Proszę używać tego identyfikatora do cytowań lub wstaw link do tej pozycji:
http://hdl.handle.net/11320/6554
Pełny rekord metadanych
Pole DC | Wartość | Język |
---|---|---|
dc.contributor.author | Coghetto, Roland | - |
dc.contributor.author | Grabowski, Adam | - |
dc.date.accessioned | 2018-05-11T07:20:22Z | - |
dc.date.available | 2018-05-11T07:20:22Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Formalized Mathematics, Volume 25, Issue 4, Pages 289–313 | - |
dc.identifier.issn | 1426-2630 | - |
dc.identifier.uri | http://hdl.handle.net/11320/6554 | - |
dc.description.abstract | In the article, we continue the formalization of the work devoted to Tarski’s geometry - the book “Metamathematische Methoden in der Geometrie” by W. Schwabhäuser, W. Szmielew, and A. Tarski. After we prepared some introductory formal framework in our two previous Mizar articles, we focus on the regular translation of underlying items faithfully following the abovementioned book (our encoding covers first seven chapters). Our development utilizes also other formalization efforts of the same topic, e.g. Isabelle/HOL by Makarios, Metamath or even proof objects obtained directly from Prover9. In addition, using the native Mizar constructions (cluster registrations) the propositions (“Satz”) are reformulated under weaker conditions, i.e. by using fewer axioms or by proposing an alternative version that uses just another axioms (ex. Satz 2.1 or Satz 2.2). | - |
dc.language.iso | en | - |
dc.publisher | DeGruyter Open | - |
dc.subject | Tarski’s geometry axioms | - |
dc.subject | foundations of geometry | - |
dc.subject | Euclidean plane | - |
dc.title | Tarski Geometry Axioms. Part III | - |
dc.type | Article | - |
dc.identifier.doi | 10.1515/forma-2017-0028 | - |
dc.description.Affiliation | Coghetto Roland - Rue de la Brasserie 5, 7100 La Louvière, Belgium | - |
dc.description.Affiliation | Grabowski Adam - Institute of Informatics, University of Białystok, Poland | - |
dc.description.references | 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. | - |
dc.description.references | 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. | - |
dc.description.references | Roland Coghetto and Adam Grabowski. Tarski geometry axioms - Part II. Formalized Mathematics, 24(2):157-166, 2016. doi: 10.1515/forma-2016-0012. | - |
dc.description.references | Sana Stojanovic Durdevic, Julien Narboux, and Predrag Janičic. 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. | - |
dc.description.references | 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. | - |
dc.description.references | Haragauri Narayan Gupta. Contributions to the Axiomatic Foundations of Geometry. PhD thesis, University of California-Berkeley, 1965. | - |
dc.description.references | Timothy James McKenzie Makarios. A mechanical verification of the independence of Tarski’s Euclidean Axiom. Victoria University ofWellington, New Zealand, 2012. Master’s thesis. | - |
dc.description.references | Timothy James McKenzie Makarios. The independence of Tarski’s Euclidean Axiom. Archive of Formal Proofs, October 2012. Formal proof development. | - |
dc.description.references | Timothy James McKenzie Makarios. A further simplification of Tarski’s axioms of geometry. Note di Matematica, 33(2):123-132, 2014. | - |
dc.description.references | 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. | - |
dc.description.references | William Richter, Adam Grabowski, and Jesse Alama. Tarski geometry axioms. Formalized Mathematics, 22(2):167-176, 2014. doi: 10.2478/forma-2014-0017. | - |
dc.description.references | Wolfram Schwabhäuser, Wanda Szmielew, and Alfred Tarski. Metamathematische Methoden in der Geometrie. Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 1983. | - |
dc.identifier.eissn | 1898-9934 | - |
dc.description.volume | 25 | - |
dc.description.issue | 4 | - |
dc.description.firstpage | 289 | - |
dc.description.lastpage | 313 | - |
dc.identifier.citation2 | Formalized Mathematics | - |
Występuje w kolekcji(ach): | Artykuły naukowe (WInf) Formalized Mathematics, 2017, Volume 25, Issue 4 |
Pliki w tej pozycji:
Plik | Opis | Rozmiar | Format | |
---|---|---|---|---|
forma-2017-0028.pdf | 359,35 kB | Adobe PDF | Otwórz |
Pozycja ta dostępna jest na podstawie licencji Licencja Creative Commons CCL