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Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

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Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6167))

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Abstract

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems, definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.

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Author information

Authors and Affiliations

  1. Radboud University, Nijmegen

    Josef Urban

  2. University of Miami,  

    Geoff Sutcliffe

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  1. Josef Urban
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  2. Geoff Sutcliffe
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Editor information

Editors and Affiliations

  1. German Research Center for Artificial Intelligence Bremen, Germany

    Serge Autexier

  2. Karlsruhe Institute of Technology, Germany

    Jacques Calmet

  3. CEDRIC/CNAM, Paris, France

    David Delahaye

  4. American Mathematical Society, Ann Arbor, USA

    Patrick D. F. Ion

  5. INRIA Sophia-Antipolis, France

    Laurence Rideau

  6. École Nationale Supérieure d’Informatique pour l’industrie et l’Entreprise, Evry, France

    Renaud Rioboo

  7. School of Computer Science, Edgbaston, University of Birmingham, B15 2TT, Birmingham, UK

    Alan P. Sexton

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Urban, J., Sutcliffe, G. (2010). Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar. In: Autexier, S., et al. Intelligent Computer Mathematics. CICM 2010. Lecture Notes in Computer Science(), vol 6167. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14128-7_12

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  • DOI: https://doi.org/10.1007/978-3-642-14128-7_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-14127-0

  • Online ISBN: 978-3-642-14128-7

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