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Theorem Proving in Large Formal Mathematics as an Emerging AI Field

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Automated Reasoning and Mathematics

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 7788))

Abstract

In the recent years, we have linked a large corpus of formal mathematics with automated theorem proving (ATP) tools, and started to develop combined AI/ATP systems working in this setting. In this paper we first relate this project to the earlier large-scale automated developments done by Quaife with McCune’s Otter system, and to the discussions of the QED project about formalizing a significant part of mathematics. Then we summarize our adventure so far, argue that the QED dreams were right in anticipating the creation of a very interesting semantic AI field, and discuss its further research directions.

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Author information

Authors and Affiliations

  1. Radboud University Nijmegen, The Netherlands

    Josef Urban

  2. Czech Technical University, Czech Republic

    Jiří Vyskočil

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  1. Josef Urban
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  2. Jiří Vyskočil
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Editor information

Editors and Affiliations

  1. Dipartimento di Informatica, Università degli Studi di Verona, 37134, Verona, Italy

    Maria Paola Bonacina

  2. Artificial Intelligence Center, SRI International, 333 Ravenswood Avenue, 94025, Menlo Park, CA, USA

    Mark E. Stickel

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Urban, J., Vyskočil, J. (2013). Theorem Proving in Large Formal Mathematics as an Emerging AI Field. In: Bonacina, M.P., Stickel, M.E. (eds) Automated Reasoning and Mathematics. Lecture Notes in Computer Science(), vol 7788. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36675-8_13

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  • DOI: https://doi.org/10.1007/978-3-642-36675-8_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-36674-1

  • Online ISBN: 978-3-642-36675-8

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