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Solving Some Geometry Problems of the Náboj 2023 Contest with Automated Deduction in GeoGebra Discovery 利用 GeoGebra 发现中的自动演绎功能解决 Náboj 2023 竞赛中的一些几何问题
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.14
Amela Hota, Zoltán Kovács, Alexander Vujic
{"title":"Solving Some Geometry Problems of the Náboj 2023 Contest with Automated Deduction in GeoGebra Discovery","authors":"Amela Hota, Zoltán Kovács, Alexander Vujic","doi":"10.4204/EPTCS.398.14","DOIUrl":"https://doi.org/10.4204/EPTCS.398.14","url":null,"abstract":"In this article, we solve some of the geometry problems of the N'aboj 2023 competition with the help of a computer, using examples that the software tool GeoGebra Discovery can calculate. In each case, the calculation requires symbolic computations. We analyze the difficulty of feeding the problem into the machine and set further goals to make the problems of this type of contests even more tractable in the future.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"26 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139610552","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Considerations on Approaches and Metrics in Automated Theorem Generation/Finding in Geometry 关于几何中自动定理生成/查找的方法和度量标准的思考
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.12
Pedro Quaresma, Pierluigi Graziani, Stefano M. Nicoletti
{"title":"Considerations on Approaches and Metrics in Automated Theorem Generation/Finding in Geometry","authors":"Pedro Quaresma, Pierluigi Graziani, Stefano M. Nicoletti","doi":"10.4204/EPTCS.398.12","DOIUrl":"https://doi.org/10.4204/EPTCS.398.12","url":null,"abstract":"The pursue of what are properties that can be identified to permit an automated reasoning program to generate and find new and interesting theorems is an interesting research goal (pun intended). The automatic discovery of new theorems is a goal in itself, and it has been addressed in specific areas, with different methods. The separation of the\"weeds\", uninteresting, trivial facts, from the\"wheat\", new and interesting facts, is much harder, but is also being addressed by different authors using different approaches. In this paper we will focus on geometry. We present and discuss different approaches for the automatic discovery of geometric theorems (and properties), and different metrics to find the interesting theorems among all those that were generated. After this description we will introduce the first result of this article: an undecidability result proving that having an algorithmic procedure that decides for every possible Turing Machine that produces theorems, whether it is able to produce also interesting theorems, is an undecidable problem. Consequently, we will argue that judging whether a theorem prover is able to produce interesting theorems remains a non deterministic task, at best a task to be addressed by program based in an algorithm guided by heuristics criteria. Therefore, as a human, to satisfy this task two things are necessary: an expert survey that sheds light on what a theorem prover/finder of interesting geometric theorems is, and - to enable this analysis - other surveys that clarify metrics and approaches related to the interestingness of geometric theorems. In the conclusion of this article we will introduce the structure of two of these surveys - the second result of this article - and we will discuss some future work.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"7 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139524061","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
OK Geometry OK 几何
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/eptcs.398.3
Zlatan Magajna
{"title":"OK Geometry","authors":"Zlatan Magajna","doi":"10.4204/eptcs.398.3","DOIUrl":"https://doi.org/10.4204/eptcs.398.3","url":null,"abstract":"","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"66 16","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611603","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formalization, Automatization and Visualization of Hyperbolic Geometry 双曲几何的形式化、自动化和可视化
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/eptcs.398.2
Filip Marić
{"title":"Formalization, Automatization and Visualization of Hyperbolic Geometry","authors":"Filip Marić","doi":"10.4204/eptcs.398.2","DOIUrl":"https://doi.org/10.4204/eptcs.398.2","url":null,"abstract":"","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"6 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139524132","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formalization, Arithmetization and Automatization of Geometry 几何形式化、算术化和自动化
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/eptcs.398.1
Julien Narboux
{"title":"Formalization, Arithmetization and Automatization of Geometry","authors":"Julien Narboux","doi":"10.4204/eptcs.398.1","DOIUrl":"https://doi.org/10.4204/eptcs.398.1","url":null,"abstract":"","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"65 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611614","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Automation of Triangle Ruler-and-Compass Constructions Using Constraint Solvers 利用约束求解器实现三角形尺规构造自动化
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.10
Milan Bankovi'c
