On Weakly Associative Lattices and Near Lattices

[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_17Search in Google Scholar

[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/s10817-017-9440-6604425130069070Search in Google Scholar

[3] Garrett Birkhoff. Lattice Theory. Providence, Rhode Island, New York, 1967.Search in Google Scholar

[4] B.A. Davey and H.A. Priestley. Introduction to Lattices and Order. Cambridge University Press, 2002.10.1017/CBO9780511809088Search in Google Scholar

[5] Ervin Fried and George Gr¨atzer. Some examples of weakly associative lattices. Colloquium Mathematicum, 27:215–221, 1973. doi:10.4064/cm-27-2-215-221.10.4064/cm-27-2-215-221Search in Google Scholar

[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/s10817-015-9333-5Search in Google Scholar

[7] 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.Search in Google Scholar

[8] 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-2018-0017Search in Google Scholar

[9] 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.Search in Google Scholar

[10] 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:10.15439/2015F229.10.15439/2015F229Search in Google Scholar

[11] George Gr¨atzer. General Lattice Theory. Academic Press, New York, 1978.10.1007/978-3-0348-7633-9Search in Google Scholar

[12] George Gr¨atzer. Lattice Theory: Foundation. Birkh¨auser, 2011.10.1007/978-3-0348-0018-1Search in Google Scholar

[13] Dominik Kulesza and Adam Grabowski. Formalization of quasilattices. Formalized Mathematics, 28(2):217–225, 2020. doi:10.2478/forma-2020-0019.10.2478/forma-2020-0019Search in Google Scholar

[14] William McCune. Prover9 and Mace4. 2005–2010.Search in Google Scholar

[15] William McCune and Ranganathan Padmanabhan. Automated Deduction in Equational Logic and Cubic Curves. Springer-Verlag, Berlin, 1996.10.1007/3-540-61398-6Search in Google Scholar

[16] Ranganathan Padmanabhan and Sergiu Rudeanu. Axioms for Lattices and Boolean Algebras. World Scientific Publishers, 2008.10.1142/7007Search in Google Scholar

[17] Piotr Rudnicki and Josef Urban. Escape to ATP for Mizar. In First International Workshop on Proof eXchange for Theorem Proving-PxTP 2011, 2011.Search in Google Scholar

[18] Stanisław łukowski. Introduction to lattice theory. Formalized Mathematics, 1(1):215–222, 1990.Search in Google Scholar