Have a personal or library account? Click to login
Formalization of Quasilattices Cover
Open Access
|Jan 2021

References

  1. [1] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.10.1007/978-3-319-20615-8_17
  2. [2] Grzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, and Karol Pąk. The role of the Mizar Mathematical Library for interactive proof development in Mizar. Journal of Automated Reasoning, 61(1):9–32, 2018. doi:10.1007/s10817-017-9440-6.10.1007/s10817-017-9440-6604425130069070
  3. [3] Garrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967.
  4. [4] B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.10.1017/CBO9780511809088
  5. [5] G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M. Mislove, and D.S. Scott. A Compendium of Continuous Lattices. Springer-Verlag, Berlin, Heidelberg, New York, 1980.10.1007/978-3-642-67678-9
  6. [6] Adam Grabowski. Mechanizing complemented lattices within Mizar system. Journal of Automated Reasoning, 55:211–221, 2015. doi:10.1007/s10817-015-9333-5.10.1007/s10817-015-9333-5
  7. [7] Adam Grabowski and Robert Milewski. Boolean posets, posets under inclusion and products of relational structures. Formalized Mathematics, 6(1):117–121, 1997.
  8. [8] Adam Grabowski and Markus Moschner. Managing heterogeneous theories within a mathematical knowledge repository. In Andrea Asperti, Grzegorz Bancerek, and Andrzej Trybulec, editors, Mathematical Knowledge Management Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 116–129. Springer, 2004. doi:10.1007/978-3-540-27818-4_9. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19–21, 2004.10.1007/978-3-540-27818-4_9
  9. [9] Adam Grabowski and Damian Sawicki. On two alternative axiomatizations of lattices by McKenzie and Sholander. Formalized Mathematics, 26(2):193–198, 2018. doi:10.2478/forma-2018-0017.10.2478/forma-2018-0017
  10. [10] Adam Grabowski and Christoph Schwarzweller. Translating mathematical vernacular into knowledge repositories. In Michael Kohlhase, editor, Mathematical Knowledge Management, volume 3863 of Lecture Notes in Computer Science, pages 49–64. Springer, 2006. doi:https://doi.org/10.1007/11618027_4. 4th International Conference on Mathematical Knowledge Management, Bremen, Germany, MKM 2005, July 15–17, 2005, Revised Selected Papers.
  11. [11] Adam Grabowski, Artur Korniłowicz, and Christoph Schwarzweller. Equality in computer proof-assistants. In Ganzha, Maria and Maciaszek, Leszek and Paprzycki, Marcin, editor, Proceedings of the 2015 Federated Conference on Computer Science and Information Systems, volume 5 of ACSIS-Annals of Computer Science and Information Systems, pages 45–54. IEEE, 2015. doi:10.15439/2015F229.10.15439/2015F229
  12. [12] George Grätzer. General Lattice Theory. Academic Press, New York, 1978.10.1007/978-3-0348-7633-9
  13. [13] George Grätzer. Lattice Theory: Foundation. Birkhäuser, 2011.10.1007/978-3-0348-0018-1
  14. [14] William McCune. Prover9 and Mace4. 2005–2010.
  15. [15] William McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.10.1007/3-540-61398-6
  16. [16] Ranganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.10.1142/7007
  17. [17] Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.
  18. [18] Stanisław Żukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215–222, 1990.
DOI: https://doi.org/10.2478/forma-2020-0019 | Journal eISSN: 1898-9934 | Journal ISSN: 1426-2630
Language: English
Page range: 217 - 225
Accepted on: May 31, 2020
Published on: Jan 9, 2021
Published by: University of Białystok
In partnership with: Paradigm Publishing Services
Publication frequency: 1 issue per year

© 2021 Dominik Kulesza, Adam Grabowski, published by University of Białystok
This work is licensed under the Creative Commons Attribution-ShareAlike 4.0 License.