{"title":"Automation of Triangle Ruler-and-Compass Constructions Using Constraint Solvers","authors":"Milan Bankovi'c","doi":"10.4204/EPTCS.398.10","DOIUrl":"https://doi.org/10.4204/EPTCS.398.10","url":null,"abstract":"In this paper, we present an approach to automated solving of triangle ruler-and-compass construction problems using finite-domain constraint solvers. The constraint model is described in the MiniZinc modeling language, and is based on the automated planning. The main benefit of using general constraint solvers for such purpose, instead of developing dedicated tools, is that we can rely on the efficient search that is already implemented within the solver, enabling us to focus on geometric aspects of the problem. We may also use the solver's built-in optimization capabilities to search for the shortest possible constructions. We evaluate our approach on 74 solvable problems from the Wernick's list, and compare it to the dedicated triangle construction solver ArgoTriCS. The results show that our approach is comparable to dedicated tools, while it requires much less effort to implement. Also, our model often finds shorter constructions, thanks to the optimization capabilities offered by the constraint solvers.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"78 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139611317","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Showing Proofs, Assessing Difficulty with GeoGebra Discovery 用 GeoGebra 发现显示证明、评估难度
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-20 DOI: 10.4204/EPTCS.398.8
Z. Kovács, Tom'as Recio, M. P. Vélez
{"title":"Showing Proofs, Assessing Difficulty with GeoGebra Discovery","authors":"Z. Kovács, Tom'as Recio, M. P. Vélez","doi":"10.4204/EPTCS.398.8","DOIUrl":"https://doi.org/10.4204/EPTCS.398.8","url":null,"abstract":"In our contribution we describe some on-going improvements concerning the Automated Reasoning Tools developed in GeoGebra Discovery, providing different examples of the performance of these new features. We describe the new ShowProof command, that outputs both the sequence of the different steps performed by GeoGebra Discovery to confirm a certain statement, as well as a number intending to grade the difficulty or interest of the assertion. The proposal of this assessment measure, involving the comparison of the expression of the thesis (or conclusion) as a combination of the hypotheses, will be developed.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"11 18","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139523730","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Proceedings 14th International Conference on Automated Deduction in Geometry 第 14 届几何自动演绎国际会议论文集
Electronic Proceedings in Theoretical Computer Science Pub Date : 2024-01-19 DOI: 10.4204/EPTCS.398
Pedro Quaresma, Zolt'an Kov'acs
{"title":"Proceedings 14th International Conference on Automated Deduction in Geometry","authors":"Pedro Quaresma, Zolt'an Kov'acs","doi":"10.4204/EPTCS.398","DOIUrl":"https://doi.org/10.4204/EPTCS.398","url":null,"abstract":"ADG is a forum to exchange ideas and views, to present research results and progress, and to demonstrate software tools at the intersection between geometry and automated deduction. The conference is held every two years. The previous editions of ADG were held in Hagenberg in 2021 (online, postponed from 2020 due to COVID-19), Nanning in 2018, Strasbourg in 2016, Coimbra in 2014, Edinburgh in 2012, Munich in 2010, Shanghai in 2008, Pontevedra in 2006, Gainesville in 2004, Hagenberg in 2002, Zurich in 2000, Beijing in 1998, and Toulouse in 1996. The 14th edition, ADG 2023, was held in Belgrade, Serbia, in September 20-22, 2023. This edition of ADG had an additional special focus topic, Deduction in Education. Invited Speakers: Julien Narboux, University of Strasbourg, France\"Formalisation, arithmetization and automatisation of geometry\"; Filip Mari'c, University of Belgrade, Serbia,\"Automatization, formalization and visualization of hyperbolic geometry\"; Zlatan Magajna, University of Ljubljana, Slovenia,\"Workshop OK Geometry\"","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"45 8","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139613143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An Interpretation of E-HA^w inside HA^w 解读 HA^w 内部的 E-HA^w
Electronic Proceedings in Theoretical Computer Science Pub Date : 2023-11-17 DOI: 10.4204/EPTCS.396.5
Félix Castro
{"title":"An Interpretation of E-HA^w inside HA^w","authors":"Félix Castro","doi":"10.4204/EPTCS.396.5","DOIUrl":"https://doi.org/10.4204/EPTCS.396.5","url":null,"abstract":"Higher Type Arithmetic (HA$^w$) is a first-order many-sorted theory. It is a conservative extension of Heyting Arithmetic obtained by extending the syntax of terms to all of System T: the objects of interest here are the functionals of higher types. While equality between natural numbers is specified by the axioms of Peano, how can equality between functionals be defined? From this question, different versions of HA$^w$ arise, such as an extensional version (E-HA$^w$) and an intentional version (I-HA$^w$). In this work, we will see how the study of partial equivalence relations leads us to design a translation by parametricity from E-HA$^w$ to HA$^w$.","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"67 4","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139263466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Practicality and Soundness of Refinement Types 论精炼类型的实用性和合理性
Electronic Proceedings in Theoretical Computer Science Pub Date : 2023-11-17 DOI: 10.4204/eptcs.396.1
Niki Vazou
{"title":"On the Practicality and Soundness of Refinement Types","authors":"Niki Vazou","doi":"10.4204/eptcs.396.1","DOIUrl":"https://doi.org/10.4204/eptcs.396.1","url":null,"abstract":"","PeriodicalId":30085,"journal":{"name":"Electronic Proceedings in Theoretical Computer Science","volume":"49 12","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139264759","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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