. The representational gap between formal mathematics and most users of digital mathematics resources is a challenge for any approach to mathematical knowledge management which aims to combine the benefits of formal and informal mathematics. In this chapter we study this gap in the context o ..."

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Abstract. The representational gap between formal mathematics and most users of digital mathematics resources is a challenge for any approach to mathematical knowledge management which aims to combine the benefits of formal and informal mathematics. In this chapter we study this gap in the context of a digital library of mathematics based on the Mizar Mathematical Library and make recommendations for improving such formal systems support for MKM. 1

### 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 long-term 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.

### 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 high-level language, we argue that more should be learned from the mathematical practice in order to improve the applicability of formal systems.