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Automating Formalization by Statistical and Semantic Parsing of Mathematics

  • Conference paper
Interactive Theorem Proving (ITP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10499))

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Abstract

We discuss the progress in our project which aims to automate formalization by combining natural language processing with deep semantic understanding of mathematical expressions. We introduce the overall motivation and ideas behind this project, and then propose a context-based parsing approach that combines efficient statistical learning of deep parse trees with their semantic pruning by type checking and large-theory automated theorem proving. We show that our learning method allows efficient use of large amount of contextual information, which in turn significantly boosts the precision of the statistical parsing and also makes it more efficient. This leads to a large improvement of our first results in parsing theorems from the Flyspeck corpus.

C. Kaliszyk—Supported by the ERC Starting grant no. 714034 SMART.

J. Urban and J. Vyskočil—Supported by the ERC Consolidator grant no. 649043 AI4REASON. This work was supported by the European Regional Development Fund under the project AI&Reasoning (reg. no. CZ.02.1.01/0.0/0.0/15_003/0000466).

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Notes

  1. 1.

    In general, a grammar could pick only some subtree depths instead of their contiguous intervals, but we do not use such grammars now.

  2. 2.

    About 1% of the longest Flyspeck formulas were removed from the evaluation to keep the parsing times manageable.

  3. 3.

    If the context-free version parsed only a few terms, but with the best rank, its average rank would be 1, but the method would still be much worse in terms of the overall number of correctly parsed terms.

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Authors and Affiliations

  1. University of Innsbruck, Innsbruck, Austria

    Cezary Kaliszyk

  2. Czech Technical University in Prague, Prague, Czech Republic

    Josef Urban & Jiří Vyskočil

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  1. Cezary Kaliszyk
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  2. Josef Urban
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  3. Jiří Vyskočil
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Correspondence to Cezary Kaliszyk .

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Editors and Affiliations

  1. University of Brasília, Brasília D.F., Brazil

    Mauricio Ayala-Rincón

  2. NASA, Hampton, VA, USA

    César A. Muñoz

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Kaliszyk, C., Urban, J., Vyskočil, J. (2017). Automating Formalization by Statistical and Semantic Parsing of Mathematics. In: Ayala-Rincón, M., Muñoz, C.A. (eds) Interactive Theorem Proving. ITP 2017. Lecture Notes in Computer Science(), vol 10499. Springer, Cham. https://doi.org/10.1007/978-3-319-66107-0_2

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  • DOI: https://doi.org/10.1007/978-3-319-66107-0_2

  • Publisher Name: Springer, Cham

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