Mizar: State-of-the-art and Beyond

  • Grzegorz Bancerek
  • Czesław Byliński
  • Adam Grabowski
  • Artur Korniłowicz
  • Roman Matuszewski
  • Adam NaumowiczEmail author
  • Karol Pa̧k
  • Josef Urban
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9150)


Mizar is one of the pioneering systems for mathematics formalization, which still has an active user community. The project has been in constant development since 1973, when Andrzej Trybulec designed the fundamentals of a language capable of rigorously encoding mathematical knowledge in a computerized environment which guarantees its full logical correctness. Since then, the system with its feature-rich language devised to approximate mathematics writing has influenced other formalization projects and has given rise to a number of Mizar modes implemented on top of other systems. However, the information about the system as a whole is not readily available to developers of other systems. Various papers describing Mizar features have been rather incremental and focused only on particular newly implemented Mizar aspects. The objective of the current paper is to give a survey of the most important Mizar features that distinguish it from other popular proof checkers. We also go a step further and describe most important current trends and lines of development that go beyond the state-of-the-art system.


Natural Deduction Proof Assistant Automate Theorem Prove Proof Step Inaccessible Cardinal 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Grzegorz Bancerek
    • 1
  • Czesław Byliński
    • 2
  • Adam Grabowski
    • 3
  • Artur Korniłowicz
    • 3
  • Roman Matuszewski
    • 4
  • Adam Naumowicz
    • 3
    Email author
  • Karol Pa̧k
    • 3
  • Josef Urban
    • 5
  1. 1.Association of Mizar UsersBiałystokPoland
  2. 2.Section of Computer Systems and Teleinformatic NetworksUniversity of BiałystokBiałystokPoland
  3. 3.Institute of InformaticsUniversity of BiałystokBiałystokPoland
  4. 4.Department of Applied Linguistics, Faculty of PhilologyUniversity of BiałystokBiałystokPoland
  5. 5.Radboud UniversityNijmegenThe Netherlands

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