Tarski Geometry Axioms. Part V – Half-planes and Planes

[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. Search 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. Search in Google Scholar

[3] Michael Beeson and Larry Wos. OTTER proofs in Tarskian geometry. In International Joint Conference on Automated Reasoning, volume 8562 of Lecture Notes in Computer Science, pages 495–510. Springer, 2014. doi:10.1007/978-3-319-08587-6 38. Search in Google Scholar

[4] Gabriel Braun and Julien Narboux. A synthetic proof of Pappus’ theorem in Tarski’s geometry. Journal of Automated Reasoning, 58(2):23, 2017. doi:10.1007/s10817-016-9374-4. Search in Google Scholar

[5] Roland Coghetto. Tarski’s parallel postulate implies the 5th Postulate of Euclid, the Postulate of Playfair and the original Parallel Postulate of Euclid. Archive of Formal Proofs, January 2021. https://isa-afp.org/entries/IsaGeoCoq.html, Formal proof development. Search in Google Scholar

[6] Roland Coghetto and Adam Grabowski. Tarski geometry axioms – Part II. Formalized Mathematics, 24(2):157–166, 2016. doi:10.1515/forma-2016-0012. Search in Google Scholar

[7] Roland Coghetto and Adam Grabowski. Tarski geometry axioms. Part III. Formalized Mathematics, 25(4):289–313, 2017. doi:10.1515/forma-2017-0028. Search in Google Scholar

[8] Roland Coghetto and Adam Grabowski. Tarski geometry axioms. Part IV – right angle. Formalized Mathematics, 27(1):75–85, 2019. doi:10.2478/forma-2019-0008. Search in Google Scholar

[9] Sana Stojanovic Durdevic, Julien Narboux, and Predrag Janičić. Automated generation of machine verifiable and readable proofs: a case study of Tarski’s geometry. Annals of Mathematics and Artificial Intelligence, 74(3-4):249–269, 2015. Search in Google Scholar

[10] Adam Grabowski. Tarski’s geometry modelled in Mizar computerized proof assistant. In Maria Ganzha, Leszek Maciaszek, and Marcin Paprzycki, editors, Proceedings of the 2016 Federated Conference on Computer Science and Information Systems (FedCSIS), volume 8 of ACSIS – Annals of Computer Science and Information Systems, pages 373–381, 2016. doi:10.15439/2016F290. Search in Google Scholar

[11] Adam Grabowski and Roland Coghetto. Tarski’s geometry and the Euclidean plane in Mizar. In Joint Proceedings of the FM4M, MathUI, and ThEdu Workshops, Doctoral Program, and Work in Progress at the Conference on Intelligent Computer Mathematics 2016 co-located with the 9th Conference on Intelligent Computer Mathematics (CICM 2016), Białystok, Poland, July 25–29, 2016, volume 1785 of CEUR-WS, pages 4–9. CEURWS.org, 2016. Search in Google Scholar

[12] Haragauri Narayan Gupta. Contributions to the Axiomatic Foundations of Geometry. PhD thesis, University of California-Berkeley, 1965. Search in Google Scholar

[13] Timothy James McKenzie Makarios. A mechanical verification of the independence of Tarski’s Euclidean Axiom. Victoria University of Wellington, New Zealand, 2012. Master’s thesis. Search in Google Scholar

[14] Timothy James McKenzie Makarios. The independence of Tarski’s Euclidean Axiom. Archive of Formal Proofs, October 2012. Formal proof development. Search in Google Scholar

[15] Timothy James McKenzie Makarios. A further simplification of Tarski’s axioms of geometry. Note di Matematica, 33(2):123–132, 2014. Search in Google Scholar

[16] Julien Narboux. Mechanical theorem proving in Tarski’s geometry. In F. Botana and T. Recio, editors, Automated Deduction in Geometry, volume 4869 of Lecture Notes in Computer Science, pages 139–156. Springer, 2007. Search in Google Scholar

[17] William Richter, Adam Grabowski, and Jesse Alama. Tarski geometry axioms. Formalized Mathematics, 22(2):167–176, 2014. doi:10.2478/forma-2014-0017. Search in Google Scholar

[18] Wolfram Schwabhäuser, Wanda Szmielew, and Alfred Tarski. Metamathematische Methoden in der Geometrie. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. Search in Google Scholar