### 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

### Learning To Parse on Aligned Corpora (Rough Diamond)

"... Abstract. One of the first big hurdles that mathematicians encounter when considering writing formal proofs is the necessity to get acquainted with the formal terminology and the parsing mechanisms used in the large ITP libraries. This includes the large number of formal symbols, the grammar of the ..."

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Abstract. One of the first big hurdles that mathematicians encounter when considering writing formal proofs is the necessity to get acquainted with the formal terminology and the parsing mechanisms used in the large ITP libraries. This includes the large number of formal symbols, the grammar of the formal languages and the advanced mechanisms in-strumenting the proof assistants to correctly understand the formal ex-pressions in the presence of ubiquitous overloading. In this work we start to address this problem by developing approximate probabilistic parsing techniques that autonomously train disambiguation on large corpora. Unlike in standard natural language processing, we can filter the resulting parse trees by strong ITP and AR semantic methods such as typechecking and automated theorem proving, and even let the probabilistic methods self-improve based on such semantic feedback. We describe the general motivation and our first experiments, and build an online system for parsing ambiguous formulas over the Flyspeck library. 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

### 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

### 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