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Refining Algebraic Hierarchy in Mathematical Repository of Mizar

  • Adam GrabowskiEmail author
  • Artur Korniłowicz
  • Christoph Schwarzweller
Chapter
  • 9 Downloads
Part of the Studies in Computational Intelligence book series (SCI, volume 889)

Abstract

Mathematics, especially algebra, uses plenty of structures: groups, rings, integral domains, fields, vector spaces to name a few of the most basic ones. Classes of structures are closely connected—usually by inclusion—naturally leading to hierarchies that has been reproduced in different forms in different mathematical repositories. We give a brief overview of some existing algebraic hierarchies and report on the latest developments in the Mizar computerized proof assistant system. In particular we present a detailed algebraic hierarchy that has been defined in Mizar and discuss extensions of the hierarchy towards more involved domains, using internal mechanisms available in the system.

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Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Adam Grabowski
    • 1
    Email author
  • Artur Korniłowicz
    • 1
  • Christoph Schwarzweller
    • 2
  1. 1.Institute of InformaticsUniversity of BiałystokBiałystokPoland
  2. 2.Department of Computer ScienceUniversity of GdańskGdańskPoland

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